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

-1.2cm TFPT — Frontier items\\[2mm] [formula in source] , [formula in source] , the Koide relation, dark matter and quantum gravity —\\ the honest status, not forced onto the ladder

Frontier and open physical interfaces

-1.2cm TFPT — Frontier items\\[2mm] [formula in source] , [formula in source] , the Koide relation, dark matter and quantum gravity —\\ the honest status, not forced onto the ladder

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documents/tfpt_4_frontier/preamble.tex · lines 1 to 37

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Front matter / support

Frontier and open physical interfaces

The honest frontier: which physics has a genuine TFPT handle and which does not. For each of [formula in source] , [formula in source] , the Koide relation, dark matter and full quantum gravity, this note states the genuine structural handle, the precision with which it currently lands, and — crucially — what is not a clean compiler power and is deliberately not forced onto the ladder. This document is the status aut

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documents/tfpt_4_frontier/sections/001-source.tex · lines 1 to 90

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explicit file citation v187_ftransfer_laws.py
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explicit file citation v402_ftransfer_suite.py
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explicit file citation v35_quark_qcd_boundary.py
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explicit file citation v792_ftransfer_kms_coset.py
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explicit file citation v188_frontier_wording_guard.py
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explicit script identifier v212_leptogenesis_decuple.py
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explicit script identifier v371_ftransfer_pole.py
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explicit file citation v213_ftransfer_functor.py
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explicit file citation v777_ftransfer_clock_jets.py
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explicit file citation v397_external_clock_probe.py
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Baryon asymmetry [formula in source] — a downstream readout from the closed [formula in source]

Frontier and open physical interfaces

There are two independent handles, and they agree.

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documents/tfpt_4_frontier/sections/001-source.tex · lines 91 to 94

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Route A — from the closed baryon fraction.

Frontier and open physical interfaces

The seed already fixes the baryon fraction (the [formula in source] decoder): [formula in source] matching the observed [formula in source] . The baryon-to-photon ratio is then the standard cosmological readout [formula in source] . With the TFPT Hubble value ( [formula in source] , from [formula in source] ), [formula in source] So [formula in source] is a downstream cosmological readout from the closed [formula in

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documents/tfpt_4_frontier/sections/001-source.tex · lines 95 to 109

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Route B — leptogenesis interface ( ).

Frontier and open physical interfaces

The TFPT branch fixes the neutrino spectrum, the CP phase structure ( [formula in source] , [formula in source] , both closed) and a plausible washout anchor [formula in source] meV. The heavy-mass input, however, remains scenario-level: [formula in source] is viable but does not close [formula in source] — [formula in source] is the seesaw scale [formula in source] , not a compiler power, so the relation relocates t

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documents/tfpt_4_frontier/sections/001-source.tex · lines 110 to 188

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explicit file citation v212_leptogenesis_decuple.py
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explicit file citation v1001_nu_pentagon_chain.py
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explicit file citation fboltzmann_solve.py
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explicit file citation v986_nu_scalaron_rung.py
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explicit file citation v184_etaB_anchored_boltzmann.py
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explicit file citation v169_etaB_boltzmann_interface.py
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Proton/electron ratio [formula in source] — a cross-sector ratio

Frontier and open physical interfaces

[formula in source] is closed on the [formula in source] -ladder ( [formula in source] ). The proton mass is not a Yukawa: it is QCD-dominated, [formula in source] a few [formula in source] , and [formula in source] arises by dimensional transmutation from [formula in source] running (scheme level). Hence [formula in source] mixes two different sectors. It is no single [formula in source] power: [formula in source] a

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documents/tfpt_4_frontier/sections/001-source.tex · lines 189 to 261

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explicit file citation v723_phys_modular_clock.py
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explicit file citation v725_phys_vgeo_torsor_audit.py
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explicit file citation v164_qcd_scale.py
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The Higgs quartic — near-criticality from the free seam

Frontier and open physical interfaces

The seam UV is the free chiral [formula in source] fixed point ( v158_fixed_point_stable.py): Gaussian, with no relevant and no marginal interactions. The Higgs self-coupling [formula in source] is the one marginal scalar coupling, so a free seam forces it to the Gaussian point there: [formula in source] the Shaposhnikov–Wetterich double-criticality condition — here derived from the free seam rather than postulated.

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documents/tfpt_4_frontier/sections/001-source.tex · lines 262 to 300

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The Koide relation — near [formula in source] , computed exactly

Frontier and open physical interfaces

With the closed lepton source masses [formula in source] the Koide ratio is a pure number (the common prefactor cancels): [formula in source] The measured pole-mass value is famously [formula in source] . So TFPT predicts a Koide ratio that is near [formula in source] but not exactly [formula in source] at source level.

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documents/tfpt_4_frontier/sections/002-source.tex · lines 1 to 154

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explicit file citation v183_koide_f_corner_transfer.py
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explicit file citation v420_fpole_qed_running.py
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explicit file citation v25_frontier_conjectures.py
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Dark matter — the candidate is fixed, the scale is pending

Frontier and open physical interfaces

TFPT does contain a dark-matter candidate, and it is not ad hoc: the determinant-line axion of the strong-CP sector (the determinant-line axion interface of the closed branch, ). Its candidate identity is fixed by the [formula in source] scan (below) and the domain-wall number [formula in source] winds once per primitive seam winding. The relic density is the standard misalignment-plus-string expression [formula in s

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documents/tfpt_4_frontier/sections/002-source.tex · lines 155 to 280

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explicit file citation v25_frontier_conjectures.py
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The muon anomalous magnetic moment — a seam vertex readout

Frontier and open physical interfaces

A \ downstream readout (archive integration), not a compiler power. The carrier algebra carries a second-order topological defect beyond the one that fixes [formula in source] : with [formula in source] and the carrier compression quotient [formula in source] ( v51_boundary_half_step.py), [formula in source] . Projected through the seam-loop phase [formula in source] (the same [formula in source] unit that normalises

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documents/tfpt_4_frontier/sections/002-source.tex · lines 281 to 314

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explicit file citation v204_muon_seam_g2.py
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Full quantum gravity — induced from the boundary kernel

Frontier and open physical interfaces

Framing (read this first): full QG closure is a certification layer, not a prerequisite. TFPT does not need the complete quantum-gravity measure to test its Standard-Model and cosmology readouts — those run through [formula in source] and [formula in source] and are falsifiable now (JUNO, CMB-S4, EDM). [formula in source] certifies the metric sector; its absence narrows what can be claimed, not what can be tested. \\

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documents/tfpt_4_frontier/sections/003-source.tex · lines 1 to 376

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Front matter / support

Frontier and open physical interfaces

Earlier research update through Round 27 (2026-09-07). The shipped non-RH theory contracts now extend to the original finite-regulator [formula in source] scalar/charge model, with every integer charge and E8 phase retained. A complete charge-diagonal reference [formula in source] gives [formula in source] by all-block pinching and joint scalar/charge H\"older. The artificial extra charge heat-trace factor is removed

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documents/tfpt_4_frontier/sections/004-source.tex · lines 1 to 140

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Summary

Frontier and open physical interfaces

tocsectionSummary @p2.9cmcY@ Item & Status & Honest handle / what is missing \\ [formula in source] & & downstream readout [formula in source] from closed [formula in source] ; leptogenesis interface, cleanest scenario [formula in source] , [formula in source] (shared decuple, no seesaw scale) \\ [formula in source] & & cross-sector (QCD scale / closed [formula in source] ); typed runnable solver with [formula in sou

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documents/tfpt_4_frontier/sections/004-source.tex · lines 141 to 197

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Appendix: computational verification

Frontier and open physical interfaces

These are the frontier items: most carry \ (open) or \ (conditional) and are therefore not part of the pass/fail suite. The one quantitative handle that is reproduced is [formula in source] (whence the [formula in source] order) in verification/v7_gravity_cosmo.py. The [formula in source] structure and the gap-decoupling of the physical QG sector are machine-checked ( v28_gravity_fR.py, v36_spectral_action_g2.py); th

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documents/tfpt_4_frontier/sections/004-source.tex · lines 198 to 213

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Front matter / support

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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Front matter / support

\\[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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Front matter / support

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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External works built upon

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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Modular theory and algebraic quantum field 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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Conformal nets, vertex operator algebras and lattice constructions.

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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