76 sections found. Current publication documents are listed before historical material.
Architecture, E8 and the electromagnetic fixed point
[formula in source] as a structure-bearing transition set, since [formula in source] . Open: a structure-preserving map (roots, lengths, Weyl data), not only the count. [formula in source] reads [formula in source] as the least common refinement of the occupancy lattice and the [formula in source] phase lattice; [formula in source] reads it as a rank- [formula in source] structure over the [formula in source] non-emp
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 304 to 330
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v88_ cp_ phase_ audit.py
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 331 to 348
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Architecture, E8 and the electromagnetic fixed point
The Cabibbo angle is the Bernoulli width of the seed. The exact CKM phase is the family transport holonomy (document 3), [formula in source] ; on the small-area branch this has the compact readout form (with an [formula in source] remainder) The coefficient [formula in source] is the family number [formula in source] : weak CP is the [formula in source] base angle [formula in source] plus [formula in source] times th
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documents/tfpt_1_architecture_e8/sections/008-source.tex · lines 349 to 384
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v18_ quark_ yukawa.py v20_ lepton_ c_ derivation.py
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 1 to 26
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Architecture, E8 and the electromagnetic fixed point
The source masses on the [formula in source] branch are [formula in source] . Their product is a pure decuple in the seed: with [formula in source] . So the charged-lepton Yukawa powers [formula in source] are the three carrier numbers [formula in source] , and the lepton determinant carries the same decuple ( [formula in source] ) that the cosmological constant carries in the gauge sector ( [formula in source] ): [f
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 27 to 49
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Architecture, E8 and the electromagnetic fixed point
The transport length [formula in source] is a Froggatt–Nielsen-type charge with expansion parameter [formula in source] : The top sits at [formula in source] (the unwound carrier direction), so [formula in source] ( [formula in source] ); every other charged fermion is suppressed by integer powers of [formula in source] . Numerically (with [formula in source] sector prefactors [formula in source] ): @lcccccccc@ [form
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 50 to 73
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Architecture, E8 and the electromagnetic fixed point
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 74 to 116
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v74_ compiler_ micro_ lemmas.py
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 117 to 134
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v36_ spectral_ action_ g2.py v4_ flavor_ matrix.py
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 135 to 179
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Architecture, E8 and the electromagnetic fixed point
Machine checks for this section: v22_ open_ gates_ audit.py
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 180 to 271
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Architecture, E8 and the electromagnetic fixed point
A small grammar generates many sectors: the Standard-Model packet, flavor, the electroweak hierarchy, the cosmological constant, the metrology, and the inflation/CMB interface. The strongest new statements are exact: the decuple bridge ties [formula in source] to the tenth power of the stripped electroweak scale with [formula in source] ; the Hubble scale is the square root of [formula in source] ; and the Einstein n
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 272 to 327
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Architecture, E8 and the electromagnetic fixed point
This short companion compresses the TFPT bridge layer to a single discrete object. The claim is that the Standard-Model family, the cosmological action ladder, the [formula in source] counting data, the flavor budget, inflation and the cosmological constant are not independent coincidences but projections of one structure: the even-weight code [formula in source] on [formula in source] slots, together with its [formu
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documents/tfpt_1_architecture_e8/sections/009-source.tex · lines 328 to 365
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 1 Let [formula in source] be the rank- [formula in source] carrier, split [formula in source] (color [formula in source] , weak [formula in source] ). The one-generation spinor packet is the even exterior algebra, equivalently the even-weight binary code The two carrier roots [formula in source] , [formula in source] generate all hypercharges ( [formula in source] , [formula in source] , [formula in
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 1 to 34
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 2 On [formula in source] the flip [formula in source] is even, so [formula in source] . The three relations [formula in source] form a symmetric association scheme (the even Hamming scheme on five bits) with The eigenvalues (computed directly) are [formula in source] and [formula in source] , with [formula in source] . The two graphs are named objects: The Standard-Model family is the valency side [
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 35 to 93
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 3 Requiring the even family to equal the action truncation through pair degree, [formula in source] , i.e. the unique positive-integer solution. At [formula in source] the two sides equal [formula in source] , so carrier exhaustion [formula in source] and the Coxeter period [formula in source] coincide only at five slots: [formula in source] and [formula in source] .
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 94 to 106
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 4 From the three atoms [formula in source] , with [formula in source] and [formula in source] : The [formula in source] exponents are the primitive residues modulo [formula in source] , and [formula in source] . The local SM algebra and the root atlas are the two arithmetic projections of [formula in source] :
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 107 to 125
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 5 The directed even-flips of [formula in source] are the complete graph [formula in source] : ( [formula in source] .) So the positive [formula in source] roots are the unordered transitions of one family; the second hypercharge moment, the positive-root count and the sum of the [formula in source] exponents coincide at [formula in source] . The CP pairing [formula in source] of the exponents gives
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 126 to 151
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 6 All discrete budgets and the seam seed are functions of [formula in source] : Two-graph product table. With the carrier-pair graph [formula in source] ( [formula in source] ) and the family-corner graph [formula in source] on [formula in source] ( [formula in source] , [formula in source] ), every large budget is a product of the two graphs: i.e.\ ( [formula in source] , [formula in source] , [for
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documents/tfpt_1_architecture_e8/sections/010-source.tex · lines 152 to 227
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 7 Since [formula in source] , one has the standard chain [formula in source] , with the exact branching (verified dimensions and root/weight counts): The adjoint [formula in source] of [formula in source] is [formula in source] and its spinor [formula in source] is [formula in source] . The TFPT dictionary makes each summand a known object: @llY@ piece & value & TFPT reading \\ [formula in source] &
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documents/tfpt_1_architecture_e8/sections/011-source.tex · lines 1 to 248
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Architecture, E8 and the electromagnetic fixed point
tocsectionTheorem 8 — anchor microcode The parabolic flavor bundle [formula in source] on [formula in source] has splitting type [formula in source] , whose power sums [formula in source] generate the whole compiler budget:
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documents/tfpt_1_architecture_e8/sections/011-source.tex · lines 249 to 305
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