User:Miui/Drafts/Demagogy(spec)

Specification

Given V-E+F where f(x)=e iff λ ≤ ν there exists a fixed point in x > 39mod(40,44023) > y. This is sufficient for a finite-state machine which corresponds to the specification of Fading Shout.

Characteristics (Mantissa)

• Digit = 39
• Base(Characteristic) = 40
• Base(Modulus) = 44023

The table below shows the how the modular divisor works as a mantissa.

Mantissa

0xAC00	44032
A	10 x 163 = 10 x 4096 = 40960
C	12 x 162 = 12 x 256 = 3072
0	0 x 162 = 0 x 16 = 0
0	0 x 160 = 0 x 1 = 0

Evaluations of input arithmetize over a low-degree transition function. This is demonstrated by the hexadecimal representation of the modular divisor of the equality operator (0XAC00) in Demagogy.

Tape emulation

Demagogy is able to emulate a tape which is suitable for an implementation of Fading Shout. A screenshot of the relation graph is included (created with GrafEQ by Pedagoguery Software.) Functions are arithmetized within the red region (which extends infinitely to the right and down.)

Axiom Schema

The specification is a variadic type system so this section relates to the Axiom Schema of Characterization A rough draft of the schema follows (it is likely incorrect): A statement is characterized a relation to the mixed-product of "A, E, I, O, U and sometimes Y." and "I before E except after C." where:

• A has an Euler characteristic of 1
• E has an Euler characteristic of 2
• A word is a group of elements of a finite field with a characteristic function of arithmetic on the limits in a free-algebraic ring equivalent to a K-field where the elements retain totiency at most 2A with respect to a constant C.

A axiom is considered advanced when an axiomatic specification satisfies the fixed-point theorem, this is the limit of the language L for the solution S and precedes an axiomatic specification of the characteristics of a language.

Opcodes/words

Borrowing from the User:Miui/Drafts/Nomea#More_developed_draft prototype and the bf/aheui compiler retrieved from here. Demagogy uses 38 words. The first 8 listed:

1. ABCDEFGHIJKLMNOPQRSTUVWXYZ-
2. ABCDEFGHIJKLMNOPQRSTUVWXYZ0
3. ETIANMSURWDKGOHVFLPJBXCYZQ+
4. SATOR
5. AREPO
6. TENET
7. DAFNE
8. NOMEA

Commands

The other 30 machine words are the same as OEIS lexicon (minus nice and unkn.)

1. allocated – An A-number which has been set aside for a user but for which the entry has not yet been approved (and perhaps not yet written).
2. base – The results of the calculation depend on a specific positional base. For example, 2, 3, 5, 7, 11, 101, 131, 151, 181 ... A002385 are prime numbers regardless of base, but they are palindromic specifically in base 10. Most of them are not palindromic in binary. Some sequences rate this keyword depending on how they are defined. For example, the Mersenne primes 3, 7, 31, 127, 8191, 131071, ... A000668 does not rate "base" if defined as "primes of the form 2^n − 1". However, defined as "repunit primes in binary," the sequence would rate the keyword "base".
3. bref – "sequence is too short to do any analysis with", for example, A079243, the number of isomorphism classes of associative non-commutative non-anti-associative anti-commutative closed binary operations on a set of order n.
4. changed The sequence is changed in the last two weeks.
5. cofr – The sequence represents a continued fraction, for example the continued fraction expansion of e (A003417) or π (A001203).
6. cons – The sequence is a decimal expansion of a mathematical constant, such as e (A001113) or π (A000796).
7. core – A sequence that is of foundational importance to a branch of mathematics, such as the prime numbers (A000040), the Fibonacci sequence (A000045), etc.
8. dead – This keyword used for erroneous sequences that have appeared in papers or books, or for duplicates of existing sequences. For example, A088552 is the same as A000668.
9. dumb – One of the more subjective keywords, for "unimportant sequences," which may or may not directly relate to mathematics, such as popular culture references, arbitrary sequences from Internet puzzles, and sequences related to numeric keypad entries. A001355, "Mix digits of pi and e" is one example of lack of importance, and A085808, "Price is Right wheel" (the sequence of numbers on the Showcase Showdown wheel used in the U.S. game show The Price Is Right) is an example of a non-mathematics-related sequence, kept mainly for trivia purposes.[26]
10. easy – The terms of the sequence can be easily calculated. Perhaps the sequence most deserving of this keyword is 1, 2, 3, 4, 5, 6, 7, ... A000027, where each term is 1 more than the previous term. The keyword "easy" is sometimes given to sequences "primes of the form f(m)" where f(m) is an easily calculated function. (Though even if f(m) is easy to calculate for large m, it might be very difficult to determine if f(m) is prime).
11. eigen – A sequence of eigenvalues.
12. fini – The sequence is finite, although it might still contain more terms than can be displayed. For example, the sequence field of A105417 shows only about a quarter of all the terms, but a comment notes that the last term is 3888.
13. frac – A sequence of either numerators or denominators of a sequence of fractions representing rational numbers. Any sequence with this keyword ought to be cross-referenced to its matching sequence of numerators or denominators, though this may be dispensed with for sequences of Egyptian fractions, such as A069257, where the sequence of numerators would be A000012. This keyword should not be used for sequences of continued fractions; cofr should be used instead for that purpose.
14. full – The sequence field displays the complete sequence. If a sequence has the keyword "full", it should also have the keyword "fini". One example of a finite sequence given in full is that of the supersingular primes A002267, of which there are precisely fifteen.
15. hard – The terms of the sequence cannot be easily calculated, even with raw number crunching power. This keyword is most often used for sequences corresponding to unsolved problems, such as "How many n-spheres can touch another n-sphere of the same size?" A001116 lists the first ten known solutions.
16. hear – A sequence with a graph audio deemed to be "particularly interesting and/or beautiful", some examples are collected at the OEIS site.
17. less – A "less interesting sequence".
18. look – A sequence with a graph visual deemed to be "particularly interesting and/or beautiful". Two examples out of several thousands are A331124 A347347.
19. more – More terms of the sequence are wanted. Readers can submit an extension.
20. mult – The sequence corresponds to a multiplicative function. Term a(1) should be 1, and term a(mn) can be calculated by multiplying a(m) by a(n) if m and n are coprime. For example, in A046970, a(12) = a(3)a(4) = −8 × −3.
21. new – For sequences that were added in the last couple of weeks, or had a major extension recently. This keyword is not given a checkbox in the Web form for submitting new sequences; Sloane's program adds it by default where applicable.
22. nonn – The sequence consists of nonnegative integers (it may include zeroes). No distinction is made between sequences that consist of nonnegative numbers only because of the chosen offset (e.g., n3, the cubes, which are all nonnegative from n = 0 forwards) and those that by definition are completely nonnegative (e.g., n2, the squares).
23. obsc – The sequence is considered obscure and needs a better definition.
24. recycled – When the editors agree that a new proposed sequence is not worth adding to the OEIS, an editor blanks the entry leaving only the keyword line with keyword:recycled. The A-number then becomes available for allocation for another new sequence.
25. sign – Some (or all) of the values of the sequence are negative. The entry includes both a Signed field with the signs and a Sequence field consisting of all the values passed through the absolute value function.
26. tabf – "An irregular (or funny-shaped) array of numbers made into a sequence by reading it row by row." For example, A071031, "Triangle read by rows giving successive states of cellular automaton generated by "rule 62."
27. tabl – A sequence obtained by reading a geometric arrangement of numbers, such as a triangle or square, row by row. The quintessential example is Pascal's triangle read by rows, A007318.
28. uned – The sequence has not been edited but it could be worth including in the OEIS. The sequence may contain computational or typographical errors. Contributors are encouraged to edit these sequences.
29. walk – "Counts walks (or self-avoiding paths)."
30. word – Depends on the words of a specific language. For example, zero, one, two, three, four, five, etc. For example, 4, 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8, 7, 7, 9, 8, 8 ... A005589, "Number of letters in the English name of n, excluding spaces and hyphens."

Correspondence/reduction

Operation on finite fields with few or less elements, tag-systems and brainfuck reductions can be used instead of the above model construction. A zero-instruction set machine such a Darkside10 can be used but can only evaluate a boolean(True/False) of the beta-decay.

brainfuck specification

This syntax of brainfuck is called Fading Shout Ice (based on Fading Shout) and is a one-way (i.e. constrained and uses I/O) implementation of an algebraic bf loosely based on kcufniarb. Fading Shout Ice describes the instruction set in terms of machine word length. A word f(x)=ω; r^ω as (n) of the arithmetic function of ω corresponds to the set of intervals [0,30], [31,42], [43, 60], [61,66], [67,70], [71,78], [79,84], [85,90] iff ω(n)=3^[1] & σ_k(n)≤90.

+	Increment the tape element pointed to by the tape pointer	Word length 30
-	Decrement the tape element pointed to by the tape pointer	Word length 11
<	Move the tape pointer to the left	Word length 17
>	Move the tape pointer to the right is tape element pointed to by the tape pointer is negative	Word length 5
,	Set the tape element pointed to by the tape pointer to the character code of one character read from input	Word length 3
.	Output the tape element pointed to by the tape pointer as the character with that character code	Word length 7
[	Jump to the matching ] if the tape element pointed to by the tape pointer is zero	Word length 5
]	Jump to the matching [ if the tape element pointed to by the tape pointer is positive	Word length 5

The TAU (Tetrahedral Arithmetic Unit) is a variadic system solver which follows the order of operations [, ], >. A program in Demagogy language is therefore required to specify some pointers of ternary operation at 36 (mod63). The principal differentiation from pure kcufniarb is that a pointer can be set algebraically with or without the corresponding ; and : commands.

Architecture

The computer architecture specification is a modified Von Neumann architecture which uses a Tetrahedral Arithmetic Unit to solve for variadic-type systems. One would formalize the arithmetic logic in accordance with the Axiom Schema of Characterization. General correspondence and reduction is considered "Geodetic^[2]".

CPU

The processing unit corresponds to the flux of the volume of a Gaussian surface with respect to a given Dehn invariant (which is represented as input to a function.) The geodetic architecture implies a dipolar relationship in <3>₂ and <5>₁ and is a result of Gauss's law^[3] This provides a primitive for a programming language of discreet relations of a charge as a multivariate described as free (i.e. free charge) as a measure of the characteristics of the factorization of pi.

The memory is therefore required to efficiently compute a loop-invariant using a constant function described as a magic angle θ_M. On the system of harmonic numbers to an element of a flip-state function the flux of the processor is described by a language in the divergence between two sets of symbols in terms of their representation on a user-interface.

• _1/8(63_x⁵-70x³+15x)
• { -63{\tfrac {\sqrt {2}}{256}}}

TAU

In the tetrahedral arithmetic unit the axioms are given a free variable described by a fractal-dimension 2 > n > 1. A constant function is composed to recursion at θ_M by solving the variadic system of polynomials:

• _1/8(63_x⁵-70x³+15x)

60° rotation

Initial Axiom	Initial Heading (degrees)
F++F++F	0
Transformation	F > F-F++F-F
Element of (x)	0256,1635,2703,315257
Element of (y)	1
Order	[, ], >.
Index	[1, 375]
Corresponding relation	63°

A volume of charge (including photons, mesons, protons/neutrons and electrons) is a memory of infinite length whos flux describes the volume of any Gaussian surface which can be programmed to describe the Dehn invariant of its solution. A free-variable is defined by the fractal dimension d and the TAU for Demagogy specifically solves for an interval of [45, 63] where 5ⁿ-n(5). For Fading Shout Ice N_n is an element of N equal to a system of variadic equations. There is always a unique set of outputs to an input to solve for 1/3π,θ_M, and an index I of an integer of Murray polygons (see: Jack Cole's Murray Polygon). Each solution corresponds to the constant function C.

A logic gate is programmed as a dipolar set of sentential logical arguments about numbers who diverge in D₀ of deg(45,63). For Demgagogy all the solutions are indexed by their Murray integer modulo 63 of a fixed-point in [1559,1560].

Kernel

There is some evidence (https://phys.org/news/2026-10-ice-scientists-particles-anti.html) that a kernel can be constructed using polystyrene and iron oxide. Hence Fading Shout Ice is named after the anti-spin ice used to succeed the constant function for θm(54.7°) in the TAU. This constant function is an invariant for the frustrated loops and their solutions in <3>₅ and is "[t]he angle at which you must shoot a cue ball on a standard pool table so that it will strike all four sides and return to its origin."^[4] (~26°.565)

Program examples

Quine

The angle at which you must shoot a cue ball on a standard pool table so that it will strike all four sides and return to its origin.