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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.

Matching source sections

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

Research Contract — TFPT.TOE.COMPLETE.01 (the named AND of eight completeness gates)

Research contracts

Typing. A research contract \ (ledger row TFPT.TOE.COMPLETE.01), registered 2026-08-29 from review wave 4. This row names the AND of eight gates; it does not close any of them and it does not upgrade a marker. Dual rest: the compiler residual [formula in source] sits beside [formula in source] ; this contract is the named AND, not a closure of either.

Opening source excerpt. Formulas and the full argument remain in the original document.

Source location and explicit evidence links

documents/tfpt_research_contracts/sections/019-source.tex · lines 1 to 136

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Research Contract — FLAV.NUSCALE.06 (pentagon-class misalignment candidate)

Research contracts

Typing. A candidate \ (ledger row FLAV.NUSCALE.06); mechanism [formula in source] the [formula in source] -to-flavor operator . No seesaw closure; FLAV.NUSCALE.05 unmoved. ( v1001_ nu_ pentagon_ chain.py.)

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/019-source.tex · lines 137 to 154

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

  • explicit script identifier v9_neutrino_texture.py

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  • explicit claim identifier status_ledger.csv

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  • cross reference join tfpt_readouts.wl

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  • explicit file citation v1001_nu_pentagon_chain.py

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  • cross reference join YukawaStageDExistence.lean

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  • explicit script identifier v3_em_alpha.py

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  • explicit script identifier v270_pmns_jarlskog_assembly.py

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  • explicit claim identifier status_ledger.csv

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  • cross reference join tfpt_readouts_extension.wl

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Research Contract — FLAV.NU.TEXTURE.MECHANISM.01 (both structural nulls as binding constraints)

Research contracts

Typing. A research contract \ (ledger row FLAV.NU.TEXTURE.MECHANISM.01), registered 2026-08-29 from review wave 5. ( v1003_ nu_ structural_ nulls.py.) Executed content. Charged-sector data [formula in source] , [formula in source] (coset min-norms all [formula in source] ) . Schur-texture NULL : all [formula in source] preregistered [formula in source] combinations fail; D4 reflection forces [formula in source] ; hie

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/019-source.tex · lines 155 to 200

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Research Contract — SEAM.MILNOR.LOCALRING.01 (canonical identification of the seam collar with the reduced Milnor algebra)

Research contracts

Typing. A research contract \ (ledger row SEAM.MILNOR.LOCALRING.01), registered 2026-08-30 from review wave 6. ( v1004_ milnor_ frobenius_ gray.py.) Demand. A canonical identification between the raw seam collar / [formula in source] transition bus and the reduced Milnor algebra [formula in source] preserving simultaneously the dual-number action, the Frobenius pairing, the Gray torsor, the deck action and CP. Accept

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/019-source.tex · lines 201 to 279

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Research Contract — GRAV.WEINBERG.WITTEN.01 (Weinberg–Witten firewall before any spin-2 marker move)

Research contracts

Typing. A research contract \ (ledger row GRAV.WEINBERG.WITTEN.01), registered 2026-08-30 from review wave 6. Child of TOE gate T7; cross-link GRAV.SPIN2.EMERGENCE.01 (listed here, not back — that would cycle). Demand. The microscopic Hamiltonian family must not possess a fundamental Lorentz-covariant local conserved [formula in source] ; Lorentz symmetry, diffeomorphism Ward identities and the spin-2 mode must emerg

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/019-source.tex · lines 280 to 295

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Externalization Contract — SEAM.EQUIV.01 (the seam scaling-limit theorem, packaged for external specialists)

Research contracts

Typing. This section is a hand-off document: it packages the one remaining seam obligation as a self-contained problem statement for an outside specialist in conformal nets / vertex operator algebras / algebraic QFT. It documents, it does not close: the ledger row SEAM.EQUIV.01 stays \ (its conditional route SEAM.EQUIV.MMST.01 is closed modulo cited theorems; the unconditional parent is the target below). Nothing in

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/020-source.tex · lines 1 to 162

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

Externalization Contract — ALPHA.QUILLEN.EXACT.01 (the determinant-line variation theorem, packaged for external specialists)

Research contracts

Typing. The second hand-off document: the one remaining EM obligation, packaged for an outside specialist in determinant lines / [formula in source] -invariants / index theory. It documents, it does not close: ALPHA.QUILLEN.EXACT.01 stays \ (external math, type A, v384), and it is a face of SEAM.EQUIV.01 ( v382) — not a second independent gate. The value [formula in source] is closed \ regardless (unique root [formul

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/020-source.tex · lines 163 to 386

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Certifiability and recommended order

Research contracts

@Ylc@ Building block & Machine & Hardness \\ [formula in source] enumeration ( [formula in source] ) & Lean / Python / Wolfram & easy ( done) \\ [formula in source] fixed-locus polynomial ( [formula in source] ) & Sage / Mathematica & medium \\ selector uniqueness ( [formula in source] ) & interval arithmetic & medium \\ SNF, determinants, spectra & Lean & easy–medium \\ principal-symbol ellipticity (G1) & xAct / Cad

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Source location and explicit evidence links

documents/tfpt_research_contracts/sections/021-source.tex · lines 1 to 307

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

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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Source location and explicit evidence links

tex-artefacts/tfpt_docset.tex · lines 1 to 44

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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 · Verification reference catalog

\\[2pt] [formula in source] — the unique even unimodular rank- [formula in source] glue \ [E] exact (lattice).

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Source location and explicit evidence links

tex-artefacts/tfpt_figures.tex · lines 1 to 150

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

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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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 1 to 11

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No explicit verification citation is attached to this section in the registry.

External works built upon

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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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 12 to 19

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

Modular theory and algebraic quantum field theory.

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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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 20 to 42

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

Conformal nets, vertex operator algebras and lattice constructions.

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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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 43 to 71

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

Lattices and quadratic forms.

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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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 72 to 79

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

Singularities and geometry.

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

E. Brieskorn, Beispiele zur Differentialtopologie von Singularit\"aten, Invent.\ Math.\ 2 (1966) 1–14. J. Milnor, Singular Points of Complex Hypersurfaces, Ann.\ of Math.\ Studies 61, Princeton Univ.\ Press (1968).

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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 80 to 87

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

Spectral geometry, gravity and thermal time.

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

A. H. Chamseddine, A. Connes, The spectral action principle, Comm.\ Math.\ Phys.\ 186 (1997) 731–750. A. Connes, C. Rovelli, Von Neumann algebra automorphisms and time–thermodynamics relation in general covariant quantum theories, Class.\ Quantum Grav.\ 11 (1994) 2899–2918. R. M. Wald, Black hole entropy is the Noether charge, Phys.\ Rev.\ D 48 (1993) R3427–R3431. H. Casini, M. Huerta, R. C. Myers, Towards a derivati

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Source location and explicit evidence links

tex-artefacts/tfpt_references.tex · lines 88 to 100

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

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 · input 4 origin theory · input 5 tfpt 3 e8 audit bootstrap

Two inputs, one compiler. From the boundary constant [formula in source] (axiom P1) and the five-slot carrier [formula in source] (axiom P2) — jointly the elementary symmetric data of one anchor [formula in source] — the discrete compiler [formula in source] is built, and the Standard-Model skeleton (gauge group, three families, hypercharges, the flavor matrix), the dimensionless constants ( [formula in source] ) and

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Source location and explicit evidence links

tex-artefacts/tfpt_status.tex · lines 1 to 84

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  • explicit script identifier v330_qgamb_admissible_measure.py

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  • explicit claim identifier status_ledger.csv

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  • cross reference join tfpt_readouts.wl

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v358_grav_entropy_equilibrium.py

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  • explicit script identifier v376_seam_s3_centralcharge.py

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  • explicit script identifier v60_lambda_metrology_branch.py

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  • explicit file citation status_ledger.csv

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  • explicit script identifier v335_seam_equiv_unify.py

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  • explicit script identifier v473_entropic_action_bridge.py

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  • explicit script identifier v469_seam_crossedproduct_route.py

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  • cross reference join SeamEdgeChern.lean

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v367_seam_s3_lattice.py

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  • explicit script identifier v369_qgamb_redundancy.py

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  • explicit claim identifier status_ledger.csv

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  • explicit script identifier v368_seam_s3_inflow.py

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  • explicit script identifier v379_seam_s3_rp.py

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  • explicit script identifier v359_grav_nonlinear_einstein.py

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  • explicit script identifier v76_gmetric_reduction.py

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  • explicit script identifier v153_no_unit_theorem.py

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  • cross reference join SeamResidualAxiom.lean

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  • cross reference join SeamScalingLimit.lean

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  • explicit script identifier v378_seam_s3_modular.py

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  • explicit script identifier v336_continuum_limit.py

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  • cross reference join tfpt_readouts_extension.wl

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  • cross reference join SeamApplicabilityLedger.lean

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  • explicit script identifier v377_seam_s3_e8character.py

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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 · Verification reference catalog

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

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Source location and explicit evidence links

tex-artefacts/tfpt_style.tex · lines 1 to 145

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Front matter / support

tfpt research contracts · Research contracts

Opening source excerpt. Formulas and the full argument remain in the original document.

Source location and explicit evidence links

tex-artefacts/toe_research_20260909.tex · lines 1 to 1

These are recorded citation relations. A source citation or topic match does not establish a mathematical or physical result.

No explicit verification citation is attached to this section in the registry.

What this source index covers

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.