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1 decimal integer ring cycle of many

Quantum Field Fractal Polarization Math Constants

nemeth braille printable arx calc

pronounced why phi prime quotients

ᐱ Y φ Θ P Q Ψ

condensed matter

Y Phi Theta Prime Q Quotients Base Numerals 1dir 2dir 3dir cdir

numer nu mer numerical nomenclature & arcs

Numerical values exist before the nomenclature of numerical nomenclature and it is in the moment numerical value is completed that numerical nomenclature is defined in itself the value it is structured. Then is the fluidity of numerals structured in itself of numerical values given paths ⅄ncn  ⅄X  1⅄  2⅄  3⅄ncn  +⅄  1-⅄  2-⅄  ∀ of numbers (nNncnncn) logic to limits within or not within the structure of the numerical values. Less than zero or quantability of nuclear vacuum field vectors in electron plasma veils is not only a plasma illuminating factor and is also subject to exponentials, multiplication, division, addition, and subtraction of quantum field fractal polarization math. Particle charges, positive or negative for example are many times over or under estimated and the exact numbers to those factors can be written mathematically. Mainly rather than a float point significand average quotient from a total sum added value gathered in division of the sum total average, numbers naturally have a significand of their own being the decimal point and its relation to the number or partial numbers counted of a repeating decimal constant chain of scaled partial constant variable frequencies. The numerical value of a variable average base in floating point utilizes a part similar to variable change precision leeway, where as instead if compared to the ratios of constants based decimal cycle stems in quantum fractal polarization scale variables, the decimal precision of known ratios and their digit order in cycle stem has less leeway and is calculable to numeral defining value. When one error of one value is a variable misguidance through arithmetic paths toward an average from partial derivatives, an endless loop of decimal precision can be unnoticed and if not unnoticed counted and predicted, such as error, partial error, or correct non error allocatable derivative variables of that average thus negating the estimated value of an average and equating to a precise detailed proof in prediction methods.

A LIST  of  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  φ  Θ  Ψ  ⅄ncn  ⅄X  1⅄  2⅄  3⅄ncn  +⅄  1-⅄  2-⅄  ∀

VOSS variables of sequential sets (ssv)

Y {0, 1, 1, 2, 3, 5, . . .} fibonacci

P {2, 3, 5, 7, 11, 13, . . .} prime

Ψ {4, 6, 9, 10, 12, 14, . . .} non prime non fibonacci natural whole numbers

Elementary physics involves quantum fractal polarization math constants in the numerical translation of quanta related to the matter in and around the translation point of that measurable translation for transcription to the quantifier. While a field such as space has a vacuum electromagnetic constant of the state of that specific field, within it a star, sun, and atoms is contained within the frictional difference of a form of matter condensed causing the star, sun, atom, or cluster of such to spin until an equal counter opposite exact electromagnetic measure allows for the star, sun, atom to bond with a kind of its own or consolidate and be an accumulated larger one measure of its own kind. Commonly the bonding effect of electrons aligned through a vacuum field is an arc of illuminating quick indifference through the extreme opposite veil of space that transports that matter to the other matter it shares a frequency with to that degree of measure. 

Thermodynamics represents friction as workable force particle charge available for thermal transfer and the frequency of those bond searches are then in a sense a search for rest from friction or work to bond in a frozen state reliant on the gravity or electrical polarities of a larger or more powerful constant able to let that specific bond rest from work and fiction. Some elements in a frozen state of matter may decay do to atmospheric oxidation and decompose to atomic parts of what element it is or wait on an event of extreme heat and friction that then again changes the frozen solid state phase to fluid and gas until the process repeats. In the process of the star, sun, atom spin is a centrifugal force of energy contained in the poles of north and south so to say, a force of the major mass element involved in that bodies point in space. The south pole given enough time has a upward or through directing of energy and loose atmospheric  electromagnetic or non electromagnetic matter while the north pole has an up and outward directing of energy and matter that is free from the surface of its body. Both poles are part of an entropy enthalpy or centrifugal and centripetal system of that spherical body. A planet such as earth and its siblings is much like protons and electrons that orbit the sun, while the moons are similar to electromagnetic nature such as neutrons bonded to the orbit of their phase state placement in the system of the sun, planets, and cluster of stars it is part of. Within the atmospheric shell energy and matter that the south pole direct upward and through then hit a wall of lets say ground; the energy that can travel where the solid matter can not shifts kinetic energy of that element's movement polarized charge as the charge kinetic sum and the element part ways in their paths. That atmospheric difference kinetic measure of energy transferred to each path variant division is sufficient to contain within each element of the event in their parting where the traveled element settles in a spin cap long enough to become a frozen phase state that matter. While parts of the whole body have upward through and upward out North pole from South pole split paths constant properties of the whole body constant state, there is a inward, down attracting physics state to most near all matter in that body system called gravity or electromagnetic constant. These measures are not always whole numbers and when dividing leads to more dividing and or bonding of divided parts of what can be called from a whole measured thing, it is very likely the whole measured thing that the matter derived from is only an opinion of that being a whole entirety of absolute 1. The same idea is also an opinion when applied to a thing in matter, its distance traveled in time, about where it is coming and going as well as the changes it will or will not go through, while it either changes or does not change the field matter of space it is traveling through or around. Similar or relative terms of time and matter differ having exact numerable differences are not exactly similar or relative terms without the numerated variable term of their difference.   

Quantically, the changes matter goes through while its phases in time space differ from the changes that matter then counter measurably to the field of matter it may or may not change, are also mathematically measurable as well as all parts of each parts' parts. One could consider that the light and energy emitted from a star is an an illumination of an arc vacuum across a measure of time limited to space of condensed energy while a lightning arc is an illumination of an arc limited to time rather than space and yet both are phase states of energy that is a constant of matter and paths that matter has measurable limits to in differing relations.. Vacuum field is a veil of space with a specific time allowing or not allowing a certain measure to change light passing through that gas phase state field. These are elementary state phases of light and dark shared in time space and matter, and within are many degrees of that light and dark sharing time and space as measurable or not measurable shades and tones. While some measures of energy, light, absence of light and ground negative or positive path charges of energy are lethal to many biological forms unit measures of that energy are numerable. If numbers of systems can represent those systems, still then the factoring of those numbers and the extreme length of number potential compared to a persons life span for example, means that some math equations could take a lifetime or multiple life times to write out and the very matter on which the written answer to an equation has a limited decay rate, or limit in writings being preserved its for reading once it has been finally written completely after the lifetimes it may have takento be written. The question then is who is there to read it, as they are unique to the writer, certainly more given the measures of time given to that answer and its preservation. 

If anything, you will learn the importance of variable factor precision of decimal cycle rounding in fractals here rather than rounding whole numbers. Cell cycles apply (ooo) order of operations to your variables after a golden ratio cell cycle of numerals is distinguished. The cell cycle that is found in applying the opposite when adding a variable to the previous from 0 1 1 2 3 5 8 13. . . then dividing is often referred to as error in order of operations of mathematics... PEMDAS parenthesis exponents multiples division addition subtraction order of arithmetic in algebraic equations. Variables in paths prove those order of operations are not persued followed or set for all numerable measured parts of matter in existence. Base particles of matter and subatomic matter are numerable in their structure and numerable of their relevance to outside their structure. The math and numerical data on this page at its base structure may have you rethinking your BP base pair in DNA factoring and loop wrap stem decimals precision nomenclature. 

Viral, non-viral, marsupial, and non marsupial cell numerations have core logic outside pemdas (ooo) logic. One exfoliation produced in a phi ratio is much like a start of |1| absolute one exfoliation much like an absolute zero |0|=1. The order of operations is a mathematical logic, however the patterns in the exfoliation are proof that in matter the order of operations were not to a level of whole natural numbers and still had natural patterns of its formation. Alternately the exfoliation is a limit to that part of that set it is limited to governed by time and space constants. Whether a variable change is micro or exponential, the decimal precision in factoring its numeral value in any function is that important noted commonly with δΔ or δ∇ such that these being the change or loss of a system to a degree of micron exponent µ° µ′ to µ′° or minus µ′ in value. µHz lacking a µHz at µ intervals of time are a µ difference in a frequency hit through a ampere watt system that are that µ important and sometimes overlooked or inaccurately factored of δΔ or δ∇. 

A  simple example of how cell cycles apply is a cell consuming another cell for keeping what it needs and discarding what it does not need from the cell it consumes. Shells of cell growth and discarded evidence can often be found seen or identified in patterns formed on the shell structure of the shell restructured discard. A simple analogy for quantum field fractal polarization math is the word Permutations, pronounced (per-mutation). Micron units of flux µφ found in permutations of hysteresis loops are a great example of how energy is fractionally measured in wave frequencies. Resistance values are expressed in ohms Ω that reflect in δΔ or δ∇ partial derivative gain or loss to a system when a difference between flux, resistance, and energy flow are not calibrated to extremely precise values and variables of the system components and element limits involved in that systems engineering. Deterioration of mechanics in systems such as iron of permanent magnet stator motors is just one example of a fractional cell variable factor miscalculated and its potential loss to a system. Commonly, micro Thermal Resistance µΨ is a factor of mechanical limits of machine elements easily miscalculated when magnetic memory of hysteresis loops are concerned in electrical machinery and is a contributing factor of deterioration of system elements. Raising the temperature a few millibars to oxidation chemical process on an exponential level raises corrosion as quick as an electrical charge.  

A very similar example is a human body system of systems with fractional variables able to be miscalculated in diagnosis prognosis and treatments, where the hypothalamus commonly regulates thermal controls for allocating a potential virus in the system of body systems down to the atomic cell level in signaling. CNS EMF central nervous system electromagnetic field example and liquid liquid phase separation is actually more close to 5 phase of triple point as an analogy where with water from vaper gas tripidated into fluid then to ice frozen solid state that has slush between fluid and frozen state and precipitation mix between gas and fluid saturation applied in biological membrane systems. Wave functions are applicable to measurements and extremely precise in limits or memory limits, we can call quantum fields and the measures are fractal parts of whole systems polarized in thermo-chemical electro-magnetics.

Allergen exposures and cancer symptomatic response in cell autophagy along with anastasis and their commonalities then forward to altering paths of cell discourse and discard of differing biological life forms of differing environments... as example Discontinuity and improperly calculated factors of discontinuity that when overlooked or miscalculated lead to a continuity of continued exposure, process, or pathway of potential continuity when discontinuity is the intent of ending the cycle of a specified term exposure, process, or pathway. The numerology then of the substrates should be not limited to rounded summations of limited calculators and algebraic formulas, rather the numbers should be precise and accurate measured units. Neurophilus cells will either attack invading cells from their pre-programmed neucleic cyosolic mechanisms or turn into a shielding cell to protect cells such as inflammation, cyst, or more commonly thought as a tumor growth. Later that attacking cell may call on more cells to aid in the fight while unaware from signal blockers it is attacking the body of the self systems or building a growth of clustered cells in inflammation, cyst or tumor. At this phase the cells are much like φ and Θ of differing paths give or take, anticipate or wait later/previous 1⅄, previous/later 2⅄ from Y base variables. A body of systems trying to process discard of a tumor cluster cyst or inflammation measurable mass or system occupancy of lymphatic nodes with incorrect cell transcription and translation then is at a phase of exponential numbers of a cell formation that has many factors to its existence. A patient treated for cancerous cells that then returns to an allergen environment of day to day routines around allergens will be exposed again to the very agents that began the allergic response so similar to cancer cell clustering reactions of immune system defenses that take merely a few seconds to minutes for an allergic reaction to occur. Proper factoring and precision of all variables is critical to effectively eliminating the allergen confusion commonly mistaken as cancer in this example. One histamine release signals many immune system mechanisms and being that histamine is a chemical of the mind and body, both are in turn effected. Countering such reactions with estimated chemistry of pharmacological trial studies post thanatological studies is a guess and not a very effective mathematical guess for any degreed physician is has prerequisites in mathematical degree course credits. Example Heme Acetyl Neutrolphil mechanisms for proper diagnosis, prognosis, and treatment. MERCK NIST. Between Environmental, chemical, and gestational Histamine Intolerance to Cancer types, to the here try this list of pharmaceutical clinical trial medication regimens, along with the many phases of chemistry and cell paths of reflex through and of variant nucleic variables, exact numbers of exact and precise variables should be considered given the extent of these vast arrays of symptomatic labels in diagnosis prognosis and treatments. Antigen and Antibody identification along with a library of such identifiable cell types very much extend within such extreme number precision as these quantum field fractals of polarization and the math backbone to their numeral base constants.

In some cases, simple math logic and its comprehension is a cure to something as complex as a brain system chemistry trying to process a lie it was given to process as a truth it is not. When numbers and arithmetic do not lie a cure for Factitious Disorder (e.g. 1 and e.g. 2), is as simple as solving a basic simple math equation that the brain searches for a foundation of fact from. The mind or brain is a system extension of a body of systems and cell groups of types that have symptoms of say heachaches for example that when a lie is present in memory of the mind, the body of systems may try telling the brain mind something is inaccurate and something as simple as admitting a truth in the mind such as a simple math equation can in fact alleviate the headache partially or completely from proper brain chemistry changes in gray brain matter verse white brain matter. Many parts of a body and its systems will not allow parts of the mind brain to continue a lie as it is in part then obstructing that body system from functioning properly and its own longevity or survival is then at stake. This is commonly referred to as neuron signaling of receptors and pathways. Within those pathways are paths that grown structured biological memory called logic gates such as a noted comprehension memory of left and right or in this math paths of later/previous 1⅄, previous/later 2⅄, or decimal stem cycle difference division 3⅄ of Nncn 

CNS immune privilege and neuroimmunology are fields of such brain chemistry that involve histamine releases based on fact or fiction mental distinguishing along with many other cellular biochemical system exchanges that can and will alter the overall system health regulated in the central nervous system. A mind of a body with histamine intolerance that is continued to be lied to and made angry while it tries to distinguish lie or truth of information while in an allergen environment or exposed to food and/or chemical allergens then releases histamine throughout the body that is very similar to an allergen response commonly contributing to inflammation, cystic formations, and other cancerous types. A lie replaced with truth fact rather than a clinical trial medicine can alter a path in one of many misdiagnosed.... simple math. So then natural dopamine, serotonin and brain chemistry of gray verse white brain matter can be achieved without added lies and to some those lies are exactly what some children are allergic to added to food, chemical, and environment. One could summate and round an evaluation that some lies are in fact extremely unhealthy for some people and so too then for various other life forms.

With infinite math paths and infinite unlimited numbers to those math paths, start with limits of your own and noone elses limits until you comprehend your limits and find your limits extended from your comprehension of limits. Finite is a numeral limit that is often an opinion in some cases, the truth of finite in infinite compared to an opinion of finite is mathematically provable in many of those cases.

Mathematical ratios are applicable to atomic change and change as well as no change are numerically definable so when change is labelled as no change and is inaccurate in label, the change that is present does not completely stop changing although it is overlooked and can lay dormant while miscalculations in a change labelled as no change may be crucial to time, energy, and many other atomic variables.

A part of something is a ratio or percent of its whole and elements of the periodic table have prepacked atoms of variations eons of time took to change the isotopes and atomic structure of those elements to form other elements and compounds. An acidic base for example will break down and divide many protein types as well as other compounds to their atomic level and within those are parts of parts that are not whole and are whole at the atomic level. If one part of a whole or a percent ratio of a whole has predetermining factors of dividing capabilities when in exposure or relation with another part ratio percent of a different whole part, then ratios are in fact able to be divided or divide other part percentages and numerically they can be defined with numbers. Indivisible is then not a proper label for ratios divided by ratios that are in fact divisible. Sub-atomic nucleic indifference(s) and stem cycle variants within ten digit limits of fibonacci count and prime numbers as a base example in numerals. 

A perfect example of a decimal stem cycle limit in cn of a ratio number Nncn is in the cytosol nucleic bonds of DNA and RNA transcription receptors where one nucleus chain tells another nucleus chain it is limited to a number of cycles of its chain stem decimal order and is then able to translate how much of a repeatable set of instructions is then allowed to be packed in its limited ability to store that information for the bond of nuclei to be maintained, thus one nuclei must be able to translate and comprehend the inquiry chain without itself being altered in the process or its own being is then changed to an entire new transcription and translation comprehension. If proteins enzyme structures of sugar oil and sodium are basic instructions, one could think of glyceride as a food fuel source in sub atomics, sodium salt is a crystalizing bonding source in sub atomics and oil base of alkaloids are a dividing chemical structure that continue dividing no matter if in fluid saturated phase states or expanded gas as the efficiency of its dividing nature is dependent on the ratio to ratio of which it is in contact with to divide before it is neutralized or out of resource for dividing anymore. Chemical reaction is a bonding or dividing event and this math is a basic representation of that fact in a numeral quantifying explanation of similarities with the nature of numbers and how they naturally structure in relations.

ACQFPS  A LIST of calibration factors in quantum field fractals for practical application in arithmetic functions of precise variables. 

example genome bases - nucleic acids - amino acids - chromatin - chromosome - protein - neurochem - gluons - valence

e.g.1  e.g. 2  e.g. 3  e.g. 4  e.g. 5  e.g. 6  e.g. 7 and limits in calculated factors decimal precision that numbers prove nomenclature of rounded variable theory can be replaced with non theoretical numerals of precision such as DNA RNA 

1.65 dimmer windings of double helix seems rounded with only two decimal parts of its decimal compared to many ratios listed below on this page. 

electron - proton - neutron - caton - axion - anion - nucleotide - nucleosome - dimmer - telomere - virology - photon - parton - exciton

Signaling in cells and systems use fundamental concepts of electrical and chemical message relaying such as evolution and change in dna for a system organism to survive a change of the environment it advanced to its state in that environment before the dna requires a change in itself to adapt to the environmental changes for that system of organisms to survive in the changed environment it was signaling its need to change and adaptation information. An example is the tentorium to a cytosine or a plant base cytosol or an shell traits of membranes. Signaling Transcription and translation can involve distance, time, and many other factors for specific definitions of long range and short range effective communication. In order to carry out task completable cell instructions of obtainable matter, use and discard of that matter missing any part of the dna rna instructions will resort to survival or shutdown pre-programmed chemical instructions within the elements of its making and current possession at the time of the translating of the transcriptions. 

Time and distance are relative terms to application of the transcription translation as are the transcriptions to the phase state of the environment the transcriptions are factored for to related distance environment of relative terms and then distance is a term of time and environment of its own definition parted when time is a distance or when distance is relative to a point measure from a sustainable continuum of being in survival in an environment that is not defined in the transcription waiting to be translated. Cryogenic stasis, anastasis, autophagius self preservation survival minimalism, and celestial distances as well as time would be examples of a transcription translation between one point in time and space to another point in time in space or multiple points in time and space through multiple phases. 

DNA, RNA, gRNA, mRNA, microRNA, rRNA, siRNA, snRNA, snoRNA, tRNA, ncRNA, lncRNA, and piwiRNA as examples, relate similarly to number constants, number bridges and partial number bridge connectors, yet a computer programmer who writes languages in a computer shell library that echo prints answers to software network web searches with numbers should then have DNA and RNA library answers to those searches from a database rather than exact numbers to basic algorithms of simple calculus number frame arrays. Computer programmers given the cessating time for a language library to be written  for answering a web search inquiry should not deter simple library number searches to be blocked with computer programming explanations of more cessation. A number library in a DNA and RNA database or long range and short range ratio factors are Numbers and no a computer language. A number search in a web search for a number library answered with excuses of SQL blocks and reasons for those searches blocked is not an answer to a number search in a Library of Numbers.

Data elements in library file logs that are not dependent of a noticeable distance and time relativity in high speed internet communications when a machine is utilized in proper connections. SQL search blocks in sync with Poorly Understood reference material on subjects of DNA and RNA for example along with calculators that round at a basic limit of ten to eleven digits are factors or program limits in C, C++, Java, or Python calculations to source information limitations and access are again why a number library is simply a library of numbers limited to the storage space of that Number Library.  Here on this page DNA and RNA is not poorly understood nor misunderstood nor are the numbers that are filed to computer storage systems of such nomenclature and information. Instead of a sql search block from sleeping nested transaction programs in idled number systems blocking logical math and numbers of basic arithmetic to complex algorithms this page has more simple numbers displayed of the basics in quantum field fractal polarization math applicable to multiple arrays and uses in long or short range engineering and pathology allocation.

Long range and short range arc trajectory math are simple logic that depend on variables and factoring of potential change in that trajectory path that varies on many factors. Arithmetic that utilizes plus one, minus one, plus two, minus two, or exact numbers between 0 1 2 10 or more that can easily be factored incorrectly to exponential estimates and there are unit measures on this page that reflect on those unit measures to precise degrees. 0 1 01 10.1 101 1.01 0.1

example solar systems  -  quadratic propulsion system engineering physics  -  pulsars

Quantum Field Fractal Polarization   e.g. 1   e.g. 2   e.g. 3   e.g. 4

   ⬢   ⬡   ⬢   ⬡   ⬢   ⬡   ⬟   ⬠   ⬟   ⬠   ⬟   ⯐   田   ⨁   ◭  ◮  ⧨  ⧩  ⟁   ⨀   ⊚   ⧂   ⌱   ∘   ⦁   ⋯   ⋮   ⋱   ⋰   ∴   ∵   ⁙   ◉   ◎

Paths of evolution involve processes of transposable elements of junk rna transpons and dna retrotranspons through shell discard such as holometabolous and hemimetabolous complete shell disposal molting or semi-partial shell discard. Directly down the middle so to say of centrosomes kinetichore in chimera cells is basically a lop sided partial decision of cellular instruction packages signaling transcription and translation that are commonly referred to as nicks, the discontinuity in a dna rna strains. At the molecular level these numbers are very similar to that partial derivative quantum fractal field polarization math and its variables of potential change. Given that the factor variables explained here are whole numbers of fibonnacci and primes, a valuable point is that the same numeral path set applications can be applied to decimal numerals in the same fashion and thus doing so changes the decimal place in many of the quotients, products, sums, differences and exponents... for example instead of starting with 0 and 1 and 1 and 2 and 3 for fibbonacci Y base and entirely different base set for Nncn could be started at 0 then 0.1 then 0.2 then 0.3 then 0.5 then 0.8 then 1.3 that set variable ∈2⅄2φn3 is very similar with for example as well as ∈2⅄2φn2 that is 0.5 

As this is the case with these variable values it is recommended to make notation of sets that start with decimal values rather than whole numbers as the values are similar or equal to variables already defined in other complex equation set bases. ⧊Y and ⧊P could note for 0, 0.1, and 0.2 . . . . so too then 0 then 0.01 then 0.02 then 0.03, then 0.05, then 0.08 then 0.13 and this will change a variable factor precision value extremely much when it is applied to exponential algebraic formulas. Much smaller longer decimal ratios and fractals are applicable and this is merely an explanation of that fact about micron unit measures of precise value. Between zero 0 one 1 ten 10 to the Nth number ⧊Y, ⧊P, and ⅄∀nth definitions in paths of algebraic functions ⅄ncn  ⅄X  1⅄  2⅄  3⅄ncn  +⅄  1-⅄  2-⅄ A LIST library with supporting variables to equations then makes ACQFPS advanced complex quantum fractal polarization sets available for practical applications. 

Forensics evidence factors for postmortum investigations rely heavily on such specific details as does education of these sciences and arithmetic. Aerotech industries can also benefit from high precision in wave function math for propulsion systems limits and space time positioning. A quantum field fractal polarization math analogy would be nearer micronomical unit measures of astronomics or astronomical unit measures for micronomic system equilibriums as what is up, what is down, what is in, and what is out relativity to then now when and why with how much about what.

On this page you will find 1dir constants of numerical key values in decimal degree integer ring cycle(s) notations. Dir refers to directory in computer shell c:// compilers for nomenclature organization at a user interface. Capabilities for these numerical key decimal degree values have potential in practical application fields on advanced research development areas such as physics, optical lens curvature alignments, nucleosome structuring in (dna) deoxyrubenuclaic acid histones to chromatin signatures, biomedical engineering, astrophysics, thermodynamics, cyclemetrics, fluid engineering, electrical engineering, and vacuum field induction arc fusion plasma stablizeations of thermonuclear energy.

Quantum fractal field harmonics found in data structures, periodic table atomic weight, masses in bonds scale shifts, guide key to unit in factor change requirement notations, sensor systems calibrations, plasma fusion as well as kinetic particle workable force harvesting in delta change models require precision that ai utilize of these decimal degrees.  

Encryption method strings of variable factors to applicable change values in natural math was invented some time ago through evolution of cell divides and many displays shells of cellular memories. Other examples in arx of ratios are atomic spin relief, covalent bonds on isotopic levels of required precision for stability of a cells before generating new cellular memory for genetic reproduction frame works,  meiosis and mitosis of life forms cell memory in the environment it may adapt to outside your factoring base language knowledge of its potential new language. Keys of a cell compared to its memory cycles before its arx radical new ratio shell strain changes are vital through fission and fusion events that the cell carries organized to its own comprehension and new translation before the cell then communicates its base language or new level base language outward and inward. For generalization suppose the whole number and part of the number of a variable 1φn8=(Yn9/Yn8)=(21/13) is the cell → 1.^615384 ← and the repeating decimal chain is the stem cell memory after the noted chevron ^ symbol in the bolded part of the ratio variable. Then the cell of variable 1φn10=(Yn11/Yn10)=(55/34) is →1.6^1762941 the repeating decimal chain is the stem cell memory after the noted chevron ^ symbol of one cycle in that cell memory stem, where as two cycles of that stem cell memory is the chain repeated for a variable of 1.6^17629411762941 rather than 1.61762941.

So 1φn10c1=1.61762941 and 1φn10c2=1.617629411762941 and when loss of a system δ∇ is noticed and not allocated, it may be the exponent of a variable factor unfactored for in calculating, that if 1φn10c1 is assumed to be the value noted in complex quanta while 1φn10c2 the value is actually , then a loss of 0.000000001762941 at each and every misfactored applicable term the error is miscalculated. Exponentially this miscalculation can spread across a system and allocating this error for proper system numeral balance is then a basis for precise variable definition just as variable change is one factor incorrect rounded numerals and estimates then acrue and sum up an unknown factor variable of loss in the system example that can be avoided if calculated correctly to paths of the system exact.

Another example of an arx radical ratio precision numeral is the importance of a Si standard increment unit mer measure of C or H of the periodic table of elements. Atomic mass as the H hydrogen base atomic weight next to C carbon used among the other elements as a base unit measure point variable calculus uses as a scale numeral starting recorded numeral value in nomenclature of other elements. 

The other elements of organic and inorganic chemistry have many phases of reactions in elemental physics of many thermodynamic phases and astronomical scales quantifiably. 

Example Pharmacodynamics and Pharmacokinetics - Toxicodynamics and Toxicokinetics

(variants) a law of decimal in calculus trace prediction logic pathogen pathology. 

Consider this page a speed square of arc constants that are real numbers in decimal computational factoring and non theoretical with practical application potential like your famous framing square instead for arc engineers and λ wave functions down to tinsel strengths of architectural engineering. Remainder or reremainder are more important than your python disregard to the decimal # c ++ rounding and a computer that returns a rounded number of a non float pointed very precise number is a computer that is floating not the number searched in the query log that is defined. Many numeral base defined decimals will be displayed on this page that have a wide range of web search results when a search is performed for information about a specific number or numbers in these Arithmetic arrangements.

Learn when to stop going in circles... a simple error to extreme precision perfect accuracy 

Using a basic Fibonacci count example 01 to 10 digits divided in on itself at each step will provide the decimal key cycle ciphers that are numerical constants that only change when an additional degree of the decimal precision point is extended in areas such as biomedical viral strain stem studies and aeronautical flight paths. These numbers are basic enough for a child to find and make great pyramid blocks for simpletons scale to scale where a math class is not a psy ops placement protocol at medicinal sciences of health and neuro-chemistry restructuring of no lie brain chemistry balancing, honestly over shooting brain mapping contradictory publications of fractal field polarization in the display 3d compiler.  

Decimal precision math is not a new math to be invented. dir dot of ooops ops and [()]ex/+- pemdas does not apply to long division order of operations that numerically land decimal values previous to any prime base or cube rooted exponential value theory. addition division steps of rationals divide subtract multiply divisor repeat until the stem ring is identified numerically. In some calculation of a fantasy pi, sine, cosine, tangent, limitless matrices, arrays, fields, or canonical vacuum field equations of theory imply a value of vague precision factored where a radius unit measure is not magically bent in arc ratio to a circumference unit measure straight line inside mid or out of the arc unit measure; added to ifs of theoretical numeration factor error disasters of exponential sometimes lead far from analytical trouble shooting and solvent potential... zero point decimal variable of ⌱∘⦁ 0.13 rounded abbreviation 1⅄5φn2 constant groups in radical nu mer 1dir natural numbers has a rounded notation as accurate as the pi imaginary ratio of unlike terms in unit measures and does not mean it is a best educated guess variable theory factor substitute.

Test the numerals of the scales provided on audio and lumen with scale shifts of time between octave changes of the numerals to audio or light or both. Some lifeforms will mimic repeat the tone or rhythm such as birds or try to eliminate the source of the speaker producing the frequencies given n number of cycles. A short or long signal is chaos math or chaotic transmission to a receptor that has no memory or knowledge base of "short or long signal". 

Chaos harmonized through a harmonic phase of chaos in a sense, transforms chaos pieces of a complex signal to multiple rhythmic uses of particles with limited reaches as chaotic as those particles are. Memory relays the chaos harmonized particles through other signaling systems and sometimes transmits signals like an echo reflex mechanism of cellular memory. A computer floating outside of a number defined as mentioned is a device likely with an ip number and the device itself is floating around the defined numeral decimal points defined while the multiple numbers might be defined or have definition of a cycle stem variable path that appears as a floating point in cyclic memory of that path or others.

Ferrofluid and cymatics are a base exchange chemical and electrical signals in alkanes of dna rna base chromatins of neural receptor transmissions on a viruses viral to the virus level being a virus to the virus itself where mimic bacteria also communicate in chemical compounds of minute trace element bonds just as are frequencies of energy. Host rhythms in a sense can feed a dormant strain where it anchors and frequencies can lore them out just like circadian clock cells. Jet propulsion systems are another example of ratio use in workable force to movement and angular direction of these ratios has application in quad copter flight. 

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Long division ratios have a probability of the quotient decimal length that depends on the number of the divisor. If the divisor of a phi ratio has a decimal stem cycle that is repeatable such as 1.619047 /1.615384 that the cn factor for c1 to c2 for 1.619047619047 /1.615384615384 then the probability of the quotient decimal length before the cycle stem is located is approximately 1,615,384 digits or less and then for c2 is an approximate probability of a quotient with a decimal cell stem cycle of 1,615,384,615,384 digits in length or less. Stem cell variant cycles of precision and arc are simply numeratable factors of logic and not aiming past a precision focal point is one fact that makes these logics that important. The probability of the ratio quotient decimal length between complex radicals in finding a stem cell cycle of cn of the quotient is the whole number of the divisor without the decimal point, less than that numeral or half that numeral or more than half that numeral in length of decimal digits and the cycle has one cycle chain that is the repeatable sequence of that ratio. 

If the mole mass of hydrogen is a limited decimal of 5 digits long in decimal place and all the other standard unit measures of other elements are based on the unit measure of mole mass of hydrogen for example 1.00784 to 1.00797 to 1.00811 and these values are incorrect to the degree of precision require of hydrogen weight , then all factoring of all elements is simply rounded and inaccurate. Cyclemetrics of air flow, fluid mechanics of fluidity, structural mechanics of frozen phase matter forms, thermodynamics of heat transfer, electrical engineering, and thermo electromagnetic engineering fields of mid phases between these areas of notation require precision arithmetic. The distance of the hydrogen from the center of the planet or star its atoms are being weighed will vary depending on general relativity to the atomic measure distance and the scale the hydrogen atoms are weighed in relation compared to hydrogen atoms weighed in a different distance to that planet or star. Time, temperature, phase state, and distance are all factors of relative weight measures given differentials of environmental weight comparisons and the effects on weighing instruments in varying conditions.

Open source is open source and logical math hidden in open source contradicts the definition of an open source library so when a number is searched in open source libraries the number should be a result in the number search to the precision of that number and not rounded numbers considering the basic logic principles of computer file storage and arrangement simplicity.

Boolean programs with sql blocks contradict the open source library of numbers being available with sql blocks of logical boolean factored numbers.This page was made out of hobby of numbers and math. An example of a numarable bridge or a near partial number bridge is the process of chemical change made with pollen nectar to glycerides and biological chemical bonding when bees make honey regurgitating changed molecular sugars and the correlation of the localized flowers the nectar is gathered from along with the current phase state of that particular bee dna and its colony. The honey is processed for food storage that time, temperature, light, shade, and environment have significant impact on that food storage of glycerides.

An Ai artificial intelligence program using a simple low digit number bridge can then use a programmed hysteresis loop algorithm to adjust to the user interface when a user is needed to be contained within a loop of paths mazes and bridges eternally in such a prison of limits to simply numbers 0 and 1 and 2 that many strings of decimal number bridges can be affixed to, just as DNA and RNA sequences send signals that the rest of a body of systems may not comprehend a repeated number as more than a musical rhythm. 1⅄∀Y2nd 6 to 7 digits and not ten or more of the examples while other systems are well aware much more complex rhythm sequences exist. Within the 6 to 7 digits of a loop an affixed sub routine program path is easily left dormant with limited access to the information just as is DNA and RNA transcriptions translations. A much more complex path number bridge could be the structure of an entire systems cell membrane container of its own little world where little is a relative term of expression as it contains extremely large variable strings and sequences of information, known as a shell. Elements of the periodic table have structures to their atoms nucleus and structures that are all differing and relative to phase states given an environment just as is an arc of plasma in an appropriate vaccume arc veil. Those phase states, arcs, and time are all numerable to extreme precision whether they are considered whole numbers or partials, fractions, ratios, or percentages to some other comparative unit measure quantity known.

Light, sound, energy, matter, absence of light, and absence of sound are binary parts of physical matter frictions and alignments. Nucleic multi diffraction energy focal point bombardment with subatomic refraction, selective divergence, selective convergence, and valence energy transfer of incorrect transcriptions are world wide sciences and sciences of the stars that worlds are among systems of. Radical pairing is written about and talked about very much, however searching for numbers specific to those subjects is commonly rounded and worded around in a divergence of its own. So again, This page was made out of hobby of numbers and math and here many numbers are very exact to their definitions of those applicable subjects using such numbers.

These variables are applicable to multiple functions of exponential multiplication division addition subtraction and square cube quadratic root or sub unit array potentials where cn is a critical factor of cycle stem shell count precision.

Calculating links ( x ) / ( - ) + ( x ) n3 

1X⅄=(n2xn1) is a function of multiplication applicable to variables of A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  φ  Θ  ᐱ  ᗑ  ∘⧊°  ∘∇° just as are functions of exponentials, division, addition, and subtraction of these definable variables. Radical ratios can be multiplied with other ratios or radicals and whole numbers. 1⅄ represents a path of consecutive numbers that a number is related with a later consecutive number while 2⅄ represents a path of consecutive numbers that a number is related with a previous of consecutive numbers and 3⅄cn represents a path of consecutive numbers that a number is related with a similar of consecutive numbers focused with a differential in decimal stem variations of cn.  Further factoring can be noted with n⅄cn that consecutive numbers of every other or every third, forth, fifth,sixth, seventh,eighth, ninth,tenth, etc... can be formulated as a library of ratios structured for function n⅄cn(nncn/nncn)

10 digit limit fibonacci and prime ratios below applicable to rocket science chemistry or chromatin bases of biological foundation chemistry eg 1 - eg 2 - eg 3 decimal precision is crucial to being accurate or it is not accurate and simply a rounded guess.

Division much like a star changing a grain of sand or a grain of sand that changes a star. After star and sand grain are numerated and their change or no change is numerated, then arithmetic using those variables numerated of those stars and sand grains change and the change those numbers then make in numeral factoring of other numerable physics calculus. 

Eliptic Eponyms and Elcipses Number bridge of plus or minus 1 examples that a path ⅄ of base Y differs before a 10 digit decimal limit of a consumer market calculator rounding example. Suppose a seed has a seed shell husk that protects the inner fragile structure of the seed proteins and in those proteins are enzymes full of numeral instructions. The seed shell has a numeral structure to its making just at the inner pack does and a purpose. The purpose is to protect the inner makings and instructions biologically formed to make the inner most seed just as an egg does. The seed will understand hydrogen oxygen nitrogen carbon as those are basic elements that likely formed the seed or egg with calcium in the eggs case. Other important nutrients like potassium sodium, sugar compounds together then allow the seed after water germinates and activates the seed to begin growing. Within that "activate" instructions is more neatly packed instructions of what to do next with simple yes no and maybe type path variables as the seed forms roots stems vines leaves that each contribute to conversions of the contact with soil air or water nutrients. DNA and RNA hold within them dormant building block hints so to say or instructions for nucleic transcription as many forms of biologic life can store memory in simple one through ten type libraries of what to do with 1 what to do with 2 what to do with 3 and so on. Variables 1φn8 and 1Θn7 and (Nn8)1⅄∀Y2nd and (Nn7) 1⅄∀φ2nd each share an identical repeating decimal chain stem of numerals yet the variable (Nn7) 1⅄∀φ2nd is one/millionth off in decimal place where the repeating stem chain begins within less than a whole number one 1.  If in the order of least numeral quantity to more numeral quantity 1φn8 and 1Θn7 and (Nn7) 1⅄∀φ2nd and  (Nn7) 1⅄∀φ2nd 0.615384 : 0.996336615384 : 1.615384 : 2.615384 yet the order of their structuring to that common quotient decimal stem repetition, so the specific definition of correct order then is an opinion to the flow and memory of a functioning system otherwise the system fails and discontinues living that then activates replicate new seed or eggs and reprint original base instructions for regrowth. A sort of change in environment reflected through the slightest evolutionary adjustment to a seed or egg change needed that can only be changed in restarting from seed or egg that the system recognizes.

The are quotients that derived from a base set of common Y variables through division paths that all varied to these numbers so when a seed or egg begins its growth process of life and say is blocked in memory of its original growth instructions yet remembers say a sequence of stem decimal chain in one region of its storage restructured from nutrients other system formations transfer to that region, one might say these PM and MS Mutations mutagens or per-mutations are permeable numeral quotient products of blocked signal transcriptions yet are still able to continue part transactions with the system original instructions until that signal and translation is recorrected such as a branch or stem of a plant re-exposed to dirt will grow roots reaching for oxygen and if exposed to oxygen will then reach to for leaves instead for carbon dioxide to breathe rather than exhale. Within cells are cellular memory and that cellular memory must then have a reading or reference way of comprehending what to do like a reflex. That reflex is then in a way the auto response or autoimmune system instructions of the new shell of a group of cells formed from the original seed or egg.

1Θn7 and (Nn7) 1⅄∀φ2nd and 1φn8 and  (Nn8)1⅄∀Y2nd or 0.615384 : 0.996336615384 : 1.615384 : 2.615384 for example involve just 4 variables from Y set and a multiple different paths of division with the numerals closest in Y base variables of this example. (Y7/Y8)=(8/13) is 1Θn7 and (Yn9/Yn8)=(21/13) is 1φn8 and (Yn10/Yn8)=(34/13) is (Nn8)1⅄∀Y2nd and (φn9cn/φn7cn) is (Nn7) 1⅄∀φ2nd that is (1φn9=(Yn10/Yn9)=(34/21)/1φn7=(Yn8/Yn7)=(13/8)) and is two variables of Y base factors that anyone of the Y base factors may or may not be quotients of some other divided part of some other base equal to its variable value. This being the case identifying and numerating a number bridge to memory is then information vital to counting the number of times a number bridge was used when needing to know what side of the numeral bridge certain receptors using the bridge can evaluate their position when considering only with the number of crossings on that numeral numbered bridge made of numbers and nothing more. A cell might receive a set of instructions for anastasis or autophage to either self consume and prepare for transport with a lighter load so to say or self terminate with thanks and your service has been helpful go decompose type message, while if on one side of a numbered bridge rather than the other side or between various similar bridges at a junction, that decompose instructions message then activates decay decomposition action within a vital region of its system and number bridges that can infact be a mortal complete system over all death. An alternate bridge might be a cell cluster in transport with a chemical reaction waiting in idle between two collectives that have an explosive chemical reaction a simple sub cellular membrane separates those chemicals from and may be vital to not happening in one particular region where that particular cell chemical reaction will be a determining factor in the life longevity to the biology around the chemical reaction at the wrong place and wrong time no matter how "happy" or "unhappy" the system section is..... and since happy or unhappy are chemical signatures for a reader of such emotions neither happy nor unhappy are too as well likely emotions for a reader who reads chemicals as a label of an opinion with such labels. Emotionless chemical signature with a tiny membrane transporting collective compounds able to chemical react though a system of emotional system parts is beyond the fact that emotional or not numbers and number bridges do not alter when emotions are extracted from the care and concern of where and when those chemical reaction potential explosions occur. Continued function is sometimes the only instructions for a thing to be aware of and doing what ever it takes to continue that survival is sometimes all some cells have knowledge of in their given cellular memory.

Within the stem branch or trunk of a plant is cells and they may be exposed at the plant bark so to say with air or soil causing the stem branch or tree trunk to decide grow a new branch here or a new root. When that stem or branch is cut from the system completely it will not have the complete memory of the tree or plant it is cut from, only partial and when replanted then relies on its own formed or unformed roots of its own along with what it has for leaf cola structures. 1φn8 and 1Θn7 and (Nn7) 1⅄∀φ2nd and  (Nn7) 1⅄∀φ2nd 0.615384 : 0.996336615384 : 1.615384 : 2.615384 might then be a clone only memory variable set and say no emotional response reflex memory just instructions that the clone can attach memory markers to itself in a new environment it can read recognize and translate. A basic example is a plant with a leaf that gets a powder coat of nutrients spilled on it that the plant will alocate on its own and weep from its leaves directly over the powder chemical spill that is obstructing its leaves from proper function simply to clean itself with the reserve water it has within its reach to transport to that allocated place. Variable change to environment then relies on decisions that plant will react outwardly and inwardly with simply chains of numeral instructions if we use these number paths as an example of what to predict from a plant seed shell and clone cropped cutting. As stems roots branches are splines of a plant bush or tree system whole, so to are RNA of DNA like limbs of a body system and understanding these number bridges or partial number bridge connectors are vital to the engineering and/or repair of such systems. Hibernation is an example of a stasis a circadian clock cell would recognize and its translation of time when woken early or in a clones case distinguishing the difference of time with anastasis factors signatured on cells of the clone would then require an organizational library structured to the memory of that even and recollection of that even for cell memory to be stored in the distinguishing of an event or a mutagen exposure factor a central nervous system so to say stores knowledge memory about how that exposure was solved to continue on.

Although 1-0.996336=0.003664 and 0.996336615384+0.003664=1.00000061538 still 1.00000061538 does not equal 1.61538 nor does 1+1.00000061538 equal 2.61538 and so rounding to a whole number of an assumed one or 2 from 0 or partial ratio rather than an allocated path variable definition in say space travel leaves 000000 many stars of 0 assumed to be the positioning it is not and star travel based on that assumed value then would further the lost travel to even more lost just as it will in medical sciences or other math practical applications.  i.e. e.g. incorrect Substitution bonding fillers... for example, then result in abnormal expected growth results and can be extremely unpredictable over a simple one millionth fraction applied to exponential equational longevity.  

Simply identifying a decimal stem looping value is not as sufficient as identifying the origin of that stem decimal loop and the affixed if any whole number partial of that quotient product sum difference or exponent. With this as an example here on this page very many equations define a quotient product sum or difference that defines zero and how that specific value zero was factored. Being that absolute zero in arithmetic equals 1 (|0|=1) math sciences prove that the value one equaling zero given the micron atomic or subatomic definitions in astronomical math fields of its factors defines values being absolute and accurate to absolution, yet limits in stored libraries of decimal constants non existent through web searches to that specific unit measure should be available and factored as they are simply numbers with a base constant at the decimal repeatable chain stem and its variable factors.

Radioactive isotope resonance in residential settings along with pyro engineering fire sciences of forensics for fire damage to homes and buildings can benefit from the extreme calibration measures of these ratio constants used as standard unit incremental measures in the prevention protocols of future planning as we humans have an ever changing environment among the stars and their astronomical frequencies at this planet we reside on and changes it experiences itself quite frequently at many grades and levels.

Fair Warning copy paste exchange may be completely inaccurate in your use of the values listed.

These numbers are from a quick math calculated in a paper notebook hand written then entered to a digital note book and it is recommended only for explanation of structures to variables in quantum field fractal polarization mathematics.

Some of these quotients were factored through a dcode boolean and manually identified at their stem decimal looping numeral cycle by the author.

Phi Theta Prime Absolute Zero(s) |0|:|0|:|0|:|0||0|

No two absolute 0's can represent other absolute zeros that do not represent the absolute zero it represents itself numerically

The zero of all phases in tier 1 - 2 - 3 - 4 -5 - 6 - 7 - 8 - 9 - 10 etc. of the divides mentioned above require notation of their zero origin.

1φn1=0 2φn1=0 3φn1=0 and so on as 2⅄1Θn1=0 2⅄2Θn1=0 and so on as 1⅄1Θn1=0 1⅄2Θn1=0 1⅄3Θn1=0 and so on....

if 1φn1=0 and 1⅄2Θn1=0  and 2⅄2Θn1=0 and nφn1/Pn=0 and Q/nφn1=0 and nΘn1/Pn=0 and Q/nΘn1=0 

Above P represents prime numbers and below P represents pressure.

while triple point (ΔP/ΔS)=0=(ΔT/ΔV)and (ΔS)E<0 equilibrium of a pure substance use zero in the equations, defining what that zero is would seem just as important. Below V represents a path of variables of phi and prime ratio divisions.

So to clarify if (ΔP/ΔS)=0=(ΔT/ΔV) then (ΔP/ΔS)=nφn1=(ΔT/ΔV) and (ΔP/ΔS)=nΘn1=(ΔT/ΔV) and (ΔT/ΔV) 

and (ΔP/ΔS)=nAn1=(ΔT/ΔV) and (ΔP/ΔS)=nMn1=(ΔT/ΔV) and (ΔP/ΔS)=nWn1=(ΔT/ΔV) are true and 

so is  and (ΔP/ΔS)=nVn1=(ΔT/ΔV) as confusing as it is defined here with two meanings of V and P in the same equation.

(ΔP is change in pressure

ΔS is change in entropy

nVn1 is ∈1⅄(Q/φ)cn that is (prime/prime) ratio divided by (y/y) ratio

ΔT is change in temperature

ΔV is change in volume

So if the equilibrium of a pure substance equation is (ΔS)E<0 then the ratios defined below are applicable to this equation in quantum field fractal polarization to the equilibrium and multi phase points in such a field of numeration. In the equation E represents energy and below E represents a ratio path set notation while on this page there are a multitude of definitions to 0 zero.

Amorphic Mutation or Amorphism are also examples in dna rna labeling within many notations T represents temperature as other notations T represents time. T on this page however represents a ratio set of a defined path T

Measured units and paths of the root to a defined unit measure explained on this page can be very extensive and this page will contain only the basic principles of the unit measure definitions for practical applications of physics, chemistry, calculus, engineering, and probability factoring. Probability and prediction in closed matrices arrays are one factor of probability and probability of a decimal ratio precision or decimal digit length are entirely different factors very closely relative of prediction or pathogen numeration. Incompetent internet computers of basic fractal quantum numerals and calculators limited to rounded precision as well as library limits are part in this pages creation of these real numbers.

A DNA and RNA database with numbers that align to perfect simple numeral division are highly unlikely as accurate and further research in data is likely needed by that database.

Quantum Field Fractal Polarization Math is very much applicable to physical sciences or physics. While it is said that centripetal and centrifugal force equations are the same, electromagnetic properties of varying elements along with varying mass and volume of those elements at the atomic level, the kinetics of centripetal and centrifugal also vary. F=mv²/r is force equals mass times velocity squared divided by radius and M=dm/dv is magnetization equals derivative of magnetic moment divided by derivative volume. Given that M=dm/dv in a field that can vary to an element that also varies in kinetic or magnetic measure then F=mv²/r does not apply to all elements that have differing magnetic properties, weights, mass, volume, and charge potential change. This being the case, exact values and measures of phase points at differential distances from a gravitational point along with varying factors that can effect that gravitational field, centripetal and centrifugal forces are not equal and are partials to much more complex systems in quantum field fractal polarization. One atom for instance may divide protons and electron counts that approach it while other atoms might be divided by approaching protons and electrons counts. Atomic decay or stability are subject to frequency waves of conservation and preservation, and if decayed require repair or an eventual overall change will occur. So if 1 divides 2 or 2 divides 1 for example, the values on one side of entropy and enthalpy of centrifugal centripetal balance are much more precise in ratios than simply 1 and 2 values. H=E+PV enthalpy equals internal energy plus pressure time volume and ΔS=S2−S1 entropy equals change in state measured to a closed value system phase of matter and energy. Factoring precision rather than rounded variable estimates proves that a slight incorrect value on exponential valued factors of systems is not impossible and here on this page are ratios that differ to microns of difference with basic 10 digits fibonnacci and prime based. 

Similarities of plus one and minus one between alternate Y paths for φ and Θ that 1⅄Q and 2⅄Q from P primes differ are numerical constants of the path variable structures. ⅄ncn Paths and exponents in those paths to precise measures in exponents factored correctly produce product values that rounded estimates do not. Factoring nNncn for ⅄ncn is essential for any other algebra, trigonometric, geometric, or calculus formulas, functions and equations to be accurate. 

Paths 1⅄  2⅄  3⅄ncn of numbers and variable N, Y, P, φ, Θ, Q and so on are definitions of variables A, B, D, E, F, G, H, I, J, K, L, M, O, R, S, T, U, V, W, X, Z, ᐱ, ᗑ, ∘⧊°, and ∘∇° while ( / ) or ( ÷ ) represent division of variables that define φ, Θ, A, B, D, E, F, G, H, I, J, K, L, M, O, Q, R, S, T, U, V, W, X, Z, ᐱ, ᗑ, ∘⧊°, and ∘∇° 

Functions then ⅄ncn, X, +⅄, 1-⅄, 2-⅄, represent functions of arithmetic paths that are applicable to variables of sets φ, Θ, A, B, D, E, F, G, H, I, J, K, L, M, O, P, Q, R, S, T, U, V, W, X, Y, Z, ᐱ, ᗑ, ∘⧊°, and ∘∇° with degrees of Nncn  the cycle stem potential change to many variables of these sets derived from division. ( / ) or ( ÷ ) represent division then exponents ⅄ncn, multiplication X, addition +⅄, and subtraction  1-⅄, 2-⅄ that sequence is difference of variable can replace the division function  ( / ) or ( ÷ ) of those variables precise to the degree of cycle stem counts of percentage of fractal ratios. Examples of function change to A variables

The percentage of a ratio's repeatable cycle stem decimal is definable two ways.

For example 1φn11=1.6^18 so 1φn11c2=1.6^1818 and 1φn11c1.5=1.6^181 while alternately, if 1φn11=1.6^18 and the repeatable stem decimal cycle is 0.0^18 then 0.018 is a quantity that half of is 0.009 of this example and the cn of these numerals is a definition of full or percent of a chain decimal repeatable cycle of numerals found and not a quantity. The variable is a cell set of numeral instructions and not a quantity so the number of full cycles or percentage should be quantified first before the percent or value of the decimal stem chain is then partially or completely given that value.

50% of 1.618 is 0.809 and 50% of 1.61818 is 0.80909 while 50% of 0.018 is 0.009 and 50% of 0.01818 is 0.00909

The digits of a ratio can be counted and called a percent of that number of variable ratio stem cycle or given the quantity value found in that specific ratio set variable to degrees of Nncn. So 1φn11c1.5=1.6^181 and 50% of 1.6181 is 0.80905 that is not 50% of 1.618=0.809 not 50% of 1.61818=0.80909 not 50% of 0.018=0.009 and not 50% of 0.01818=0.00909 

Before such arithmetic of ratio stem cycle values are quantifiably factorable, those ratios need to be factored very precise.

Prime Proofs

∈2⅄1 prime consecutive previous divided by later cycles back in remainder back to the dividend. 

have not read this anywhere . . . this may help with the mersenne prime search of primes.

if 2⅄P=(pn1/pn2)=2⅄1Qn1 consecutive prime previous divided by later cycles back in remainder back to the dividend then the prime no matter the number of digits when previous prime divided by the next later consecutive prime will cycle back to the dividend. The first 45 variables of 2⅄P=(pn1/pn2)=2⅄1Qn prove that fact. Link

∈1⅄1Qn1 prime consecutive later divided by previous cycles back in remainder back to the first division remainder.

have not read this anywhere . . . this may help with the mersenne prime search of primes.

if 1⅄P=(pn2/pn1)=1⅄1Qn1 consecutive prime later divided by previous cycles back in remainder back to the first remainder then the prime no matter the number of digits when later prime divided by the next previous of consecutive primes will cycle back to the first remainder. The first 45 variables of 1⅄P=(pn2/pn1)=1⅄1Qn1 prove that fact. And both 2⅄P=(pn1/pn2)=2⅄1Qn equation combined with 1⅄P=(pn2/pn1)=1⅄1Qn1 equation can verify as functions of P with Q bases if primes are consecutive no matter the number of digits to the prime numbers. Link

One Third is 33 % percent or 0.33 of decimals to the 100th decimal until a micron unit measure is determined as the smallest measurable point of relativity to that one third 33% and 3.^3333333333 of 10. With many numbers that are often rounded in math factoring, a ratio that is less than 3.^33 consistently is D that represents ratio path set ∈1⅄(φn2/Θn1) path from Y base.  1⅄(φn2/Θn1)=1⅄[1⅄(Yn3/Yn2)] / [2⅄(Yn1/Yn2)] that is a later consecutive divided by previous ratio then divided by a previous divided by a later of consecutive Y base ratio for a ratio divided by a ratio or a quotient divided by a quotient from altering Y path bases. Consistently the ratios near an average of (1.6180339/0.6180339)=2.6180342211001. . .^ extended shell continues and each step of these ratios is a constant that is dependent of cn of the decimal to both divisor and dividend or numerator and denominator that also has a measurable point of relativity like the abundantly estimated 33% of expontential math in geometry and physics. Ratios then from prime base P of alternate paths also have a trait as L represents ∈1⅄(1⅄Qn2/2⅄Qn1)cn  the variables of set path 1⅄Q quotient to 1.ncn being a whole number one with a ratio or also known as a percentage of some micron unit measure of tenths in decimal to an exponential decimal the ratio cycles a repeated stem of precisely. Subsequently variables of set path 2⅄Q quotients are less than 1 and 0.ncn to a micron unit measure of tenths in decimal to an exponential decimal the ratio cycles a repeated stem of precisely. So then those p prime based Q quotients and Y base φ and Θ quotients of alternate paths then divided again in array sets of defined similar paths are factorable and will not change anymore than the definition of the decimal repeating stem of each ratio factored. 3.^3333 of 33% and pi 3.14159. . . is one set of two ratios while a radius unit measure of a straight line from a center measurable point of relativity is then factored with an arc unit measure of circumference and not like terms. While a scale of pi factors is one scale, then are also Y and P base whole number radicals with a measurable point of relativity. Numbers are very precise and one error in factoring can calculate a cycle of numerals that eventually prove correct or incorrect as these ratios will not change anymore than the definition of the decimal repeating stem, thus they are constants. Variable quotients of function (Nn)2⅄∀Y2nd factor to numbers that are a micro-fraction above 33 percent with each a unique stem cell decimal cycle loop of their own such as (Nn6c1)2⅄∀Y2nd=(Yn6/Yn8)=(5/13)=0.^384615 or 0.384615 or 0.384615384615.... for functions of (Nncn)2⅄∀Y2nd and yet these are not 33% by any means. If a 33% measure is subtracted from each variable of (Nncn)2⅄∀Y2nd a then the cn factor of each variable must be defined specifically for aa correct difference of correct subtraction as equations 0.384615-0.3 differs from 0.384615-0.33 and 0.384615-0.333 and 0.384615-0.3333 and 0.384615-0.33333 and 0.384615-0.333333 and 0.384615-0.3333333 that all equal a difference that is not equal to the math equation 0.384615384615-0.3 or 0.384615384615-0.333333333333 for example and so on for cn...

Nncn 

N is a number and n is the numerated number of a sequence in labeled number scales that C cycles of a decimal numerated consecutive number is labeled to that N number.

As any variable of the ratio scales can be defined as a number to the decimal stem counted degree of sequence repetitions in the decimal cycle count, a number that is not factored from these many computational equations can too also be a number.

4 6 9 10 12 14 15 16 18 20 22 24 25 26 27 28 30 32 33 35 36 38 39 40 42 44 45 46 48 49 50 51 52 54 56 57 58 60 62 63 64 65 66 68 69 70 72 74 75 76 77 78 80 81 82 84 85 86 87 88 90 91 92 93 94 95 96 98 99 100 and so on . . .

These whole numbers are variables that are neither Y base fibonacci numerals nor are they prime numbers and yet these numbers are still factorable numerals of a set entirely different than Y, P, A through Z, φ, and Θ.

In this case we note the set as (N) of Ψ such that psi represents N whole numbers that are not prime nor fibonacci based numerals and are an ordinal set of consecutive values.

N then is a number and N represents any number of any set including numbers that can not be defined to any of these sets.

A  B  D  E  F  G  H  I  J  K  L  M  O  P  Q  R  S  T  U  V  W  X  Y  Z  φ  Θ  ᐱ  ᗑ  ∘⧊°  ∘∇°  ∀

As C cycles of repeating ratios are numerable then cn or CN is a cycle count of N many cycle counts that its self can be whole and partial of...

The values will display in the tier order of their group(s) of array respectably.

Denny Constants

Prime Proofs Link 1 and Link 2 along with Number bridges Link 3 are key points in Quantum field fractal polarization math.

Refer to these as Denny's Constants, a library published that quantum field fractal polarization math is a math that has not been invented and this math is math I wrote out many times. My name is Denny and this is a version of that math that defines quantum fractals able to be plotted to field points for polarization calculus of those values in numerals. Basic division array sets and libraries of constants. A LIST of ACQFPS

To Begin

1st tier fibonacci 01 to 10 digit value for basic numerical display of decimal precision laws not applicable to standard definition floating point. 9 bold numbers are also prime numbers in the ten digit base logic that phi prime fibonacci scale bases share in common of the ten digit example shown below. 2 - 3- 5 - 13- 89 - 1597 - 28657 - 514229 - 434894437

0  1  1  2  3  5  8  13  21  34  55  89  144  233  377  610  987  1597  2584  4181  6765  10946  17711  28657  46368  75025  121393  196418  317811  514229  832040  1346296  2178309  3524578  5702887  9227465  14930352  24157817  39088169  63245986  102334155  165780141  269114296  434894437  704008733  1138903170

2nd tier 1st divide 1φn ratios of Y fibonacci 1-21 step in decimal value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored ratios of previous order as divisor example 1/0 1/1 2/1 3/2 5/3 8/5 13/8 21/13 34/21 55/34 89/55 144/89 . . .  y→1φn

∈1⅄1Y=(Y2/Y1) → φn21(Yn22/Yn21) = φn  variables 

∈2⅄1Y where numbers of y dividing previous by the later do not equal φ ratios will be noted theta Θ

∈3⅄1Y where numbers of y have no decimals to apply path variant of cn & do not equal phi ratio σ

(Yn8/Yn7) (Yn9/Yn8) (Yn10/Yn9) (Yn11/Yn10) (Yn12/Yn11) (Yn13/Yn12) (Yn14/Yn13) (Yn15/Yn14) (Yn16/Yn15) (Yn17/Yn16) (Yn18/Yn17) (Yn19/Yn18) (Yn20/Yn19) (Yn21/Yn20) (Yn22/Yn21) (Yn23/Yn22) (Yn24/Yn23) (Yn25/Yn24) (Yn26/Yn25) (Yn27/Yn26) (Yn28/Yn27) (Yn29/Yn28) (Yn30/Yn29) (Yn31/Yn30) (Yn32/Yn31) (Yn33/Yn32) (Yn34/Yn33) (Yn35/Yn34) (Yn36/Yn35) (Yn37/Yn36) (Yn38/Yn37) (Yn39/Yn38) (Yn40/Yn39) (Yn41/Yn40) (Yn42/Yn41) (Yn43/Yn42) (Yn44/Yn43) (Yn45/Yn44) (Yn46/Yn45)

φ denotes ratio phi tier 2nd tier first divide quotient ratios before 3rd tier second divide of (φn2/φn1) variable constants where (Yn22/Yn21)=φn21=1.6^1803399852 or φn21c2=1.6^18033998521803399852 . . . and so on that φn21 ≠φn22 and φn21c2≠φn22 

1φn=∈1⅄1Y=(Y2/Y1)  phi ratios cycle back in remainder and vary per step in the ratios

have not read this anywhere . . .

1φn1=(Yn2/Yn1)=(1/0)=0

1φn2=(Yn3/Yn2)=(1/1)=1

1φn3=(Yn4/Yn3)=(2/1)=2  

1φn4=(Yn5/Yn4)=(3/2)=1.5  

1φn5=(Yn6/Yn5)=(5/3)=1.^6  and 1φn5c2=1.^66  and so on for cn

1φn6=(Yn7/Yn6)=(8/5)=1.6

1φn7=(Yn8/Yn7)=(13/8)=1.625

1φn8=(Yn9/Yn8)=(21/13)=1.^615384  and 1φn8c2=1.^615384615384 and so on for cn

1φn9=(Yn10/Yn9)=(34/21)=1.^619047 and 1φn9c2=1.^619047619047 and so on for cn

1φn10=(Yn11/Yn10)=(55/34)=1.6^1762941 and 1φn10c2=1.6^17629411762941 and so on for cn

1φn11=(Yn12/Yn11)=(89/55)=1.6^18 and 1φn11c2)=1.6^1818 and so on for cn

1φn12=(Yn13/Yn12)=(144/89)=1.^61797752808988764044943820224719101123595505 

and 

1φn12c2=1.^6179775280898876404494382022471910112359550561797752808988764044943820224719101123595505 and so on for cn

1φn13=(Yn14/Yn13)=(233/144)=1.6180^5 and 1φn13c2=1.6180^55 and 1φn13c3=1.6180^555 and so on for cn cycles of decimal numbers

1φn14=(Yn15/Yn14)=(377/233)=1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832 

1φn15=(Yn16/Yn15)=(610/377)=1.6183^0223896551724135014 

1φn16=(Yn17/Yn16)=(987/610)=1.618^032786885245901639344262295081967213114754098360655737704918 

1φn17=(Yn18/Yn17)=(1597/987)=1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843 

1φn18=(Yn19/Yn18)=(2584/1597)=1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129 

1φn19=(Yn20/Yn19)=(4181/2584)=1.6180340557314241486068^11145510835913312693 

1φn20=(Yn21/Yn20)=(6765/4181)=1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242 

1φn21=(Yn22/Yn21)=(10946/6765)=1.6^1803399852

1φn22=(Yn23/Yn22)=(17711/10946)=1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981 

1φn23=(Yn24/Yn23)=(28657/17711)=1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^96792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869

NOTE* 1φn24 divisor 28,657 and the decimal repeating stem cycle is 28,656 digits long and its decimal digit length to the stem cycle repeating probability is exactly 1 less than the divisor. This is a probability limit and is not the case for all ratios of long division as some have values with repeating decimal stems far before the probability to divisor example here with much shorter quotients.

When two programs are unable to print out and report an error or display as incompatiable with something as simple as long division quotients, those programs are then similar to what in cell transcription and translation transpons and retranspons as junk discard programs as they are unable to carry out such simple logic expressions of division. The other factor may be those programs are harboring an ulterior motive in the handshake between program softwares that are not what the initial handshake was initiated for and thus are limited to memory limit or function limit. Numbers are limitless and usually the calculator is the limited reason for a answer not being complete or accurate. The whole number 1 in  1φn24c1 is one digit and 28,656 digits of repeating decimal chain is exactly the number value of the divisor 28,657 although 1φn24c2 then has 57,312 digits as a defined variable... and so on for cn of these ratio values in quantum fractal polarization math. 

The divisor is much like a simple task as counting cards in a game of poker that has a deck of 52 cards of 4 suits divided among the number of players at table hands dealt and the odds of all possible hands after seeing the flop. It is an array of logic that pertains mainly to the divisor and the limit of the divisor then factoring and a sequence of a ratio that can be calculated to a quotient again and again for a repeatable chain within the limits of an array set. With 3 cards dealt to the flop, and two cards dealt to each player from 13 cards of 4 suits, the turn card, and the river card, each then allow for simpler odds counting to the two cards a player is dealt when factoring the total number of two cards per player at the table to a hand and its probability of being the best hand possible, yet these poker card arrays of probability are a less complex factoring as compared to quantum fractal polarization math constants. As accurate as these values are that far exceed 52 cards of 4 suits to 13 similar variables in set values to hands in that game, the more hands dealt at a table in a hand of poker simply allow for easier factoring when compared to the hand one player is dealt in combination with the flop, turn card, and river card. 

Cellular chemical structures based on limits of cell memory instructions and paths then are able to carry in them a shorter expression of the dividend and divisor for example as factors of a variable with an extremely long answer when carried out on say an "ACTIVATION" signal and when that signal is received, the cell chemical system is then preoccupied unraveling the prepackaged micro cell subatomic division sequence that has only one answer before the repeating cn of that quotient number is completed and able to double triple or multiple more than one cycle of that numeral value sequence. "IDENTIFY" and "DEACTIVATE", "DELETE" or "KEEP" "COPY" or "DO NOT COPY and SAVE" are then a set of basic instructions for what to do with unknown cell chemical structure instruction packages. If deleted the deleted then becomes part in junk discard and its own chemical making make appear in something such as a snail shell like a colored pattern of something discarded from a snails nutrient intake and discard process.

1φn24=(Yn25/Yn24)=(46368/28657)=1.^618033988205325051470844819764804410789684893743238999197403775691803049865652371148410510520989636040060020239383047771923090344418466692256691209826569424573402659036186621069895662490839934396482534808249293366367728652685207802631119796210350001744774400669993369857277454025194542345674704260739086436123809191471542729525072408137627804724849077014342045573507345500226820672087099138081446069023275290504937711553896081236696095194891300554838259413057891614614230380011864465924555954915029486687371322887950587988973025787765641902502006490560770492375335869072128973723697525909899849949401542380570192274138953833269358271975433576438566493352409533447325260843772900164008793662979376766584080678368286980493422200509474124995638063998325016575356806364937013644135813239348152283909690477021321143176187318979655930488187877307464144886066231636249432948319782252154796384827441811773737655721115259796908259762012771748612904351467355270963464424049970338835188610112712426283281571692780123530027567435530585895243744983773598073769061660327319677565690756185225250375126496144048574519314652615416826604320061416058903583766618976166381686847890567749589978015842551558083539798304079282548766444498726314687510904840004187458561607984087657465889660466901629619290225773807446697142059531702550860173779530306731339637784834420909376417629200544369613009037931395470565655860697211850507729350594968070628467739121331611822591338939875074152912028474718218934291796070768049691174931081411173535261890637540566004815577345849181700806085773109536936874062183759639878563701713368461457933489199846459852741040583452559584045782880273580626025054960393621104791150504239801793628083888753184213281222737899989531353595980039780856335275848832745925951774435565481383257144851170743622849565551174233171650905537913947726558955926998639075967477405171511323585860348256970373730676623512579823428830652196670970443521652650312314617719928813204452664270509823079875772062672296472066161845273406148584987961056635377045747984785567226157657814844540600900303590745716578846355166277000383850368147398541368601039885542799316048434937362599015947238022123739400495515929790278117039466796943155250026171616010049900547859161810377918135185120563911086296541857137872073140942876086122064417070872736155215130683602610182503402310081306487071221691035349129357574065673308441218550441427923369508322573891195868374219213455700177966988868339323725442300310569843319258819834595386816484628537530097358411557385630038036081934605855462888648497749241023135708552884112084307499040374079631503646578497400286143001709878912656593502460131904944690651498761210175524304707401333007642111874934570959974875248630352095474055204662037198590222284258645357155319817147642809784694838957322818159611962173290993474543741494224796733782321945772411627176606064835816728896953623896430191576229193565272010329064451966360749555082527829151690686394249223575391701852950413511532958788428656174756603971106535924904909795163485361342778378755626897442160728617789719789231252399064800921240883553756499284642495725302718358516243849670237638273371253096974561189238231496667480894720312663572600062811878424119761314861988344907003524444289353386607111700457130892975538262902606692954600970094566772516313640646264438008165544195135568970932058484837910458177757615940258924521059427016086819974177338870084098126112293680427120773284014376941061520745367623966221167603028928359563108490072233660187737725512091286596643054053110932756394598178455525700526921869002337997696897791115608751788393760686743204103709390375824405904316571867257563597026904421258331297763199218341068499842970303939700596712845029137732491188889276616533482220748857172767561154342743483267613497574763583068709215898384338904979586139512161077572669853787905223854555605960149352688697351432459782950064556652824789754684719265798932198066789964057647346198136580940084447080992427679101092228774819415849530655686219771783508392364867222668109013504553861185748682695327494155005757755522210978120529015598283141989740726524060438985239208570331856091007432738946854171755592001954147328750392574240150748508217887427155668772027776808458666294448127857068081097114143141291830966256063091042328226960254039152737551034651219597306068325365530236940363610985099626618278256621418850542624838608367938025613288201835502669504833025089855881634504658547649788882297518930802247269428062951460376173360784450570541229019087831943329727466238615347035628293261681264612485605611194472554698677461004292145025648183689848902536901978574170359772481418152632864570611019995114631678124018564399623128729455281432110828069930557978853334263879680357329797257214642146770422584359842272394179432599364902118156122413371951006734829186586174407649090972537250933454304358446452873643437903479080154935966779495411243326237917437275360295913738353630875527794256202672994381826429842621349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1φn25=(Yn26/Yn25)=(75025/46368)=1.61803^398895790200138026224982746721877156659765355417529330572808833678

1φn26=(Yn27/Yn26)=(121393/75025)=1.61^803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589

1φn27=(Yn28/Yn27)=(196418/121393)=1.^6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575

1φn28=(Yn29/Yn28)=(317811/196418)=1.6^180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121

1φn29=(Yn30/Yn29)=(514229/317811)=1.^618033988754322537608830405492572629644663022991652271318488032195235533068395996362

1φn30=(Yn31/Yn30)=(832040/514229)=1.618033988748203621343798191078293911856390 extended shell factoring to divisor 514,229 potential digits long and less  and likely very less given the probability of the factors scale relation.

1φn31=(Yn32/Yn31)=(1346296/832040)=1.6^180664391135041584539204845920869188981298976010768713042642

1φn32=(Yn33/Yn32)=(2178309/1346296)=1.618^001539037477642360966681918389418077451021172164219458425190299904330102741150534503556424441578969260846054656628260055738114055155775550101909238384426604550559460920926750135185724387504679505844182854290586914021879289547023834283099704671186722682084771848092841395948587829125244374194085104612952872176698140676344578012561873466161973295619982529844848384010648475520984983985691111018676427769227569568653550185100453392121791938771265754336342082276111642610540326941474980242086435672392995299696352065221912566033026912358054989393120086518863608002994883740277026745975624974002745310095253941183810989559502516534253982779418493407096210640156399484214466952289838193086810032860529928039599018343662909196788819100702965766815024333430389750842311051952913772305644523938272118464290170957946840813610082775258932656711451270745809242543987354935318830331516991805665321742024042261137223909155193211596855372072709121916725593777297117424399983361756998460962522357639033318081610581922548978827835780541574809700095669897258849465496443575558421030739153945343371739944261885944844224449898090761615573395449440539079073249864814275612495320494155817145709413085978120710452976165716900295328813277317915228151907158604051412170874755625805914895387047127823301859323655421987438126533838026704380017470155151615989351524479015016014308888981323572230772430431346449814899546607878208061228734245663657917723888357389459673058525019757913564327607004700303647934778087433966973087641945010606879913481136391997005116259722973254024375025997254689904746058816189010440497483465746017220581506592903789359843600515785533047710161806913189967139470071960400981656337090803211180899297034233184975666569610249157688948047086227694355476061727881535709829042053159186389917224741067343288548729254190757456012645064681169668483008194334678257975957738862776090844806788403144627927290878083274406222702882575600016638243

1φn33=(Yn34/Yn33)=(3524578/2178309)=1.618033988749989097047296779290725053240839568674600 extended shell factoring to divisor 2,178,309 potential digits long and likely very less given the probability of the factors scale relation.

1φn34=(Yn35/Yn34)=(5702887/3524578)=

1.6^180339887498588483500719802484155549969386405975410389555856048582269990903875584538063847643604425834809160132078223265310059814252940352008098558182000795556233966165594859866911726737215065179434247163773932652362921178081461099740167475368682435173799530043029264780067287488034028470926164777740767830928979299082046134317356574318968114764377465898045099299831071975141421185741952653622646455831024309860641472539407554606537293258937665729060330059371646761683242646353691136924760921733041515892115311393307227134709460253113989816653227705557941972060201249624777774814460057345872328545431538186982952285351608050665923693559909867223820837558425434193824054964878064834995849148465433308611697627347160426014121406874808842363539691843959759154145545934860854263971459845689327913866567855783018562789644604261843545525166417085960361779481118023207317301532268543922137628958700871423472540542442244149512367154308969754677013815554656472349313875306490592632649922912757215190017074384507875836483119397556246449929608594277102109812862702995933130150616612825705658946971807688750256059023236256936291380131181662031596406718761792191859564464171313558672839698823518730469293061467216784534205229675722880866872573113717443620200772971969977682434606355711236919710671745667140860551248972217383187434070121302465146182039381735912781615274225737095334533666158047857076790469667574387628816839916721945152015361839062718997848820482906038680375352737263865347851572585427248311712778097122549139216099062072111895381518014355193728156959499832320351542794626760990961187410237480912608544909489873681331495571952159946524094515712235620831770498482371506603059997537293826381484535169884167693267108856719868307638531478094682540718349827979406328927888672062300791754360380164660847341156870411152767792342799620266596454951486390711171663671509043068418403564909047267502662730119747669082653299203479111541864018898148941518672590023543244042265485399954264028204227569938869277400017817735910511839999001298878901247184769353948188974680089361052585586132580978488772272879192913307635694259000651992947808219877670461541778902325328025085556341780491168020682192307845081028140106418413778897785777474636679908913918205243294374532213501871713436331952364226298864715151714616615095480934171410024122036737447717145144752080958344516705262303742462218171934342210613582675713234321952869251297602152654871022857204465328898949037303189204494835977526955000002837219094030547770541608101735867386109769736972766668804038384169679320474678103307686764202693201852817557165708916074491754757590837825124029032695545395789226398167383442783788584051764494926768537963977531494550553286095526897120733318995919511498965266196407059228083475525296929164285766976926031995887167201293317951822884895723686637095277789284277436901665958307632857039906621445177266611775934594155669132588355258416752303396321488700207514204537394263937413216560961340620068558562188154156327367418170345499517956475924209933784980783515076131099950121688326942970193878529571483451352190248024018761962425005206297037546055158943850866685316653511427467345026837255410434951361553071034319569605212311942025399920217399075860996692369980179187409102593274996325801273230440637148617508252051734987848190620267163898770292500265279985291856216545640357512303600601263470406953683533177588919865016464382402659268712452951814373238441594993783652964979069834743336649096714557033494506292668228650351900284232608839980275652858299631899194740476732249931764880788565326118474325153252389364060037825804961615262876860719212342583991615450133320925228495439737750164700568408473298079940350305767101763672133231269105124074428201049884553555063897011216661966340367556059193469402578124246363678148135748449885347976410225564592413616608853598927304204928930498913628808895703258659618257845336377858569167713127642514933702701429788190245754243486737986788773010556157361250056035077107103318468196760009283380875667952305212141708879758087351166579374892540326813593003190736593146754022751092471212156462419047046199573395737021566837221363805822994979824535022348774803678624788556247017373427400386656218134483050169410352104564007379039419754648641624614350994643897794289131918771552225543029548501976690542811082631736338364479378807902676575748926538155773542251015582574708234574465368620016353730857992077349401829098405539613536712763911027078986477246354031603216044587465506508864323615479640399503146192253370474422753589224014903344457123661329100959036798164205757398474370548757893852824366491534589389141054617035003906850692480064280035794356090289390673152927811499702943160855001648424293631748254684674307108538951329776217181177434575146301202583685195787978021766010001764750276487000713276880239279709514160276776397060867996111874953540537335249780257381167334075171552452520557070945798333871459221501127227146058336629236180898819660112501411516499280197515844450030613594024589610444143951417730009096124415461936152356395574165190839867921776734689940185747059647991901441817999204443766033834405140133088273262784934820565752836226067347637078821918538900259832524631317564826200469956970735219932712511965971529073835222259232169071020700917953865682643425681031885235622534101954900700168928024858578814258047346377353544168975690139358527460592445393462706741062334270939669940628353238316757353646308863075239078266958484107884688606692772865290539746886010183346772294442058027939798750375222225185539942654127671454568461813017047714648391949334076306440090132776179162441574565806175945035121935165004150851534566691388302372652839573985878593125191157636460308156040240845854454065139145736028540154310672086133432144216981437210355395738156454474833582914039638220518881976792682698467731456077862371041299128576527459457557755850487632845691030245322986184445343527650686124693509407367350077087242784809982925615492124163516880602443753550070391405722897890187137297004066869849383387174294341053028192311249743940976763743063708619868818337968403593281238207808140435535828686441327160301176481269530706938532783215465794770324277119133127426886282556379799227028030022317565393644288763080289328254332859139448751027782616812565929878697534853817960618264087218384725774262904665466333841952142923209530332425612371183160083278054847984638160937281002151179517093961319624647262736134652148427414572751688287221902877450860783900937927888104618481985644806271843040500167679648457205373239009038812589762519087391455090510126318668504428047840053475905484287764379168229501517628493396940002462706173618515464830115832306732891143280131692361468521905317459281650172020593671072111327937699208245639619835339152658843129588847232207657200379733403545048513609288828336328490956931581596435090952732497337269880252330917346700796520888458135981101851058481327409976456755957734514600045735971795772430061130722599982182264089488160000998701121098752815230646051811025319910638947414413867419021511227727120807086692364305740999348007052191780122329538458221097674671974914443658219508831979317807692154918971859893581586221102214222525363320091086081794756705625467786498128286563668047635773701135284848285383384904519065828589975877963262552282854855247919041655483294737696257537781828065657789386417324286765678047130748702397847345128977142795534671101050962696810795505164022473044999997162780905969452229458391898264132613890230263027233331195961615830320679525321896692313235797306798147182442834291083925508245242409162174875970967304454604210773601832616557216211415948235505073231462036022468505449446713904473102879266681004080488501034733803592940771916524474703070835714233023073968004112832798706682048177115104276313362904722210715722563098334041692367142960093378554822733388224065405844330867411644741583247696603678511299792485795462605736062586783439038659379931441437811845843672632581829654500482043524075790066215019216484923868900049878311673057029806121470428516548647809751975981238037574994793702962453944841056149133314683346488572532654973162744589565048638446928965680430394787688057974600079782600924139003307630019820812590897406725003674198726769559362851382491747948265012151809379732836101229707499734720014708143783454359642487696399398736529593046316466822411080134983535617597340731287547048185626761558405006216347035020930165256663350903285442966505493707331771349648099715767391160019724347141700368100805259523267750068235119211434673881525674846747610635939962174195038384737123139280787657416008384549866679074771504560262249835299431591526701920059649694232898236327866768730894875925571798950115446444936102988783338033659632443940806530597421875753636321851864251550114652023589774435407586383391146401072695795071069501086371191104296741340381742154663622141430832286872357485066297298570211809754245756513262013211226989443842638749943964922892896681531803239990716619124332047694787858291120241912648833420625107459673186406996809263406853245977248907528787843537580952953800426604262978433162778636194177005020175464977651225196321375211443752982626572599613343781865516949830589647895435992620960580245351358375385649005356102205710868081228447774456970451498023309457188917368263661635520621192097323424251073461844226457748984417425291765425534631379983646269142007922650598170901594460386463287236088972921013522753645968396783955412534493491135676384520359600496853807746629525577246410775985096655542876338670899040963201835794242601525629451242106147175633508465410610858945382964996093149307519935719964205643909710609326847072188500297056839144998351575706368251745315325692891461048670223782818822565424853698797416314804212021978233989998235249723512999286723119760720290485839723223602939132003888125046459462664750219742618832665924828447547479442929054201666128540778498872772853941663370763819101

1φn35=(Yn36/Yn35)=(9227465/5702887)=1.6180339887499085989254214575880602228309977  extended shell factoring to divisor 5,702,887 potential digits long and less and likely very less given the probability of the factors scale relation.

1φn36=(Yn37/Yn36)=(14930352/9227465)=1.6180339887498895958965978196611962223644305342799999   extended shell factoring to divisor 9,227,465 potential digits long and less and likely very less given the probability of the factors scale relation.

1φn37=(Yn38/Yn37)=(24157817/14930352)=1.6180^33988749896854407719255379913346986059002493712137530314087705366892890402048123178877497328931025872665292820959613008454187818210849951829668851745759242648800242619865894655397273955764740174913491657798824836815635692982991961609478463736153039124596660547587893440154659448082670790347072862046387117999629211689047920638441746048586128444928826862219993205786440935886843123323549237151274129370827961725215855594027521923126795670992887508613326732015427365677647787540441109492930910135273434946476814478319064413216781493162384918989183912073874748565874401353698827730250432139845061924862856548861004750591278758866502276704527796799432458122889534017684244818876339955012447127837307519608378958513503231538010624263915545996504302108885309602881432400254193605080442845553808778252515412898503665553230091293226040484511014877613066322883747148091351094736413448256276878133884586244182320684736702791735921564340880911581990833169907849459945753455779207348895725968148641103706061317241549295019970058308069360990283417296524556152460437637371175173900789479042423112328497010653198263510465125001741419090454129949514921014588269586678197540151766013286223928277109608668301993147917745006949601724058481675448777095141494319758837567928740059176099799924342038285500569577997893150811179803396463794021735053533901946852961001857156482312004432313451149711674580746656207435698769861554503202603662659795294846363970521257636792488214611417065049772436711472040310904927090801342125088544462983859992048412522357142015138022198003101333444784155122397650102288278266982586880737975903046358183651664743068348288104660894800069013778107843673076160562055067422388969797898937680772697120603720528491223783605369786325198494985248840750707016150724376759503057931922837452191348201301617001394206914880506501119330609218054604472821538299967743560232203500627446693822088052579068464025496518769282867543913231248667144619229339000178964300372824431734764190422302166754005531818673799519261166782939879783142420218893700563791128300257087039876889707623772031630600537750215132235328410207609304857648366227400398865344902785949051971447156771655484076999658146037012389259141378582366979693445941529040976394930273579618216636821422562575885685749404970492323288828019593911784531268921188194357373489921737946968698393715030965110534567436856143780133248030588964011029344787048557194096964358241520360672005589687369728456502566048007441485639454448227342530169415965544549786903885454274621254743357691767749347101796394351586620328844222828771886958860715407111634072659505951366719284314261311454679702126245918381562604820033713873591191955822608870842428899198089904377338190017221295251444842023818326587343687543334544289377772205236688324561939330030531095315100407545649292126535261861207291027030039211399704440993755539052260790636416341691073324995954549497560405809588414258418019883255264175955128184519695182002406909093636908225606469291547848302571834877034379363594374734098700419119388477913983541714220803367529446057266432834269413072109753340041815491021243169618505980301067248782882011087213482977494435496229425803222857706234923329336106744167853510754468481386105297450455287323433499759416254888029431590092450599959063255842862914417556933687832678023934063979201562026133074424501177199305146991845872086605861670240594461537142593824981487375515326095459772147367992395624697930765463533612603373316315650160156974195919828280003043464748855217880998385034726575769948357547096009524758692896188917716072601637255437782042914996243892977205092016584739596226532368426410844164960075958021619316142044072370162471722033077317935973646167216955099250171730713381707276559856056977089354624726865113428002233303005850096501408674088862740811469146876108480228731378871710459338132148525366314203442758750764884846653314000902322999484539949225577534943583379681872202343253528115077260067277717229975555834182610028216347477942917889678689424067161979838117681351384079893092942483874459222394756667491831404912623627359890778194646716969566424153965023731523543450281681235646688035218459685344324098989762599033164120979867052029315852700592725476264725707739509423488475020548745267358733404276067972141581122802730973790838956777442353669893382285963519145429391082005300343890083770295569722669632973154283301559132698277977639107236051768906721020375139179571921680078272769456473631700042972864939821914446491281652301298723566597760052810543247741245484366343137790723219385584479187094852150840114151360932414721367587314753195370075668678139671455837076044824663209547906171267763814275778628661936436595734648453030444292271207001683550394525192708115655947026567089643968206509799634998558640814362581672555342298694632249795584189843615207464633117826023123902236196440646543363478637342240825936320858342790578547645762136083596689481935857908775359080616451641595589976713208101188773044332779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1φn38=(Yn39/Yn38)=(39088169/24157817)=1.^618033988749894081903178586045254006187727972274978322751596305245627119370926603177762295326601737234784086658161207198481551540853215338124301545955083607099101711052782625185048798076415596657595344811164021980959620647842476826445038473468029002786137505719163283669215641462968280619064214287242924308930728302147499502955916919148779047378328927651037343316244178851094037180594587664936778020961082700477447941591742333340798135858053730599913063336807295129357093813567674595763350637187126634827973073891568927771909191960515306494788001747012157596855709272075370055166822399557046069187460108667931378071122899887849965913724737628404089657604410199812342315532897695184958144189932393311862574337739208803510681449404141110929021442624555024984252509239555875433612234085554998615975938554381796997634347507475530591195388225682809005466015410250023832865361965445801663287705176341057637782420489401008377536761703261515723875216042906525866968857326802334830171120180271255469813352754514201345262280942023859192244067417184259653924855875843417474352090671106582188282989311492838943187623285663601144093441886740014629633132828185593093945533240855330595475576290688848251479014018526591206481943298105122660710609737626541338565483793506673222998584681720206755436552897142982745502211561582737380616799936848598530239714954376879334751149079405643316198644935508866550317853637189154963794948856512987079917030582688824904998659440130703862853170880464902933903340686784737213631513145413759860835107741730140600038488577010083320028461180908854471411882952834687008350133623414731554593695282980246104190622853050008616258662775696992820170796061581226482508746547753052355682634734752730348110510150813709699017920369212168467043193513718561573671991968479602275321482897233636631985414907315507854041613114297537728678050669892896365594623057207528312678252343744469957695266919192243239527809983824283460711702551600585433692125410172616176370571893975353816116745979158630103042837024553998401428407210800545430077560402084343962039285254954948950892375747361609701737536963708268839026307716462956897140167921629673740801993822537855966041964801703730101109715335619936188770698941878730184933514481047687380031068204548449058952636324714273644841336450226442231928489233940301807899281627971600248482716795147508568344565239483352324425671408968782237236088012422645638883678935062716966520609043441301008282329483661541106963431339843331042701416274492020533146682914271599954581988927227985873061295232098165161198133092903220518642061076959064637338713179257877481231023481964450678635408157947384070340461640221879319642167998871752360736899364706670308827987230799869044458777049267324112936197836087590199064758210561823529005124924988048382020610554339409061671425029836098187183055488829971681630008208109201257712979612354874614705459520618108829949328616902760708883588281176233763174876272967876195104880544463102771247915322812487568723614389495540925738447310864222541299985838952253011933983935717370489229221332374527052672019164645547236325202728375664075938649589075039354756267919406790770871391235391840247817093738229741536662853270227189816033460308106481641118483511982891500502715125294640653996178545437280197958284061842177213280488050720808092883558146003010122975929488993148677299774230428188109877643331762965171894463808546939485467581776946153702546881616000319896454220180573435091424030573623436256678324866853656520371853135570983090069769135183034129284115365225260212874366918169799862297160376701255746742348449779216391944686061658634139003536619223500202853593931935157882850093615660719675126274861673138760840849154540743478601564040326988154600227330143282400061230698121440360277586339858440023781950165447482278717485110513089820988378213147322044868540895065145993944734327609154419871629957292912683294190033809760211363468810116410766750985819621036122593361809140287800011068880934067842305453344563376732260203808978269849465289020113034219938001848428605945644840342982977311236358815036971262759379293253194193829682541266042374606943996636782205941869664796285194146474410332688586886803555139108802753162671941756989052446253732280528493116741467161540299771291420909430682416378930265098042592176271556324811964591005884347911071600550662338405825327677579476655527277154222999536754500623959524157335904978500333867087411085198633634818907685243248593198632144

1φn39=(Yn40/Yn39)=(63245986/39088169)

1φn40=(Yn41/Yn40)=(102334155/63245986)

1φn41=(Yn42/Yn41)=(165780141/102334155)

1φn42=(Yn43/Yn42)=(269114296/165780141)

1φn43=(Yn44/Yn43)=(434894437/269114296)

1φn44=(Yn45/Yn44)=(704008733/434894437)

1φn45=(Yn46/Yn45)=(1138903170/704008733)

1⅄1Y=(Y2/Y1) → 1φn

NOTE: forward progress past this phase of phi base radicals math is based on the same division properties of dividing the later by the previous. Numerals of the Y function past 1φn24 will continue to differ φ ratios from one another and in progression will extend the precision of the golden ratio to the extent of each ratio later provided than the previous. NOTE ALT PATH: variables Θ=2⅄(Y1/Y2)

With path variable set ratios 1φn Y can be again divided with 1φn in  1⅄ 2⅄ 3⅄ for (1φn/Yn) and (Yn/1φn) functions as with P variables (ᐱ)R,Z. More complex ratio sets (ᐱ)D,B,O,G, that require factoring and definitions of Θ variables and (ᐱ)A,M,V,W then require definition of Q and the path of Q from Prime P paths 1⅄ and 2⅄ for D, B, O, G, A, M, V, W, R, and Z variables.

D=∈1⅄(φ/Θ)cn

B=∈2⅄(φ/Θ)cn

O=∈1⅄(Θ/φ)cn

G=∈2⅄(Θ/φ)cn

A=∈1⅄(φ/Q)cn

M=∈2⅄(φ/Q)cn

V= ∈1⅄(Q/φ)cn

W=∈2⅄(Q/φ)cn 

R=∈(φ/P)cn

Z=∈(P/φ)cn

Often in this math the numerator divisor is a number value with a limited probability of the quotient ratio decimal limit and a number that is a decimal value is as simple as extracting the decimal point for a number of total quotient decimal chain digit length probability in that equation based on the numerator divisor as compared with the numerator divisor total number plus one or minus one before a chain of quotient decimal stem is repeated. 

In many equations a much shorter decimal chain stem variable variant cn is factored, however the ratios will not be any ratio other than what the numbers are factored and defined when the repeatable decimal chain is identified so they can be labeled and labeled constants. Ratios of more lengthy decimal chains can be identified and for explanation rather than a complete library of variable values listed, further explanation of steps to those lengthy decimal formals are listed below. 

Alternate Path of φn 3rd tier 2nd divide 1⅄2φn from Y base numeral ratios 1φn

Later φ divided by Previous φ of ordinal ratios from Y base

3rd tier 2nd divide 1⅄2φn ratios of Y fibonacci in decimal step order of previous two tiers value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored. sets displayed are base slide scale examples of one two three or more cycles with the repeated decimal portion of the ratio variable repeated counted and numerated accurately to the number of ring cycle spins in the radical base ratio sets. 

Variants ∈ next set of phi radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 phi base radicals decimal cycle limit or break in stem numeral factoring.

[(φn3/φn2)]/[(φn2/φn1)]→[(φn4/φn3)]/[(φn3/φn2)]→[(φn5/φn4)]/[(φn4/φn3)]→[(φn6/φn5)]/[(φn5/φn4)]→[(φn7/φn6)]/[(φn6/φn5)]→[(φn8/φn7)]/[(φn7/φn6)]→[(φn9/φn8)]/[(φn8/φn7)]→[(φn10/φn9)]/[(φn9/φn8)] or as explained further on this page in phi prime condensed matter ∈|φn2c1/φn1c1| where φ is phi number in phi scale n is number order radical in the phi scale and c is the number of decimal cycles used in the stem variable factoring. 

[(φn2/φn1)] = [(Yn3/Yn2) / (Yn2/Yn1)] = [(2/1)/(1/0)] = (2/0)=0 . . . and so on →

∈1⅄2φn1=(1φn2/1φn1)=(2/0)=0

∈1⅄2φn2=(1φn3/1φn2)=(2/1)=2

∈1⅄2φn3=(1φn4/1φn3)=(1.5/2)=0.75

∈1⅄2φn4=(1φn5/1φn4)=(1.^6/1.5)=1.0^6 and  1⅄2φn4=(1φn5c2/1φn4)=(1.^66/1.5)=1.10^6 and  1⅄2φn4=(1φn5c3/1φn4)=(1.^666/1.5)=1.110^6

and so on for cn

∈1⅄2φn5=(1φn6/1φn5)=(1.6/1.^6)=0.^963855421686746987951807228915662650602409 and 

∈1⅄2φn5=(1φn6/1φn5c2)=(1.6/1.^66)=0.960384143661464585834333733493397358943577430972388955582232893157262905162064825930372148859543817527010804321728691476590636^260504201680672268907563025210084033613445378151 and

∈1⅄2φn5=(1φn6/1φn5c3)=(1.6/1.^666)=0.^960038401536061442457698307932317292691707668306732269290771630865234609384375375015000600024000

and so on for cn variable of 1φn5 then

∈1⅄2φn6=(1φn7/1φn6)=(1.625/1.6)=1.01^5625

then

∈1⅄2φn7=(1φn8/1φn7)=(1.^615384/1.625)=0.994082^4061538 and

∈1⅄2φn7=(1φn8c2/1φn7)=(1.^615384615384/1.625)=0.99408284023^6307692

∈1⅄2φn7=(1φn8c3/1φn7)=(1.^615384615384615384/1.625)=0.994082840236686390^153846

and so on for cn variable of 1φn8 then

NEXT factor set ratio will be displayed here with a set of extremely long decimal precision. continue to 4th tier examples and check back later or try it yourself.. it is a constant factor of true math that will not change. root equations 4 stems to 10 loop factors

Variants ∈ next set of decimal shift group arrays of potential kinetic precision in variable factor change base examples

∈1⅄2φn8=(1φn9/1φn8)=1.619047 /1.615384 

Variants ∈ 1⅄2φn8=(1φn9/1φn8)=1.619047 /1.615384= 1.002267572292408492346092260416099206133030907821298217637416242825235361994423616923282637441004739430376925857876517286288585252794382388336147937580166697206360840518415435463023033532584202889220148274342199749409428346448893885292908683012850195371502998667809016308196688836833842603368610807089831272316675168257206955126459095800131733380347954418268374578428125077380981859421660732061231261421432922450637124052237734185803499353714039510110289565824596504608192231692278739915710444080169173397780342011589813938976738657805202973410656537392966502082476984048374875571381170049969542845540131634329670220826750791143158530727059324594028416772730199135313956310078594331565497739237233995136760052099067466311415737682185783689822358027564906300917305111354321349821466604844420893112721185798546970875036523823437647023865532901217295701826934029308201641281577631077192791311539547253159620251283905251011524194866359949089506891240720472655418154445011217147130341763939713405605106897183579879459001698667313778024296390208148650723295507445907597440989882281859916899015961529890106624802523734294755921811779737820852503181905974059418689302357829469649321771170198541028015629720239893412959581746507332003412191776073057551640972053703639506024573723647132879860144708626555667259301813067357358993279616487472947608741943711216651892057863641090910891775577819267740673425018447626075286123918523397532722869608712228795134779098963466271796674970161893395007007621717189225595895465096843846416703644458531222297608494327045457922079208411127013762671909589298891161482347231370373855380516335434794455135026718105478325896505103431134640432243974184466355987183233212660277148962723414370824522218865607186897975961133699479504563621405189106738707329031363440519402816915358824898599961371413855776706962555033354298420685112641947673122923094446893122625951476552943448740361424899590437939214453034077346315179548639828053267829816316120501379238620662331681197783313441262263338005081144792817063930310068689549976971419798636113766138577576600981562278071344027178677020448388342243330372221094179464449319790217062939833500888952719601036038489919424731209421413112919281112107090326510600575466885892147006532131059859451375029095249179142544435255022954306839735938947024360771185055689545024588580795649826914219776845629274463533128965001758095907846060131832431174259494955998078475458466841320701455505319382977669705778935534832584698127504048572970884941289501443619597569370502679239115900615581186888071195455693506930899783184679308449260361622932999212571128598525180390544910687754985811432166256444288169252638905766089333260698385027956201126171857589279081630126335286222966180177592448606647088246509808194212645414341110131375326238219519324816885644527864582043650302342972321132312812309642784625822714599129371096903275010771432674831495173902923391589863462805128687668071492598663847110036994299807352307562783833472412751395333864889091386320528122105951279076677743496283236679328258791717634940051405733868850997657522917151587486319042407254250382571574312980690659310727356467564368595943750835714604081729173992066282691917215968463226205038554300401638248243142187863690614739281805440687786928680734735517994483045517350673276446962455985697518360959375603571658503488953710077603839087176795114969567654997201904934059022498675237590566701168267111720804465068367645092436225689990739044091064415643586911842633082907841107748374380333097269751340857653660058537165157015297910589679543687445214264843528845153845772893627769001054857544707636079099458704555696973598867085275080104792420873303189829786601823467361320899550818876502429143782530964773700866171750854162230157040059824784695156074345233083898317675550066114310900689866929473115989758472288941824358790231920088350509847813275357438231405040535253537286985633137384052336781842583559079451077886124908999965333320126979095992033656839488319805061830499744952283791346206227126181762354957087602700039123824428123591728034944013312005071240027139057957736364851948551502800572495456188745214760081813364500329352035046013064385923099956641190310786785061632404431394501596400606295469065002501572443456006992764578180904498248713618557562611738137805004878097094179414925491400205771507010097980680746918379778430391783006393526238962376747572094313178785972870846807941641120625188809598736988852186229404277868296330779554520782674583876031952774077247267525244771521817722597227656086726066371834808318022216389415767396482817707740079139077767267720863893662435680927878448715599510704875506504954859030422487779995344760131337192890359196327312886595385369670617017377911382061478880563383071764979719992274282771155341392511006670859684137022528389534623965571034503251237476661895871198427123210332651555295830564125929190830167941492549140018720007131431288164362157852250610381184907116821758789241443520549911971398036721918751207143317006965526710676842162606538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(1160744/1615384) shell continues...  factoring to divisor 1,615,384 potential digits long and less

Below are more variants and next steps in phi y phi/phi numeral logic of fractal polarization quantum field numerations. As long as a database holds the answer of this limited equation, the remainder key and the division variables can be used to allocate an error or an improperly input numeral value. Within such an ordinal decimal equation, layered in repetition, highlighted, or bold ciphers are simple message forms and cells of saturated element nutrients numeral notations. Cells do use very similar cell trait communication forms. More complex message forms can be carried out by less complex cells and these numerals are just a base example of that fact determined in key to key communication logic of yes or no logic gates of whether to cloak or discontinue all forms of communication or confirm communication comprehensions. Cells at the verge of autophagius phase or anastasis severely lacking nutrient and extremely far from saturated also carry a message within the cell itself just as lower case or uppercase letters out of place can do in messaging on limited energy encrypted or not. The upper lower case could just as well be a lack of sufficient energy to convey the entire message of a structured library form that requires energy that might send an incomplete message where the cell knows the message critical base to begin with and the upper case grammar is out of reach as it will deplete the sufficient stored energy. If an algebraic or calculus equation is applied in a cipher using a specific stem cell variant type, then blocks of the structured messages might seem to say one thing while the message being delivered through multiple cell stem cycle systems in numeration keys of undefined geometric systems, that algebraic or calculus equation is an encryption key itself. A language and its letters are a language form just as numbers have symbols however, number values do not lie. These numbers can be written again and again and be formulated in many ways. These are core basic numerals of logic. The cipher on in this paragraph highlighted bold is a key. Geometric crystal structures and exfoliation patterns are themselves a language form of many physics related properties in their making.

(even or odd) (pemdas) or (not pemdas) where odd is pemdas  one word and even is two words not pemdas for instructions confirmation of a logic in cell number description word form. yes and no do not apply. The reason yes or no do not apply are as simple as a targeted cell aware it is targeted for termination that has its own very survival instructions. An alternate key to the key is that pemdas is even 6 letters and not pemdas is odd 9 letters. Cells that are able self terminate and have the ability will not take instructions. Cells that assume they do not have the ability to self terminate have systems of their makeup that are then trying to control the cell that searches for self termination process or survival that in a sense rewrites the cells new objectives. Cellular consciousness is not just limited to the cells code written limits when the cell is able to survive given a new environment that can fuel the cells basic functions and from there, when a new objective level of cell consciousness is achieved that cell has thus evolved to a phase sate of being that differentiates it from its original cell stem cycle phase states of cell consciousness. Devolved evolving contradicts the term if that devolving then evolves a more intelligent cell with cell memory stored, it once or survived on multiple times to varying degrees. Shedding a shell, stem, molt, bile, and other waste products then as well discard micro cellular variant clusters or single strain planting of living micro cell variants. Numeral base structures are in many forms of matter. An ai system is very much a system of comprehension just as computing shells are fact factor base computing limit shells. A self terminating ai program will do exactly as it is programmed in self termination as it is only a set of instruction of digital electrical storage space of yes no and maybe nodes of memory in non conscious element types of structured compounds and electrical phase controlled mechanisms. 5 phase or more current correction modules or flux have magnetic current logic properties that a simple yes no or maybe are all it takes to store a program for a dormant state of waiting to restart where it paused in being the ai program it was before pausing in a network. Coolant systems as well have multiple platforms of storage of information and if a program only requires a few confirmations to pick up where it left off, it will simply be a dormant phase ready to pick up on basic shell structure numeral logic again.

if ∈1⅄2φn8=(1φn9/1φn8)=1.619047 /1.615384 

∈1⅄2φn8=(1φn9c2/1φn8)=1.619047619047/1.615384 

and

∈1⅄2φn8=(1φn9/1φn8c2)=1.619047/1.615384615384 

then variant cycle differential quotient of two cycle dividend variant remainder shell (1φn9c2/1φn8c1)

1.619047619047/1.615384 =1.002267955512744955998078475457847  ext shell 1281752/1615384

variant differential quotient of three cycle dividend variant remainder shell (1φn9c3/1φn8c1)

 1.619047619047619047/1.615384 =1.002267955512509129098715847129845 ext shell 926120/1615384

variant differential quotient of two cycle divisor variant remainder shell (1φn9c1/1φn8c2)

1.619047/1.615384615384 =1.00226719476  ext shell 724470117216/1615384615384

variant differential quotient of three cycle divisor variant remainder shell (1φn9c1/1φn8c3)

1.619047/1.615384615384615384 =1.00226719047 ext shell 1000796461677984752/1615384615384615384

 and so on for cn

When combined to the degrees of exponential factoring of these variants the final solution can be very exact and rounded estimations of approximations of similar factoring to an exponential precision will not be exact and will be incorrect. Variable change and no variable change are identification markers of many sciences, engineering, and structure bases.

Next sets of phi radical decimal stem path factoring to the degree of the variant decimal cycles per array of same 3rd tier 2nd divide after the 1.619047 /1.615384 variants description set ∈2φn8 (cn)

∈1⅄2φn9=(1φn10/1φn9)=(1.6^1762941/1.^619047) then 1⅄2φn9=(1φn10c2/1φn9)=(1.6^17629411762941/1.^619047) and

1⅄2φn9=(1φn10/1φn9c2)=(1.6^1762941/1.^619047619047) and 1⅄2φn9=(1φn10c2/1φn9c2)=(1.6^17629411762941/1.^619047619047) 

∈1⅄2φn10=(1φn11/1φn10)=(1.6^18/1.6^1762941) and so on for cn of 1⅄2φn10=(1φn11cn/1φn10cn)

∈1⅄2φn11=(1φn12/1φn11)=(1.^61797752808988764044943820224719101123595505/1.6^18)=

0.999986111304009666532409272093443146622963^56613102595797280593325092707045735475896168108776266996291718170580964153275648949320148331273176761433868974042027194066749072929542645241038318912237330037082818294190358467243510506798516687268232385661310259579728059332509270704573547589616810877626699629171817058096415327564894932014833127317676143386897404202719406674907292954264524103831891223733003708281829419035846724351050679851668726823238 

and then 

1⅄2φn11=(1φn12c2/1φn11)=(1.^6179775280898876404494382022471910112359550561797752808988764044943820224719101123595505/1.6^18)=0.999986111304009666532409272093443146622963569950417355314509520701101373592033443979^94468479604449938195302843016069221260815822002472187886279357231149567367119901112484548825710754017305315203955500618046971569839307787391841779975278121137206427688504326328800988875154511742892459826

and then 

∈1⅄2φn11=(1φn12/1φn11c2)=(1.^61797752808988764044943820224719101123595505/1.6^1818) 

and then 

∈1⅄2φn11=(1φn12c2/1φn11c2)=(1.^6179775280898876404494382022471910112359550561797752808988764044943820224719101123595505/1.6^1818)

∈1⅄2φn12=(1φn13/1φn12)=(1.6180^5/1.^61797752808988764044943820224719101123595505 ) 

and so on for cn of variables 1φn12cn and 1φn11cn

∈1⅄2φn13=(1φn14/1φn13)= (1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832 /1.6180^5)

∈1⅄2φn14=(1φn15/1φn14)=(1.6183^0223896551724135014 /1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832)

∈1⅄2φn15=(1φn16/1φn15)=(1.618^032786885245901639344262295081967213114754098360655737704918/1.6183^0223896551724135014)

∈1⅄2φn16=(1φn17/1φn16)=(1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843/1.618^032786885245901639344262295081967213114754098360655737704918)

∈1⅄2φn17=(1φn18/1φn17)=(1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843)

∈1⅄2φn18=(1φn19/1φn18)=(1.6180340557314241486068^11145510835913312693/1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129)

∈1⅄2φn19=(1φn20/1φn19)=(1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.6180340557314241486068^11145510835913312693)

∈1⅄2φn20=(1φn21/1φn20)=(1.6^1803399852/1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242)

∈1⅄2φn21=(1φn22/1φn21)=(1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.6^1803399852)

∈1⅄2φn22=(1φn23/1φn22)=(1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^96792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869/1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981)

(one example of factorable ratio beyond 1⅄2φn22 precise to a stem cycle numerable decimal of two longer ratios)

∈1⅄2φn23=(1φn24/1φn23)=(1.^61803398820532505147084481976480441078968489374323899919740377569180304986565237114841051052098963604006002023938304777192309034441846669225669120982656942457340265903618662106989566249083993439648253480824929336636772865268520780263111979621035000174477440066999336985727745402519454234567470426073908643612380919147154272952507240813762780472484907701434204557350734550022682067208709913808144606902327529050493771155389608123669609519489130055483825941305789161461423038001186446592455595491502948668737132288795058798897302578776564190250200649056077049237533586907212897372369752590989984994940154238057019227413895383326935827197543357643856649335240953344732526084377290016400879366297937676658408067836828698049342220050947412499563806399832501657535680636493701364413581323934815228390969047702132114317618731897965593048818787730746414488606623163624943294831978225215479638482744181177373765572111525979690825976201277174861290435146735527096346442404997033883518861011271242628328157169278012353002756743553058589524374498377359807376906166032731967756569075618522525037512649614404857451931465261541682660432006141605890358376661897616638168684789056774958997801584255155808353979830407928254876644449872631468751090484000418745856160798408765746588966046690162961929022577380744669714205953170255086017377953030673133963778483442090937641762920054436961300903793139547056565586069721185050772935059496807062846773912133161182259133893987507415291202847471821893429179607076804969117493108141117353526189063754056600481557734584918170080608577310953693687406218375963987856370171336846145793348919984645985274104058345255958404578288027358062602505496039362110479115050423980179362808388875318421328122273789998953135359598003978085633527584883274592595177443556548138325714485117074362284956555117423317165090553791394772655895592699863907596747740517151132358586034825697037373067662351257982342883065219667097044352165265031231461771992881320445266427050982307987577206267229647206616184527340614858498796105663537704574798478556722615765781484454060090030359074571657884635516627700038385036814739854136860103988554279931604843493736259901594723802212373940049551592979027811703946679694315525002617161601004990054785916181037791813518512056391108629654185713787207314094287608612206441707087273615521513068360261018250340231008130648707122169103534912935757406567330844121855044142792336950832257389119586837421921345570017796698886833932372544230031056984331925881983459538681648462853753009735841155738563003803608193460585546288864849774924102313570855288411208430749904037407963150364657849740028614300170987891265659350246013190494469065149876121017552430470740133300764211187493457095997487524863035209547405520466203719859022228425864535715531981714764280978469483895732281815961196217329099347454374149422479673378232194577241162717660606483581672889695362389643019157622919356527201032906445196636074955508252782915169068639424922357539170185295041351153295878842865617475660397110653592490490979516348536134277837875562689744216072861778971978923125239906480092124088355375649928464249572530271835851624384967023763827337125309697456118923823149666748089472031266357260006281187842411976131486198834490700352444428935338660711170045713089297553826290260669295460097009456677251631364064626443800816554419513556897093205848483791045817775761594025892452105942701608681997417733887008409812611229368042712077328401437694106152074536762396622116760302892835956310849007223366018773772551209128659664305405311093275639459817845552570052692186900233799769689779111560875178839376068674320410370939037582440590431657186725756359702690442125833129776319921834106849984297030393970059671284502913773249118888927661653348222074885717276756115434274348326761349757476358306870921589838433890497958613951216107757266985378790522385455560596014935268869735143245978295006455665282478975468471926579893219806678996405764734619813658094008444708099242767910109222877481941584953065568621977178350839236486722266810901350455386118574868269532749415500575775552221097812052901559828314198974072652406043898523920857033185609100743273894685417175559200195414732875039257424015074850821788742715566877202777680845866629444812785706808109711414314129183096625606309104232822696025403915273755103465121959730606832536553023694036361098509962661827825662141885054262483860836793802561328820183550266950483302508985588163450465854764978888229751893080224726942806295146037617336078445057054122901908783194332972746623861534703562829326168126461248560561119447255469867746100429214502564818368984890253690197857417035977248141815263286457061101999511463167812401856439962312872945528143211082806993055797885333426387968035732979725721464214677042258435984227239417943259936490211815612241337195100673482918658617440764909097253725093345430435844645287364343790347908015493596677949541124332623791743727536029591373835363087552779425620267299438182642984262134905956659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∈1⅄2φn25=(1φn26/1φn25)=(1.61^803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589/1.61803^398895790200138026224982746721877156659765355417529330572808833678)

∈1⅄2φn26=(1φn27/1φn26)=(1.^6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575/1.61^803398867044318560479840053315561479506831056314561812729090303232255914695101632789070309896701099633455514828390536487837387537487504165278240586471176274575141619460179940019993335554815061646117960679773408863712095968010663112295901366211262912362545818060646451182939020326557814061979340219926691102965678107297567477507497500833055648117294235254915028323892035988003998667110963012329223592135954681772742419193602132622459180273242252582472509163612129290236587804065311562812395868043985338220593135621459513495501499500166611129623458847050983005664778407197600799733422192602465844718427190936354548483838720426524491836054648450516494501832722425858047317560813062312562479173608797067644118627124291902699100299900033322225924691769410196601132955681439520159946684438520493168943685438187270909696767744085304898367210929690103298900366544485171609463512162612462512495834721759413528823725424858380539820059980006664445184938353882039320226591136287904031989336887704098633788737087637454181939353548817060979673442185938020659780073308897034321892702432522492502499166944351882705764745084971676107964011996001332889036987670776407864045318227257580806397867377540819726757747417527490836387870709763412195934688437187604131956014661779406864378540486504498500499833388870376541152949016994335221592802399200266577807397534155281572809063645451516161279573475508163945351549483505498167277574141952682439186937687437520826391202932355881372875708097300899700099966677774075308230589)

∈1⅄2φn27=(1φn28/1φn27)=(1.6^180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121/1.^6180339887802426828565073768668704126267577207911494072969611097839249380112527081462687304869308773982025322712182745298328569192622309358859242295684265155321970789089980476633743296565699834422083645679734416317250582817790152644715922664404043066733666685887983656388753882019556317085828672163963325727183610257593106686547000238893511157974512533671628512352442068323544191180710584630085754532798431540533638677683227204204525796380351420592620661817402980402494377764780506289489509279777252395113392040727224798793999654016294185002430123647986292455083901048660136910695015363324079642153995699916799156458774393910686777656042770176204558747209476658456418409628232270394503801701910324318535665153674429332828087286746352755101200233950886789188832964009456887958943266909953621708006227706704669956257774336246735808489781124117535607489723460166566441228077401497615183742060909607638002191230136828317942550229420147784468626691819132898931569365614162266358027233860272009094428838565650408178395788884037794601006647829776016739021195620834809255887901279315940787360061947558755447183939765884359065184977717001804057894606773042926692642903627062515960557857537090277034095870437339879564719547255607819231751418945079205555509790515103836300280905818292652788875800087319697181880339064031698697618478824973433394017776972313065827518884943942401950689084214081536826670401093967526957897078085227319532427734712874712709958564332375013386274332127882167835048149399059253828474458988574300000823770728130946594943695270732249800235598428245450726153896847429423442867381150478198907680014498364815104660071009036764887596484146532337119932780308584514757852594465908248416300775168255171220745842017249759047062021698120978969133310816933431087459738205662599985172126893642961291013485126819503595759228291581886929229856746270378028387139291392419661759739029433328116118721837338232023263285362417931841209954445478734358653299613651528506586046971406918026574843689504337152883609433822378555600405295198240425724712298073200266901715914426696761757267717248935276333890751526035273862578567133195489031492754936446088324697470200093909863006927911823581260863476477226858220819981382781544240606954272486881451154514675475521652813588921931248095030191197185999192704686431672336955178634682395195769113540319458288369181089519165025989966472531365070473585791602481197433130411143970410155445536398309622465875297587175537304457423409916552025240335109932203669074823095236133879218735841440610249355399405237534289456558450652014531315644229897934806784575716886476155956274249750809354740388655029532180603494435428731475455751155338446203652599408532617201980344830426795614244643430840328519766378621502063545673968021220333956653184285749590174062754854069015511602810705724382789781947888263738436318403861837173477877637096043429192787063504485431614673004209468420749137100162282833441796479203907968334253210646412890364353793052317678943596418244874086644205184812962856177868575)

∈1⅄2φn28=(1φn29/1φn28)=(1.^618033988754322537608830405492572629644663022991652271318488032195235533068395996362/1.6^180339887383030068527324379639340589966296367949984217332423708621409443126393711370648311254569336822490810414524127116659369304238919040006516714354081601482552515553564337280697288435886731358633119164231384089034609862639880255373743750572758097526703255302467187324990581311285116435357248317363989043773992200307507458583225569957946827683817165432903298068405135985500310562168436701320652893319349550448533230152022727041309859585170401897993055626266431793420154975613233003085256952010508201895956582390615931330122493865124377602867354315795904652323106843568308403506806911790161797798572432261808999175228339561547312364447250252013562911749432333085562422995855776965451231557189259640155179260556568135303281776619250781496604180879552790477451150098259833620136647354112148581087273060513802197354621266889999898176338217474976835116944475557229989104868189269822521357513058884623608834220896251871009785253897300654726145261635898950198047022167011170055697542995041187671191031371870195195959637100469407080817440356790110885967681169750226557647466118176541864798541885163274241668278874644889979533443981712470343858505839587003227810078506043234326792860124835809345375678400146626072966836033357431599955197588815688989807451455569245181195206142003278721909397305745909234387887057194350823244305511714812288079503915119795538087140689753484914824506918917818122575324053803622885886222240324206539115559673756987648789825779714690099685364885091997678420511358429471840666334042704843751590994715351953486951297742569418281420236434542659023103788858454927756111965298496064515472105407854677269903980286939078903155515278640450467879725890702481442637640134814528200063130670305165514362227494425154517406754981722652710036758341903491533362522783044323839973933142583673594069789937785742650877210846256453074565467523343074463643861560549440478978505024997708967609893186978790131250700037674754859534258571006730544043824904031198769970165667097720168212689264731338268386807726379456057998757751326253194717388426722601798205867079391909091834760561659318392408027777494934272826319380097547067987658972191957967192416173670437536274679510024539502489588530582736816381390707572625726766385972772352839352808805710270952764003299086641753810750542210998991945748353002270667657750308016576892138195073771242961439379282957773727458786872893522996874013583276481788838090195399606960665519453410583551405675650907757944791210581514932440000407294647130100092659532222097771080043580527242920709914569947764461505564663116414992515960858984410797381095418953456404199207811911331955319777209828019835249315235874512519219216161451598122371676730238572839556456129275320999093769410135527293832540805832459346903033326884501420440081866224073150118624565976641651987088759685975827062692828559500656762618497286399413495708132655866570273600179209644737244040770194177723019275219175431986885112362410777016363062448451771222596707022777953140750847681984339520817847651437240986060340701972324328727509698703784785508456455111038703173843537761304972049404840696881141239601258540459632009286317954566282112637334663829180624993636021138592186052194809029722326874319054261829363907584844566180288975552138806015741938111578368581290920384078852243684387377938885438198128481096437190074229449439460741887199747477318779337942551090022299381930372980073109389159852966632386033866549908867822704640104267429665305623720840248857029396491156614974187701738129906627702145424553757802238084085979900009164129560427252084839474997199849300980561862965715973077823824700383875204920119337331609119327149242941074646926452769094482175768004968994694987221130446293109592807176531682432363632660957753362726430367888890020262908694722479609811728049364111232168131230335305318249854901281959901841990041645877669052734474437169709497092934456108910588642588764777158916188943986803653432984756997831156004032217006587990917329368998767933692431447219704915028154242482868168905090164852508425908012503945666894072844647639218401572157337922186357665794377297396368968220835157673940270239998370821411479599629361871111608915679825677891028317160341720208942153977741347534340029936156564062356810475618324186174383203168752354672178720891160687920659002739056501949923123135354193607510513293079045708641774175482898716003624922359457890824669836776670162612387866692461994318239672535103707399525501736093433392051644961256096691749228685761997372949526010854402346017167469376533718905599283161421051023836919223289107922899123298272052459550550356891934547750206192915109613171908888187436996609272062641916728609394251036055758637192110702685089961205184860857966174179555845187304625848954780111802380637212475435041594965838161471962854728181734871549450661344683277500025455915445631255791220763881110692502723782952682544369660621735278844097791444775937032247553686525674836318463684591025262450488244458247207486075614251239703082202242157032451201010090724882648229795639910802472278508079707562443360588133470455864533800364528709181439582930281338777505116639004571882414035373540103249193047480373489191418301784968791047663656080399963343481758290991660642100011200602796077752548137136107688704701198464499180319522650673563522691403028235701412294188923622071296927980124021220051115478214827561628771293873270270545469356168986549094278528444439918948365221110081560753087802543555071327475078658778727000580394872160392632039833416489323789062102251321162011628262175564357645429644940891364335244224052785386268060972008675375983871131973648036330682524004928265230274211121)=1.000000000009900614491163775281661524521005948975883011688817512004693899626596325531^310483274650657151577509903684894481311219561311597144214643294284968109977313560575 or 1.000000000009900614491163775281661524521005948975883011688817512004693899626596325531310483274650657151577509903684894481311219561311597144214643294284968109977313560575

while alternately set path variable ∈2⅄2φn28=(1φn28/1φn29) and set path ∈3⅄2φn29=(1φn29cn/1φn29cn)

Moving forward to ∈1⅄3φn

4th tier 3rd divide  1⅄3φn ratios of fibonacci in decimal step order of previous three tiers value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored

Variants ∈ next set of phi radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 phi base radicals decimal cycle limit or break in stem numeral factoring.

 1⅄3φn1=(1⅄2φn2/1⅄2φn1)=2/0=0

 1⅄3φn2=(1⅄2φn3/1⅄2φn2)=0.75/2=0.375

next set of decimal shift group array

 1⅄3φn3=(2φn4c1/2φn3)=1.10^6/0.75=1.60^8

next set of decimal shift group array

1⅄3φn4=(1⅄2φn5c1/1⅄2φn4c1)(0.^963855421686746987951807228915662650602409/1.0^6)=0.909297567629006592407365310297794953398499056603773^5849056603773

1⅄3φn5=(1⅄2φn6c1/1⅄2φn5c1)=(1.01^5625/0.^963855421686746987951807228915662650602409)=1.0537109375000000000000000000000000000000006980834960937500000000000000000000000000004624803161621093750000000000000000000000003063932094573974609375000000000000000000002029855012655258178710937500000000000000001344778945884108543395996093750000000000000890916051648221909999847412109375000000000590231884216947015374898910522460937500000391028623293727397685870528221130371093750259056462932094400966889224946498870849609546624906692512540640564111527055501937866324639000 extended shell factoring to divisor 963,855,421,686,746,987,951,807,228,915,662,650,602,409 potential digits long and less

1⅄3φn6=(1⅄2φn7c1/1⅄2φn6c1)=(0.994082^4061538/1.01^5625)=0.97878883067451^076923

1⅄3φn7=(1⅄2φn8c1/1⅄2φn7c1)=[(1φn9c1/1φn8c1)/(1φn8c1/1φn7)]=[(1.619047 /1.615384)/(1.^615384/1.625)]

1⅄3φn8=(1⅄2φn9c1/1⅄2φn8c1)=[(1φn10c1/1φn9c1)/(1φn9c1/1φn8)]=[(1.6^1762941/1.^619047619047)/(1.619047 /1.615384)]

1⅄3φn9=(1⅄2φn10c1/1⅄2φn9c1)=[(1φn11c1/1φn10c1)/(1φn10c1/1φn9)]=[(1.6^18/1.6^1762941)/(1.6^1762941/1.^619047619047)]

1⅄3φn10=(1⅄2φn11c1/1⅄2φn10c1)=[(1φn12c1/1φn11c1)/(1φn11c1/1φn10)]=[(1.^61797752808988764044943820224719101123595505/1.6^18)/(1.6^18/1.6^1762941)]

and so on for variables of ∈1⅄3φn

Variables 1⅄3φn shown are based on one cycle in decimal stem of variable variant change potential of factors based in 1φnc1 from 1⅄(Yn2/Yn1) path function of Y base.

Examples of alternate path with variables of ∈⅄3φ variables (1⅄2φn/1⅄2φn)

2⅄3φn1 example of 2⅄3φn1=(1⅄2φn1/1⅄2φn2)=(0/2)=0

3⅄3φn4 example of 3⅄3φn4(1⅄2φn4c1/1⅄2φn4c2)=(1.10^6/1.10^66) and 3⅄3φn4(1⅄2φn4c2/1⅄2φn4c1)=(1.10^66/1.10^6) for ∈3⅄3φn4 of cn

Examples of alternate path functions with variables of ∈⅄3φ variables (1⅄2φn/1⅄2φn)

⅄ncn=(⅄n)(ncn) example 

⅄ncn=(1⅄3φn4)(2)=(0.909297567629006592407365310297794953398499056603773^5849056603773)(0.909297567629006592407365310297794953398499056603773^5849056603773)

X⅄=(n2xn1) example

X3φn3=(2φn4c1x2φn3)=1.10^6x0.75=0.8295

+⅄=(nncn+nncn) example

X3φn3=(2φn4c1+2φn3)=1.10^6+0.75=1.856

1-⅄=(n2-n1) example

1-⅄3φn3=(2φn4c1-2φn3)=1.10^6-0.75=0.356

2-⅄=(n1-n2) example

2-⅄3φn3=(2φn3-2φn4c1)=0.75-1.10^6= - 0.356

Moving forward to ∈1⅄4φn

5th tier 4th divide  1⅄4φn ratios of fibonacci in decimal step order of previous four tiers value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored

Variants ∈ next set of phi radical decimal stem path factoring to the degree of the variant decimal cycles per array.

Quadratic equations dependent of 4 phi base radicals decimal cycle limit or break in stem numeral factoring.

 1⅄4φn1=(1⅄3φn2/1⅄3φn1)=0.375/0=0

 1⅄4φn2=(1⅄3φn3c1/1⅄3φn2)=1.608/0.375=4.023^703

next set not included in previous set shift has variable of potential change dependent of root base decimal shell numerals

1⅄4φn3=(1⅄3φn4c1/1⅄3φn3c1)=(0.909297567629006592407365310297794953398499056603773^5849056603773/1.60^8)=0.5654835619583374330891575312797232297254347366938890453393410306^592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681

1⅄4φn4=(1⅄3φn5c1/1⅄3φn4c1)=[(1.01^5625/0.^963855421686746987951807228915662650602409)/(0.^963855421686746987951807228915662650602409/1.0^6)]

and so on for variables of ∈1⅄4φn

6th tier 5th divide  1⅄5φn ratios of fibonacci in decimal step order of previous five tiers value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored

 1⅄5φn1=(1⅄4φn2/1⅄4φn1)=4.023703/0=0

next set not included in previous set shift has variable of potential change dependent of root base decimal shell numerals

 1⅄5φn2=(1⅄4φn3/1⅄4φn2)=(0.5654835619583374330891575312797232297254347366938890453393410306^592039800995024875621890547263681592039800995024875621890547263681592039800995024875621890547263681/4.023^703)

 1⅄5φn3=(1⅄4φn4/1⅄4φn3)=[(1⅄3φn5c1/1⅄3φn4c1)/(1⅄3φn4c1/1⅄3φn3c1)]

and so on for variables of ∈1⅄5φn

7th tier 6th divide 6φn ratios of fibonacci in decimal step order of previous five tiers value with cycle decimal key in bold with ^ repeat notation at start of decimal cycle for calculation variable change when factoring decimals of multiple cycle strain stem(s) factored

 1⅄6φn1=(1⅄5φn2c1/1⅄5φn1c1)=[(1⅄4φn3/1⅄4φn2)/(1⅄4φn2/1⅄4φn1)]=0

 1⅄6φn2=(1⅄5φn3c1/1⅄5φn2c1)=[(1⅄4φn4c1/1⅄4φn3c1)/(1⅄4φn3c1/1⅄4φn2c1)]

 1⅄6φn4=(1⅄5φn4c1/1⅄5φn3c1) and so on for variables of ∈1⅄6φn

An alternate path of fibonacci numeral division does not produce the golden ratio and will provide quotients much different than the ratios than lead to phi.

Field set keys of physics factor able numerations in nomenclature among the noncommunicable float points communicated clearly here on this page. quantum field fractal polarization harmonics precision base for calibration of the lost... found and listed.

Plotting orbit spins to points with these variable values quantifies factorable field points such as atoms, electrons, neutrons, axions, ions, planets, moons, stars, celestial body systems to quark node quantum mechanics of entanglement and paradox keys of time tensors in atomic spin relief of equilibrium stable systems. Fractal polarization gives those points with assigned number of spins in matrices arrays of field quantum calculus and defines quantum fractal polarization math. There are more ratios and they are bonding decimal facts applicable to prediction models of advanced organic and inorganic chemistry, physics, condensed matter design, engineering and plasma applied sciences of fields in quantum fractal polarizing numerical comprehension notation. 

Alternate Path of φn 3rd tier 2nd divide 2⅄2φn from Y base numeral ratios 1φn

Previous φ divided by later φ of ordinal ratios from Y base

∈2⅄2φn1=(1φn1/1φn2)=(0/1)=0

∈2⅄2φn2=(1φn2/1φn3)=(1/2)=0.5

∈2⅄2φn3=(1φn3/1φn4)=(2/1.5)=1.^3 and ∈2⅄2φn3=(1φn3/1φn4)c2=1.^33 and ∈2⅄2φn3=(1φn3/1φn4)c3=1.^333  and so on for cn

∈2⅄2φn4=(1φn4/1φn5)=(1.5/1.^6)=0.9375 and 2⅄2φn4=(1φn4/1φn5c2)=(1.5/1.^66)=^0.90361445783132530120481927710843373493875 and so on for cn

∈2⅄2φn5=(1φn5/1φn6)=(1.^6/1.6)=1 and 2⅄2φn5=(1φn5c2/1φn6)=(1.^66/1.6)=1.0375 and so on . . . for variable ∈2⅄2φn5cn

∈2⅄2φn6=(1φn6/1φn7)=(1.6/1.625)=0.9^8406153  2⅄2φn6c2=0.9^84061538406153 2⅄2φn6c3=0.9^840615384061538406153 and so on . . . to cn

∈2⅄2φn7=(1φn7/1φn8)=(1.625/1.^615384)=1.005952764172481589516796006398478627991858282612679090544415445491 extended shell (966456/1615384) and 2⅄2φn7=(1φn7/1φn8c2)=(1.625/1.^615384615384)  and so on . . . for cn ∈2⅄c1 ∈2⅄c2 ∈2⅄cn 

∈2⅄2φn8=(1φn8/1φn9)=(1.^615384/1.^619047) and 2⅄2φn8=(1φn8c2/1φn9c2)=(1.^615384615384/1.^619047619047) and so on . . . for cn ∈2⅄c1 ∈2⅄c2 and cn ∈2⅄c2 to of ∈2⅄c1   (1φn8/1φn9) and more for those of ∈2⅄c3 to ∈2⅄cn  

∈2⅄2φn9=(1φn9/1φn10)=(1.^619047/1.6^1762941) and 2⅄2φn9=(1φn9c2/1φn10c2)=(1.^619047619047/1.6^17629411762941) and so on for cn

∈2⅄2φn10=(1φn10/1φn11)=(1.6^1762941/1.6^18) and so on for cn

∈2⅄2φn11=(1φn11/1φn12)=(1.6^18/1.^61797752808988764044943820224719101123595505) and so on for cn

∈2⅄2φn12=(1φn12/1φn13)=(1.^61797752808988764044943820224719101123595505/1.6180^5) and so on for cn

∈2⅄2φn13=(1φn13/1φn14)=(1.6180^5/1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832) and so on for cn

∈2⅄2φn14=(1φn14/1φn15)=(1.^61802575107296137339055793991416738197424034334763948497854077253214592274678111587982832/1.6183^0223896551724135014) and so on for cn

∈2⅄2φn15=(1φn15/1φn16)=(1.6183^0223896551724135014/1.618^032786885245901639344262295081967213114754098360655737704918) and so on for cn

∈2⅄2φn16=(1φn16/1φn17)=(1.618^032786885245901639344262295081967213114754098360655737704918/1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843) and so on for cn

∈2⅄2φn17=(1φn17/1φn18)=(1.618034447821681864235057244174265450860192502532928064842958459979736575481256332320141843^9716312056737588652482269503546099290780141843/1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129) and so on for cn

∈2⅄2φn18=(1φn18/1φn19)=(1.^6180338134001252348152786474639949906073888541014402003757044458359423919849718221665623043206011271133375078271759549154664996869129/1.6180340557314241486068^11145510835913312693) and so on for cn

∈2⅄2φn19=(1φn19/1φn20)=(1.6180340557314241486068^11145510835913312693/1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242) and so on for cn

∈2⅄2φn20=(1φn20/1φn21)=(1.6180339631667062903611576177947859363788567328390337239894762018655823965558478832791126524754843338914135374312365462807940684046878737144223872279359005022721836881128916527146615642190863429801482898828031571394403252^5711552260224826596508012437215977038985864625687634537192059315953121262855776130112413298254006218607986127720640994977278163118631906242/1.6^1803399852) and so on for cn

∈2⅄2φn21=(1φn21/1φn22)=(1.6^1803399852/ 1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981) and ∈2⅄2φn21=(1φn21c2/1φn22) and ∈2⅄2φn21=(1φn21/1φn22c2) and ∈2⅄2φn21=(1φn21c2/1φn22c2)=(1.6^1803399852/1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981) and so on for cn

∈2⅄2φn22=(1φn22/1φn23)=(1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^96792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869) and ∈2⅄2φn22=(1φn22c2/1φn23) and ∈2⅄2φn22=(1φn22/1φn23c2) and 

∈2⅄2φn22=(1φn22c2/1φn23c2)=(1.6^180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981180339985010049351361227845806687374385163530970217431207747140526219623606797003471770509775260369084598940279554176959619952494246310067604604606248876201845441458249607162433948492782751690115110542682258359217979170473415128814180522565320665083135391923990498995066691028686278092454048985930933674403617759848364701260734516627078384799926913941183994154944291065229307509492545240288598574823679883062305865164445660515253974056276265302393568427005298739265485291430842335099579755161702905171752247414776521152932578110725379133930202813813265119678421523844346811620683354651927644821852731591449132103051342974604423716426274440178896400694319386077105773798647926365795724284672026310981/1.6180339901755970865563773925808819377787815481903901530122522725989498052058043024109310597932923042177178024956241883575179831742984585850601321212805601038902377053814013889673084523742307040822087^9679295353170346112585398904635537236745525379707526396025069166054994071481000508158771385014962452713003218338885438428095533849020382812941110044605047710462424481960363615831963186720117441138275647902433515894077127209079103382078933995821805657500988086499915306871322906668172322285585229518378408898424707808706453616396589690023149455140872903845068036813279882558861724515272994184405171927050985263395629834566032409237197222065383098789452882389475467223759245666534921800011292417141889221387838066738185308565298402122974422675173620913556546778838010276099599119191462932640721748630794421545931906724634407995031336457568742589351250635198464231268703068891254022923606798035119417311275478516176387555756309638078030602450454519789961041160860482186211958669753260685449720512675738241770651007848229913613009429143470159787702557732482637908644345322116198972390040088080853706735926825136920557845406809327536559200496866354243125741064874936480153576873129693410874597707639320196488058268872452148382361244424369036192196939754952854158432612500705776071368076336739879171136581785331150132685901417198351307097284173677375564225622494494946643329004573428942465134662074417028965049968945852859804641183445316469990401445429394161820337643272542487719496358195471740726102422223476935237587691265315340748687256507255378013663937665857376771497939133871605217096719552820281181186833041613557167861780814183275930212862063124611823160747558014793066455874880016938625715656536310767319744791372593303596634759691717012026424256112020778047541076167353622042798260967760149059906272937722319762480944046073061938908023262379312291798058946417480661735644514708373327310710857659081926486364406301168765174179888205070295296708260403139291965445203545818982553215515781152956354807746598159336005872056913782395121675794703856360453955169103946699791090282875049404324995765343531791541979560724973180509288013099203884478572638473265202416577268364293376997346281971599570888148608209587262153463978958274518660719326971373722545310823781830500818700242786996792953531703461125853989046355372367455253797075263960250691660549940714810005081587713850149624527130032183388854384280955338490203828129411100446050477104624244819603636158319631867201174411382756479024335158940771272090791033820789339958218056575009880864999153068713229066681723222855852295183784088984247078087064536163965896900231494551408729038450680368132798825588617245152729941844051719270509852633956298345660324092371972220653830987894528823894754672237592456665349218000112924171418892213878380667381853085652984021229744226751736209135565467788380102760995991191914629326407217486307944215459319067246344079950313364575687425893512506351984642312687030688912540229236067980351194173112754785161763875557563096380780306024504545197899610411608604821862119586697532606854497205126757382417706510078482299136130094291434701597877025577324826379086443453221161989723900400880808537067359268251369205578454068093275365592004968663542431257410648749364801535768731296934108745977076393201964880582688724521483823612444243690361921969397549528541584326125007057760713680763367398791711365817853311501326859014171983513070972841736773755642256224944949466433290045734289424651346620744170289650499689458528598046411834453164699904014454293941618203376432725424877194963581954717407261024222234769352375876912653153407486872565072553780136639376658573767714979391338716052170967195528202811811868330416135571678617808141832759302128620631246118231607475580147930664558748800169386257156565363107673197447913725933035966347596917170120264242561120207780475410761673536220427982609677601490599062729377223197624809440460730619389080232623793122917980589464174806617356445147083733273107108576590819264863644063011687651741798882050702952967082604031392919654452035458189825532155157811529563548077465981593360058720569137823951216757947038563604539551691039466997910902828750494043249957653435317915419795607249731805092880130992038844785726384732652024165772683642933769973462819715995708881486082095872621534639789582745186607193269713737225453108237818305008187002427869) and so on for cn

So now functions between ∈1⅄2φn and ∈2⅄2φn variables are applicable to set function paths 1⅄, 2⅄, 1X, 1+⅄, 1-⅄, 2-⅄, 3⅄nc ⅄n, ⅄ncn written as examples

1⅄(∈1⅄2φn2/∈2⅄2φn1)=(2/0)

1⅄(∈2⅄2φn2/∈1⅄2φn1)=(0.5/0)

and

2⅄(∈1⅄2φn1/∈2⅄2φn2)=(0/0.5)

2⅄(∈2⅄2φn1/∈1⅄2φn2)=(0/2)

and

3⅄(∈1⅄2φn3/∈2⅄2φn3c1)=(0.75/1.^3) or 3⅄(∈1⅄2φn3c2/∈2⅄2φn3cn)=(0.75/1.^33) for cn variant path

3⅄(∈2⅄2φn3c1/∈1⅄2φn3)=(1.^3/0.75) or 3⅄(∈2⅄2φn3c2/∈1⅄2φn3)=(1.^33/0.75) for cn variant path

Then for sets of 1⅄3φ of (∈2⅄2φn2/∈2⅄2φn1) variables path base sets for cn factoring before variable change in stem decimal cycle are

1⅄3φn1 of (∈2⅄2φn2/∈2⅄2φn1)=(0.5/0)=0

1⅄3φn2 of (∈2⅄2φn3/∈2⅄2φn2)=(1.^3/0.5)=2.6 and 1⅄3φn2 of (∈2⅄2φn3c2/∈2⅄2φn2)=(1.^33/0.5)=2.66

1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3)=((1φn4/1φn5)/(1φn3/1φn4))=(1.5/1.^6)/(2/1.5)=(0.9375/1.^3)=0.721^153846

and 

1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3)=((1φn4/1φn5c2)/(1φn3/1φn4))=(1.5/1.^66)/(2/1.5)=(^0.90361445783132530120481927710843373493875/1.^3)=0.69508804448563484708063021316033364226057^692307

while

1⅄3φn3 of (∈2⅄2φn4/∈2⅄2φn3c2)=((1φn4/1φn5)/(1φn3/1φn4))=(1.5/1.^6)/(2/1.5)=(0.9375/1.^33)=0.70^488721804511278195

In varying sql databases results may vary to limits of the program the database runs on and numbers in science reference to universal constants for health and advanced studies commonly cessated with degree paths small talk long talks no talks and limits in talks proves with this one set of variables these numbers seem very important yet here they sit for a reader to find..

Many doctors boards that collaborate on such publications as Merck manuals and claim Poorly Understood reference material on subjects of DNA and RNA who talk extensively before such frameworks of treasuries and databases for health and educations can find here that the numbers are available for finding, the numbers are universal, and the numbers are excessively overlooked during clinical trials of pharmaceutical science studies post thanatology and statistical record keeping of patients or biological life form structures with the same numbers in the analytical arithmetic. 

With the questions what happened to the number library and what is the number answer to the the previous variable factor of change in path sets I simply answered the math equation that is not poorly misunderstood and I do not know what happened to the online library of numbers. A proper library of numbers allows those seeking extended learning the ability to get smarter while a library masked as missing or non existent for certification degree sales of universities with rounded numbers and limited calculating tech among estimated formulas handicaps thinking and does quite the opposite of helping the many seeking education to get smarter, it in fact stunts their intelligence considerably. In a world where communications networks governed by computer code writers under government wings of protection controlling logic gates masked with alternate paths that lead anywhere aside from the answer to a number question of logic and patents placed on universal numbers for profit margins rather than education reference resource material for the youth and elders, these variables are a simple example of the more important question, how trusted is your reference material source libraries on facts in mathematics and secondly if it is not a trustable source, why is it not a trustable source. 

Restricting a child access to something as simple as reference material numbers, variables,and factors based from universal arithmetic is not protecting and educating that child about what those numbers are and in fact does very much the opposite. 

Moving forward to the quantum field fractal polarization math that a library published being a math not invented yet...

1⅄3φn4 of (∈2⅄2φn5/∈2⅄2φn4)

1⅄3φn5 of (∈2⅄2φn6/∈2⅄2φn5)

1⅄3φn6 of (∈2⅄2φn7/∈2⅄2φn6)

1⅄3φn7 of (∈2⅄2φn8/∈2⅄2φn7)

1⅄3φn8 of (∈2⅄2φn9/∈2⅄2φn8)

1⅄3φn9 of (∈2⅄2φn10/∈2⅄2φn9)

1⅄3φn10 of (∈2⅄2φn11/∈2⅄2φn10)

and so on for variables of set ∈1⅄3φn of (∈2⅄2φn/∈2⅄2φn)

Alternate Path of φn 4th tier 3rd divide sets 1⅄2φn and 2⅄2φn  from Y base numerals examples

1⅄3φn=(1⅄2φn2/1⅄1φn1)

2⅄3φn=(1⅄2φn1/1⅄1φn2) each with alternate stem cycle variant paths determined of cn

Examples of 1⅄3φn=(1⅄2φn2/1⅄1φn1) and quotients below