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The published foundations of TFPT

Read the original registered statements beside their paper sections, assumptions and verification sources. The later reviewed research stays connected through a separate record.

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183 matching active claims. Showing at most 20 per page. Original statement text and long numerical details open within each claim.

Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)

Research contracts

Original identifier and classification

WOIT.BETA3.DUALITY.01Identity [E] (exact sympy algebra on generic block parameters -- block theorem, branch dichotomy, signature-mirror theorem, kill emptiness, unique induced member, exact rational-pi placement arithmetic, exact lattice regressions) + two 40-digit inertia certificates + [C] (the declared conventions: seam line, seam preservation, RP-side placement, torsor relabeling; contract-level identification, not a derivation); verdict SUCCESS, kill branch empty by algebra, no marker moves

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=150 2026-07-31 (XI) (the continuous half of the cross-ratio check executed and closed: UNIFLOW-DEGENERATE ( v575 promoted) — the native exports are forced degenerate by the single-flow theorem, so the continuous half closes onto v425; both halves of the preregistered check are now executed)

TFPT — Introduction and reading guide

Original identifier and classification

FTR.CRCONT.01Identity [E] + typed closure [C] (exports recomputed; degeneracy theorem exact; the closure onto v425 typed)

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=150 2026-08-01 (XXXII) (the interacting gamma slice lands at toy level ( v615 promoted): the gamma battery executed ON the RP-surviving interaction class (the alignment bit [formula in source] , positive coupling, v534) — THE INTERACTING MIRROR FLIP: at the forced twist [formula in source] the mirror state's odd sector is STRICTLY NEGATIVE DEFINITE on every cut and every coupling [formula in source] (bounded away from zero: kill test (3) cannot fire on the surviving class — v608 upgraded from [formula in source] to the full grid); the mark transport exists interacting (kill test (7) does not fire); the odd transfer spectrum stays multiplicity-free; and the dead member has no RP home — the dynamical bit selection and the chirality data CO-LOCATE on the same member)

TFPT — Introduction and reading guide

Original identifier and classification

WOIT.GAMMA.FREE.01Exact [E] sector/spectrum/incidence statements on the explicit v524 net + [C] the gamma reading (free slice; A_hol untouched)

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=150 2026-08-01 (XXXII) (the interacting gamma slice lands at toy level ( v615 promoted): the gamma battery executed ON the RP-surviving interaction class (the alignment bit [formula in source] , positive coupling, v534) — THE INTERACTING MIRROR FLIP: at the forced twist [formula in source] the mirror state's odd sector is STRICTLY NEGATIVE DEFINITE on every cut and every coupling [formula in source] (bounded away from zero: kill test (3) cannot fire on the surviving class — v608 upgraded from [formula in source] to the full grid); the mark transport exists interacting (kill test (7) does not fire); the odd transfer spectrum stays multiplicity-free; and the dead member has no RP home — the dynamical bit selection and the chirality data CO-LOCATE on the same member)

TFPT — Introduction and reading guide

Original identifier and classification

WOIT.GAMMA.TOY.01Float-track certificates (tolerances declared) + exact combinatorics + [C] toy fence (numpy/sympy)

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=150 2026-08-01 (XXXVI) (the covered seam lands ( v623 promoted) — the lattice skeleton of the covering-level identification: the seam lifted to the [formula in source] -cover is ONE 48-site NS circle for the uniform weights (the alternating pair DISCONNECTS it — a new independent kill), the lifted clock has EXACT ORDER 12 with [formula in source] deck ( [formula in source] as lattice combinatorics), the v622 kernel identity generalizes verbatim to [formula in source] , and the deck-character mode grid is the 12-grid ( [formula in source] ) with the untwisted sector equal to the base seam VERBATIM and the twisted pair carrying [formula in source] on bilinears (the [formula in source] sheets); the fermionic deck lift satisfies [formula in source] (the spin double))

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.SEAMID.01Exact [E] mode-sum/dictionary identities (sympy) + must-fail control + [C] the covering residue typing

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Group-theoretic audits (optional)

input 5 tfpt 3 e8 audit bootstrap

Original identifier and classification

QGEO.BONDDEF.01Lattice theorem [E] (exact unitary equivalence + gauge pin + exclusion census, honest isospectral documentation) + [C] typed continuum remainder (Python-only per GATE.WOLFRAM.02).

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The holomorphic restriction of E₈ invariants

Architecture, E8 and the electromagnetic fixed point

Original identifier and classification

E8.QUARTICHALF.01Symbolic [PROOF] mu4-orbit vanishing + [E] G31 invariance/independence/mirror census + [E, kill] complex-structure controls + [cited] Chevalley basic-invariant theorem (exact arithmetic; Python-only per GATE.WOLFRAM.02).

Topic connection recorded by an authored Atlas relation.

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