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Search the paper sections, open their original context and follow the checks they actually cite. The knowledge atlas explains the result; this library locates its source.

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76 sections found. Current publication documents are listed before historical material.

-1.2cm TFPT — Architecture and the [formula in source] Compiler\\[2mm] The two axioms [formula in source] , the derivation map, and the Coxeter–cyclotomic [formula in source] construction

Architecture, E8 and the electromagnetic fixed point

arrows.meta,positioning,calc,fit,backgrounds,shapes.geometric,shapes.misc,decorations.pathmorphing,decorations.pathreplacing,patterns,angles,quotes,matrix =3.5em

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documents/tfpt_1_architecture_e8/preamble.tex · lines 1 to 96

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Front matter / support

Architecture, E8 and the electromagnetic fixed point

The architecture layer: how the two axioms [formula in source] and [formula in source] build the Coxeter–cyclotomic compiler — the carrier [formula in source] , the family geometry [formula in source] , the [formula in source] glue [formula in source] , the EM fixed point [formula in source] (with its ablation), and the whole number alphabet [formula in source] as carrier traces.

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documents/tfpt_1_architecture_e8/sections/001-source.tex · lines 1 to 21

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Architecture and the derivation map

Architecture, E8 and the electromagnetic fixed point

This document develops the architecture layer of TFPT: the two axioms, the derivation map, and the explicit [formula in source] construction. The thesis is that the bridge layer of TFPT is governed by three nested grammars: a carrier grammar (from [formula in source] come charges, families, hypercharge, [formula in source] , [formula in source] ), a seed grammar (one seed [formula in source] generates the Cabibbo ang

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documents/tfpt_1_architecture_e8/sections/001-source.tex · lines 22 to 50

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How to read this document

Architecture, E8 and the electromagnetic fixed point

Notation convention. We write [formula in source] for the root-lattice direct sum (used in the glue/lattice statements: discriminant forms, [formula in source] glue, [formula in source] as an even unimodular lattice), and [formula in source] for the group/representation branching (used for subalgebra embeddings and [formula in source] -rep decompositions). The objects are the same atoms; the symbol marks whether the

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documents/tfpt_1_architecture_e8/sections/001-source.tex · lines 51 to 391

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Front matter / support

Architecture, E8 and the electromagnetic fixed point

The [formula in source] forcing census (2026-08-05): the glue pattern itself forces the four marks ( v781_one_object_clock_census.py, [formula in source] , one-object-partial [formula in source] clock-fiber-dead): the TFPT glue conditions (cyclic isotropic glue, evenness, unimodularity [formula in source] ) admit an even unimodular diagonal glue of [formula in source] iff [formula in source] (exact census [formula in

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documents/tfpt_1_architecture_e8/sections/002-source.tex · lines 1 to 395

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Front matter / support

Architecture, E8 and the electromagnetic fixed point

The global Gaussian shell theorem (2026-08-08, round 36): the [formula in source] census law above is now a theorem for all shells ( v875_shell_global_lean.py, [formula in source] , shell-global-theorem): on [formula in source] , for every [formula in source] , [formula in source] for all [formula in source] (the division exact), [formula in source] , and at every odd [formula in source] : [formula in source] exactly

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documents/tfpt_1_architecture_e8/sections/003-source.tex · lines 1 to 398

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Front matter / support

Architecture, E8 and the electromagnetic fixed point

equilibrium kernel witnesses carry the full [formula in source] mixing at zero entropy production — no non-equilibrium state is needed, and whether the deployed pure-i wiring is compiler-forced became the registered successor contract ( v908_seam_equilibrium_wiring.py, SEAM.STATE.WIRING.SELECTOR.01); the \ premise stays unmoved. Dated addendum (2026-08-12, rounds 69–71): the successor contract is closed, and the answ

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documents/tfpt_1_architecture_e8/sections/004-source.tex · lines 1 to 243

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Headline: the Pascal compiler on five carrier slots

Architecture, E8 and the electromagnetic fixed point

The strongest new statement is that three of the theory's separate structures are the same truncated row of Pascal's triangle on the five-slot carrier.

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documents/tfpt_1_architecture_e8/sections/004-source.tex · lines 244 to 301

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[formula in source] as the Pascal closure

Architecture, E8 and the electromagnetic fixed point

A family is exactly the complete Pascal truncation to degree two: the unique positive-integer solution of [formula in source] . Proof of uniqueness. Direct evaluation gives [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] , [formula in source] ; so [formula in source] is the only root in [formula in source] . For [formula in source] the forward difference is

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documents/tfpt_1_architecture_e8/sections/004-source.tex · lines 302 to 350

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One master moment generates [formula in source] , [formula in source] , [formula in source] , [formula in source]

Architecture, E8 and the electromagnetic fixed point

With [formula in source] , the quadratic hypercharge trace on one family is [formula in source] , and it generates the whole integer chain: The flavor budget, the [formula in source] budget, the [formula in source] count and the second seam defect all hang on the second hypercharge moment [formula in source] . \ Round-22 sharpening: the moment itself is one symbolic identity, [formula in source] — the Coxeter number

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documents/tfpt_1_architecture_e8/sections/004-source.tex · lines 351 to 366

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explicit file citation v810_cutcode_moment.py
literal source filename/path in TeX

Compact [formula in source] compression and the role of [formula in source]

Architecture, E8 and the electromagnetic fixed point

with [formula in source] and [formula in source] . . The right-handed neutrino [formula in source] is the Pascal singleton [formula in source] that closes [formula in source] ; removing it breaks the truncation and shifts [formula in source] by [formula in source] .

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 1 to 12

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The [formula in source] compiler: [formula in source] as a closure, not an input

Architecture, E8 and the electromagnetic fixed point

This section upgrades the [formula in source] atlas (Section lattice construction. The whole content is consolidated and verified in the standalone companion note ``The Even Carrier Code and the [formula in source] Coxeter Compiler.'' The thesis: the carrier code is the [formula in source] half-spinor, the family geometry is an [formula in source] , and [formula in source] is the standard unimodular glue closure of [

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 13 to 114

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literal source filename/path in TeX

Carrier [formula in source] (proved)

Architecture, E8 and the electromagnetic fixed point

The [formula in source] even-occupation states [formula in source] are exactly the weights of the [formula in source] half-spinor [formula in source] (even number of minus signs). The flip-weight- [formula in source] relation is the Clebsch graph [formula in source] and the flip-weight- [formula in source] relation is its complement [formula in source] ; the affine automorphism group of the scheme (translations [form

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 115 to 131

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explicit file citation v810_cutcode_moment.py
literal source filename/path in TeX

Family [formula in source] from [formula in source] (proved, with the metric settled)

Architecture, E8 and the electromagnetic fixed point

The carrier geometry fixes [formula in source] , [formula in source] , rigid [formula in source] generated by [formula in source] . The twelve puncture-difference cycles [formula in source] carry the residue pairing [formula in source] and form the [formula in source] root system: The corner rotation [formula in source] acts on [formula in source] as the [formula in source] Coxeter element (order [formula in source]

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 132 to 165

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explicit file citation v219_icosahedral_mckay.py
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explicit file citation v223_coxeter_totative_clock.py
literal source filename/path in TeX

The [formula in source] glue and the [formula in source] discriminant theorem (proved)

Architecture, E8 and the electromagnetic fixed point

The two factors have equal discriminant groups and [formula in source] is unimodular, so the glue index is exactly [formula in source] : The discriminant-form norms sum to the [formula in source] root norm, and — strikingly — they are pre-existing TFPT constants: This is literally the [formula in source] spinor-root split [formula in source] , [formula in source] .

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 166 to 229

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cross reference join tfpt_readouts.wl
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explicit file citation v1_e8_glue.py
literal source filename/path in TeX
cross reference join tfpt_readouts_extension.wl
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Glue-norm arithmetic, and three readings of [formula in source] , [formula in source] , [formula in source]

Architecture, E8 and the electromagnetic fixed point

The two glue norms generate the carrier integers through sum, difference and product. With [formula in source] : so the glue already contains the full carrier exhaustion [formula in source] , the [formula in source] rank, and the non-trivial transition count [formula in source] ; and [formula in source] is the inverse displacement of the two norms from the unit norm.

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documents/tfpt_1_architecture_e8/sections/005-source.tex · lines 230 to 384

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cross reference join tfpt_readouts_extension.wl
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explicit file citation v115_anchor_residue.py
literal source filename/path in TeX
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explicit file citation v142_frame_integrality.py
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explicit file citation v116_resonance_uniqueness.py
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explicit file citation v91_spine_tetrahedron.py
literal source filename/path in TeX
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explicit file citation v117_monodromy_weyl_a3.py
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explicit file citation v145_pairing_atoms.py
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explicit file citation v141_deck_selection.py
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explicit file citation v222_cm_norm_duality.py
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What the compiler outputs for the Standard Model and our reality

Architecture, E8 and the electromagnetic fixed point

Every entry below is an output of [formula in source] through the [formula in source] compiler; none is an independent input. ``Reads'' names the lattice object the observable comes from.

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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 1 to 45

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Grammar I — the carrier grammar ( [formula in source] )

Architecture, E8 and the electromagnetic fixed point

Machine checks for this section: v2_ carrier_ pascal.py

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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 46 to 61

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explicit file citation v2_carrier_pascal.py
literal source filename/path in TeX
cross reference join ArfSpinorCompiler.lean
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cross reference join tfpt_readouts.wl
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Dual-root dictionary (everything from two charges)

Architecture, E8 and the electromagnetic fixed point

Two carrier roots generate the family and the transport cusps . With [formula in source] and [formula in source] (the determinant-normalised carrier eigenvalues), the full one-family hypercharge spectrum and the flavor-transport cusps are sums of the two roots: [formula in source] [formula in source] [formula in source] All residuals are exactly zero. The Standard-Model charge table is not assumed; it is built by add

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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 62 to 106

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Carrier arithmetic (proved identities)

Architecture, E8 and the electromagnetic fixed point

The discrete coefficients are not isolated numbers; they are exact carrier traces: So: [formula in source] is a Pythagorean carrier identity ( [formula in source] ); equivalently the anchor-product form [formula in source] reads ``all four glue corners times all ten carrier pairs, plus the one leftover Higgs slot''; the electroweak exponent [formula in source] is the hypercharge variance times the [formula in source]

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documents/tfpt_1_architecture_e8/sections/006-source.tex · lines 107 to 131

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The public registry includes 116 document views, 6,693 section records and 985 physical LaTeX sources. Active publication documents, research material and archives retain their recorded roles. This is source navigation, not a new semantic review or proof run.

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