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-1.2cm Topological Fixed-Point Theory (TFPT)\\[1.5mm] A discrete compiler for the constants of physics\\[2.5mm] Two inputs — the boundary constant [formula in source] and a five-slot carrier — build [formula in source] \\ and read off the Standard Model: status assessment and reading guide

TFPT — Introduction and reading guide · Verification reference catalog

positioning,arrows.meta,fit,backgrounds,calc,shapes.geometric,shapes.misc

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documents/introduction/preamble.tex · lines 1 to 53

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Front matter / support

TFPT — Introduction and reading guide

Topological Fixed-Point Theory (TFPT) constructs, from exactly two inputs — a boundary constant [formula in source] (P1) and a five-slot carrier [formula in source] (P2) — a discrete compiler for the Standard-Model skeleton: the gauge group, three families, hypercharges and the flavor matrix, with [formula in source] ( [formula in source] ) as the consistency checksum. The algebraic core is machine-checkable and the

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documents/introduction/sections/001-section-what-this-is-about-the-jump-in-construction-prin.tex · lines 1 to 86

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What this is about: the jump in construction principle

TFPT — Introduction and reading guide

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documents/introduction/sections/001-section-what-this-is-about-the-jump-in-construction-prin.tex · lines 87 to 89

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In plain words

TFPT — Introduction and reading guide

What we found. TFPT reproduces dozens of real numbers of physics (particle masses, the fine-structure constant, dark-energy and inflation values) from a small set of inputs — and the compiler closure says why the same handful of small integers ( [formula in source] ) reappears in every sector: those numbers are not separate lucky hits. A single tiny ``machine'' — fed by just two inputs (a boundary number [formula in

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Sharper still: one anchor [formula in source] , and [formula in source] as a compiler hull ( )

TFPT — Introduction and reading guide

The two axioms are not even independent: they are the elementary symmetric polynomials of the single parabolic anchor [formula in source] (the exponents-at-infinity / splitting type [formula in source] ): [formula in source] Its power sums [formula in source] generate the big Lie data directly: [formula in source] , [formula in source] , [formula in source] , and [formula in source] with the binary ladder [formula in

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documents/introduction/sections/001-section-what-this-is-about-the-jump-in-construction-prin.tex · lines 128 to 268

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The companion documents

TFPT — Introduction and reading guide

The whole development is consolidated into eight companion documents (plus this introduction), organised in layers that build on one another; this introduction is the entry point and reading guide. Each document collects the material of its layer into self-contained parts:

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The architecture at a glance

TFPT — Introduction and reading guide

The diagram below shows the whole pipeline: two inputs on the left, the discrete compiler in the middle, the physics on the right. Everything in between is a consequence.

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documents/introduction/sections/001-section-what-this-is-about-the-jump-in-construction-prin.tex · lines 302 to 380

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The dependency DAG and the proof ledger

TFPT — Introduction and reading guide

The whole theory is a directed acyclic graph: two axioms at the source, the compiler in the middle, the observables as sinks. The DAG makes the attack surface explicit — each arrow is a named theorem or a declared input, and each node fails in exactly one way.

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documents/introduction/sections/002-section-the-dependency-dag-and-the-proof-ledger.tex · lines 1 to 59

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The compact status formula: three honest layers

TFPT — Introduction and reading guide

[formula in source] TFPT v \ closes the discrete compiler; the discrete Standard-Model structure (charges, families, flavor operators) is derived under the axioms, while [formula in source] D existence, chiral measure, mirror gap, couplings and neutrino dynamics remain open. It closes the EM fixed point, the admissible gapped IR sector and the [formula in source] spectral-action shadow. It does not yet certify a stri

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The hard reduction: the live residual as typed interfaces

TFPT — Introduction and reading guide

After the compiler closure, the entire residual is the pair of accounting formulae (the compiler rest, and the strict-physical-TOE rest of the 2026-08-27/28 contract wave; tfpt_research_contracts): [formula in source] [formula in source] The first is the compiler rest — one dimensionful scale anchor, one metric-sector inclusion, and a set of deliberately typed QFT/cosmology interfaces. The second is the strict-physic

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documents/introduction/sections/002-section-the-dependency-dag-and-the-proof-ledger.tex · lines 95 to 387

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The compiler: why [formula in source]

TFPT — Introduction and reading guide

The Coxeter number of [formula in source] is [formula in source] . Exactly these three prime factors are the three discrete atoms of the theory — that is the point of the compiler:

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documents/introduction/sections/003-section-the-compiler-why-30-2-cdot3-cdot5.tex · lines 1 to 74

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The [formula in source] glue: how [formula in source] is really built

TFPT — Introduction and reading guide

The decisive, now proved step: [formula in source] and [formula in source] have the same discriminant group [formula in source] , and their discriminant-form norms are exactly two TFPT constants which add up to the [formula in source] root norm.

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How derivation now works: the derivation map

TFPT — Introduction and reading guide

What can one concretely compute with [formula in source] ? The following map summarises what is now a consequence rather than an assumption.

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documents/introduction/sections/003-section-the-compiler-why-30-2-cdot3-cdot5.tex · lines 100 to 138

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Cosmology is the Pascal action grammar of the carrier

TFPT — Introduction and reading guide

With [formula in source] the cosmological readouts are a power tower on the five-slot carrier graph [formula in source] : [formula in source] EW is the unit [formula in source] , Hubble is the product over the [formula in source] vertices, [formula in source] is the product over the [formula in source] edges — the same Pascal triple that reads one generation, the action ladder and the [formula in source] root count [

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Physical, geometric, topological: why the architecture is plausible

TFPT — Introduction and reading guide

The closure works on three levels at once: physically, [formula in source] is the fixed point of one equation and one generator drives many scales; geometrically, the [formula in source] spinor and the puncture geometry [formula in source] produce [formula in source] and [formula in source] , glued to [formula in source] ; topologically, the common discriminant [formula in source] (the [formula in source] winding) fo

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What role [formula in source] now plays exactly

TFPT — Introduction and reading guide

[formula in source] is no longer the starting point but the output format: Bookkeeping: [formula in source] is the unimodular container in which carrier ( [formula in source] ) and family ( [formula in source] ) fit together consistently. Its numbers [formula in source] are carrier traces, not inputs. Consistency test: unimodularity ( [formula in source] ) is a hard condition; it closes only because the discriminant-

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What this means for the theory-of-everything question

TFPT — Introduction and reading guide

0.46 Flavor residual — ratios closed; only the absolute scale is the wall-selection. Mehta–Seshadri supplies the equivalence-class framework (stable parabolic [formula in source] unitary representation); the algebraic selector [formula in source] , the [formula in source] spectrum and the splitting type are fixed (now derived: [formula in source] lattice, [formula in source] from [formula in source] , v69/ v70; since

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The closure ledger: what is done, and what genuinely remains

TFPT — Introduction and reading guide

A complete theory must close the discrete structure, the dimensionless constants, the mass spectrum, gravity, and the quantum measure. The current state, graded honestly: 6pt @p4.6cmcY@ TOE piece & Status & If not complete: what closes it \\ gauge group, [formula in source] , hypercharge, [formula in source] & & — complete \\ [formula in source] , group closure & & — complete \\ bootstrap [formula in source] , `` [fo

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documents/introduction/sections/003-section-the-compiler-why-30-2-cdot3-cdot5.tex · lines 283 to 377

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TFPT in the light of algorithmic physics: Zuse–Schmidhuber–Wolfram

TFPT — Introduction and reading guide

The ``compiler'' framing places TFPT in an older lineage — the idea that physics is, at bottom, the output of a short computation — and it is worth stating precisely what TFPT shares with that lineage and where it deliberately parts company, so the family resemblance is not mistaken for a claim the theory does not make. Three landmarks fix the coordinates. Zuse ( Rechnender Raum, 1969) proposed that the universe is l

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documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex · lines 1 to 17

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Three shared instincts

TFPT — Introduction and reading guide

Minimal description length as the selection principle. ``No load-bearing free number, only [formula in source] '' is, in these terms, a Kolmogorov-style compression statement — the plausibility discussion below already names it Kolmogorov-like compression: many numbers from little — and the grammar-internal null model of the next section turns it from rhetoric into a measured bound. Deterministic, resource-bounded ge

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documents/introduction/sections/004-section-tfpt-in-the-light-of-algorithmic-physics-zuse-sc.tex · lines 18 to 37

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