65 sections found. Current publication documents are listed before historical material.
Standard Model and flavor structure
We promote the two genericity/equivalence steps to proved statements.
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documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex · lines 198 to 316
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- explicit script identifier v75_upoint_to_vgeo.py
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Standard Model and flavor structure
tocsectionStatus @p0.56 p0.08 Y@ Statement & Status & Note \\ weights [formula in source] from cusps [formula in source] data & & Mehta–Seshadri \\ [formula in source] & & exact \\ balanced bundle [formula in source] & & stable splitting \\ [formula in source] , [formula in source] degree, [formula in source] & & winding/residue split \\ [formula in source] , [formula in source] & & budget bookkeeping \\ rigid [formu
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documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex · lines 317 to 361
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Standard Model and flavor structure
Scope and honesty. This note discharges the items that were flagged ``standard but not written out,'' and now also carries the closures previously collected in the research-sprints note: the seam-fixed Starobinsky mass, the derived solar angle [formula in source] , the H2 splitting type, and the quark [formula in source] amplitude band. It does not force the items that stay typed transfer targets, never compiler powe
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documents/tfpt_2_standard_model/sections/009-section-the-parabolic-anchor-compiler.tex · lines 362 to 373
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Standard Model and flavor structure
unique limit state and exponential clustering] The admissible [formula in source] transport transfer operator has the closed spectrum [formula in source] (the cusp cubic). Hence [formula in source] The contraction ratio [formula in source] satisfies the Dobrushin uniqueness condition for a finite-range (range- [formula in source] , cyclic) transfer operator; therefore the thermodynamic limit has a unique Gibbs/vacuum
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documents/tfpt_2_standard_model/sections/010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex · lines 1 to 160
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Standard Model and flavor structure
Compactify the oriented two-dimensional normal slice [formula in source] to [formula in source] . The geometric BRST/Hodge differential, restricted to the seam-even sector with Atiyah–Patodi–Singer boundary conditions on [formula in source] , is an elliptic operator on a compact manifold; hence it is Fredholm, with finite-dimensional kernel and cokernel and an integer index. The compact bosonic Higgs index selects [f
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documents/tfpt_2_standard_model/sections/010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex · lines 161 to 183
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Standard Model and flavor structure
On the [formula in source] attractor the curvature during observable inflation is [formula in source] . Higher curvature terms [formula in source] , [formula in source] , enter with [formula in source] , so their contribution to the observables is [formula in source] . With [formula in source] this is [formula in source] ( [formula in source] ), and the leading predictions are [formula in source] matching Planck. The
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documents/tfpt_2_standard_model/sections/010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex · lines 184 to 272
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Standard Model and flavor structure
The two formerly-hardest items — the ambient (unprojected) QFT measure beyond the selector [formula in source] , and full quantum gravity beyond the [formula in source] scalaron — are not two separate problems. They are one object: the relative spectral-action measure [formula in source] with [formula in source] the matter/gauge Dirac operator and the gravitational data in the same trace. Three facts reduce both open
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documents/tfpt_2_standard_model/sections/010-section-the-explicit-mass-gap-closes-dynamics-and-cluste.tex · lines 273 to 408
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Standard Model and flavor structure
Gravity needs no separate heavy block. The whole low-curvature axis is the seam's response to its own seed, in three lines: [formula in source] with [formula in source] (exact) and the Einstein normaliser [formula in source] . Reading the anchor power sums [formula in source] , [formula in source] gives the gravity microcode: [formula in source] so the gravitational tree value is [formula in source] and the only quan
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 1 to 68
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Standard Model and flavor structure
The PMNS matrix is [formula in source] on the Majorana branch. The reactor angle is closed, [formula in source] . The solar angle is realized by a TFPT texture and reduced to the seam-misalignment lemma in three dictionary steps (the residual is the coefficient [formula in source] (leading term [formula in source] ), a [formula in source] conditional input).
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 69 to 134
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Standard Model and flavor structure
Every mass is [formula in source] with the leptons exact from the hexagonal resolvent, [formula in source] . The quark [formula in source] are outputs of the same resolvent, but the published table is only [formula in source] -digit, so their closed rationals can only be bracketed at present: @lccccccccc@ [formula in source] & [formula in source] & [formula in source] & [formula in source] & [formula in source] & [fo
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 135 to 199
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- explicit script identifier v221_seam_qecc.py
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- explicit file citation v814_k5_sixstep_transport.py
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- explicit file citation v808_petersen_sixthroot.py
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Standard Model and flavor structure
H2 (Theorem 4 of the parabolic note) is reduced to: the [formula in source] -equivariant stable parabolic structure on [formula in source] realises the spectral-selector branch. We set up the finite computation and verify the selector.
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 200 to 306
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- explicit script identifier v49_readout_rigidity.py
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- explicit file citation v27_wall_representative.py
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- explicit file citation v491_p2_partition_corollary.py
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- explicit script identifier v69_d4_q_geometry.py
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- explicit script identifier v70_q_integer_lift.py
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- explicit script identifier v53_compiler_core.py
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- explicit file citation v19_monodromy_moduli.py
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- explicit file citation v49_readout_rigidity.py
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- explicit file citation v69_d4_q_geometry.py
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- explicit file citation v70_q_integer_lift.py
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- explicit file citation v499_p2_weights_deligne_bg.py
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- explicit claim identifier status_ledger.csv
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- explicit file citation v26_flavor_frontier_unification.py
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Standard Model and flavor structure
tocsectionStatus @p5.6cmcY@ Item & Status & Result \\ Dynamics / clustering (Lemma Gravity Fredholm (Lemma [formula in source] truncation (Lemma Starobinsky [formula in source] / [formula in source] & / & [formula in source] GeV exact ; [formula in source] a \ band over [formula in source] \\ [formula in source] typing (Prop. [formula in source] (Prop. quark [formula in source] -rationals & / & hierarchy + source rat
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 307 to 358
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Standard Model and flavor structure
The Standard-Model identities used here (marked , , ) are re-derived from [formula in source] and machine-checked by the suite in the repository folder verification/; the inline tags [verification/ [formula in source] ] point to the exact script. Relevant here: v2_carrier_pascal.py — the carrier/Pascal packet ( [formula in source] , [formula in source] ). v3_em_alpha.py — the EM fixed point [formula in source] . v4_f
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documents/tfpt_2_standard_model/sections/011-subsection-seam-response-grammar-gravity-is-the-inverse-.tex · lines 359 to 376
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- explicit file citation v4_flavor_matrix.py
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- explicit file citation README.md
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- explicit file citation run_all.py
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- explicit file citation v3_em_alpha.py
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- explicit file citation v7_gravity_cosmo.py
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- explicit file citation v2_carrier_pascal.py
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · input 5 tfpt 3 e8 audit bootstrap · TFPT — Introduction and reading guide · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · E8 audit and bootstrap · Frontier and open physical interfaces · Red-team audit · Horizon readouts · Research contracts · Verification safeguards · input 4 origin theory · input 5 tfpt 3 e8 audit bootstrap
Plain language: TFPT (Topological Fixed-Point Theory) is a small discrete compiler. Two inputs — the seam constant [formula in source] and the carrier rank [formula in source] — build [formula in source] and read off the Standard-Model skeleton, the constants and the scale grammar. The series is the introduction plus five numbered papers and four companions (plus one standalone working note), best read in order: intr
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tex-artefacts/tfpt_docset.tex · lines 1 to 44
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · input 5 tfpt 3 e8 audit bootstrap · TFPT — Introduction and reading guide · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · E8 audit and bootstrap · Frontier and open physical interfaces · Red-team audit · Horizon readouts · Research contracts · Verification safeguards · input 4 origin theory · input 5 tfpt 3 e8 audit bootstrap · Verification reference catalog
\\[2pt] [formula in source] — the unique even unimodular rank- [formula in source] glue \ [E] exact (lattice).
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tex-artefacts/tfpt_figures.tex · lines 1 to 150
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · Frontier and open physical interfaces · Horizon readouts · Research contracts · input 4 origin theory
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tex-artefacts/tfpt_references.tex · lines 1 to 11
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · Frontier and open physical interfaces · Horizon readouts · Research contracts · input 4 origin theory
The TFPT discrete core (the two axioms, the [formula in source] glue, the integer skeleton) is self-contained and machine-checked. Its bridges to continuum/AQFT physics, to gravity and to the lattice/singularity picture build on established mathematics, listed here by topic; the body refers to these by author name.
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tex-artefacts/tfpt_references.tex · lines 12 to 19
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · Frontier and open physical interfaces · Horizon readouts · Research contracts · input 4 origin theory
M. Takesaki, Tomita's Theory of Modular Hilbert Algebras and its Applications, Lecture Notes in Math.\ 128, Springer (1970). J. J. Bisognano, E. H. Wichmann, On the duality condition for a Hermitian scalar field / for quantum fields, J. Math.\ Phys.\ 16 (1975) 985–1007; 17 (1976) 303–321. K. Osterwalder, R. Schrader, Axioms for Euclidean Green's functions I, II, Comm.\ Math.\ Phys.\ 31 (1973) 83–112; 42 (1975) 281–30
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tex-artefacts/tfpt_references.tex · lines 20 to 42
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · Frontier and open physical interfaces · Horizon readouts · Research contracts · input 4 origin theory
I. B. Frenkel, V. G. Kac, Basic representations of affine Lie algebras and dual resonance models, Invent.\ Math.\ 62 (1980) 23–66; G. Segal, Unitary representations of some infinite-dimensional groups, Comm.\ Math.\ Phys.\ 80 (1981) 301–342. T. J. Osborne, A. Stottmeister, Conformal field theory from lattice fermions, Comm.\ Math.\ Phys.\ 398 (2023) 219–289, arXiv:2107.13834, doi:10.1007/s00220-022-04521-8. (This is
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tex-artefacts/tfpt_references.tex · lines 43 to 71
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origin theory · tfpt research contracts · tfpt 1 architecture e8 · tfpt 2 standard model · tfpt research contracts · tfpt 1 architecture e8 · input 4 origin theory · Origin Theory · Architecture, E8 and the electromagnetic fixed point · Standard Model and flavor structure · Frontier and open physical interfaces · Horizon readouts · Research contracts · input 4 origin theory
J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd ed., Grundlehren der math.\ Wiss.\ 290, Springer (1999). C. L. Siegel, \"Uber die analytische Theorie der quadratischen Formen (the Minkowski–Siegel mass formula), Ann.\ of Math.\ 36 (1935) 527–606.
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tex-artefacts/tfpt_references.tex · lines 72 to 79
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