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

In plain words

TFPT — Introduction and reading guide

Original identifier and classification

SEAM.EQUIV.TWISTOR.01Open (research route [O]: the Costello-Li construction; preparation [E]/[C] via the CELEST.SEAM.01 work packages v492-v518)

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

Research contracts

Original identifier and classification

WOIT.BETA1.GSO.01UNDECIDED per the frozen preregistration ([E] exact Hermiticity witness + censuses, time-like reflection census, GSO 2-torsion identification, 40-digit gap-certified GSO-fixed RP certificates, exact Cl(16) Kramers restriction, Ramond/wrong-projection/site-cut/family-A controls; [C] contract precision (iii) -- prose only; [O] beta1 proper via beta2, kill tests live on A_hol); NO marker moves

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=150 2026-07-23 (I) ( v523 — the constructive [formula in source] derivation executed and promoted as the ledger row CELEST.WP5E.WM.01: `` [formula in source] is the Atiyah–Bott / zeta-determinant fixed-point factor, COMPUTED from three independent sources'' — verdict ERFOLG per the frozen preregistration; the residual \ of v516/ v520 is closed at the fibre-zero-mode level and narrows to the GLOBAL BCOV integral on [formula in source] beyond the fibre zero-mode factor; the celestial/twistor story in tfpt_3 gains Step 24 — (1) ATIYAH–BOTT (route i) : the equivariant mode ledger of the fibre [formula in source] equals the closed form [formula in source] exactly in [formula in source] for all [formula in source] ; REGULAR at [formula in source] with Abel value [formula in source] , [formula in source] ; [formula in source] Ces\`aro convergence in exact arithmetic; fixed-point splitting at EVERY truncation level [formula in source] for the phased (skeleton) AND the v520-forced unphased (completion) trace — the Abel-limit [formula in source] is the v516 contact vector COMPUTED, not declared; (2) ZETA/QUILLEN (routes ii/iii) : [formula in source] of the [formula in source] -twisted circle Laplacian [formula in source] EXACTLY (Lerch [formula in source] reflection formula symbolically, Hurwitz certificates [formula in source] ); Quillen split [formula in source] , [formula in source] , the real positive holomorphic section UNIQUE via the [formula in source] conjugation pairing; the [formula in source] [formula in source] block at the [formula in source] nodes carries the exact constant term [formula in source] (deviations [formula in source] ); (3) the CONSISTENCY CHAIN : [formula in source] ; [formula in source] at every scale; [formula in source] ; the [formula in source] budget [formula in source] forces [formula in source] uniquely (leftovers [formula in source] ); per-sector Okubo squares [formula in source] ; total [formula in source] ; [formula in source] , [formula in source] ; [formula in source] , [formula in source] ; (4) NEGATIVE CONTROLS : [formula in source] gives [formula in source] , leftovers [formula in source] , Quillen contradiction; [formula in source] gives [formula in source] ; the [formula in source] /Eguchi–Hanson anchor PASSES with the same derivation ( [formula in source] , [formula in source] , [formula in source] , [formula in source] ); the [formula in source] KILL fires; [formula in source] breaks the zeta [formula in source] AB identity itself; [formula in source] : [formula in source] — the weights wander correctly, only [formula in source] carries the [formula in source] chain; TYPED PREMISES \ (the mandatory fence): TP-REG (Abel/Ces\`aro/zeta regularisation [formula in source] the definition of the equivariant character), TP-Q (Quillen structure of BCOV [formula in source] [formula in source] v520 TP-4), TP-NUM (unphased numerator [formula in source] v520 ERFOLG-A), TP-CH (insertion channel [formula in source] ); : the global BCOV integral beyond the fibre zero-mode factor, the resolved-ALE route not built, SEAM.EQUIV.TWISTOR.01 stays Open; NO marker moves)

TFPT — Introduction and reading guide

Original identifier and classification

CELEST.WP5E.WM.01Formal/Identity [E] (exact Q(i)/Q(sqrt2)/cyclotomic mode ledgers, Abel values, tensor-trace splitting, reflection-formula zeta determinants, Quillen arithmetic, delta-1f block constant terms, the full v516 chain, all controls -- sympy/Fraction exact, Wolfram-mirrored; numeric documented: Hurwitz/Lerch and stripped block limits at 40 digits) + [C] (the typed premises TP-REG/TP-Q/TP-NUM/TP-CH) + [O] (the global BCOV integral beyond the fibre zero-mode factor)

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=150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)

TFPT — Introduction and reading guide

Original identifier and classification

DIAMOND.CENTER.QUOTIENT.01Identity [E] (exact integer linear algebra: fixed line, unimodular quotient, self-coding row sums, resolvent factorisation, honest uniqueness controls -- sympy exact, Wolfram-mirrored) + [C] (the Lie-dimension readings of the quotient ladder, audit-typed like v414) + [O] (full selector-stratum ablation)

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=150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)

TFPT — Introduction and reading guide

Original identifier and classification

COX.STAGEA.TENSOR.01Identity [E] (exact order/charpoly/trace arithmetic + honest kill-scope + coprimality controls -- sympy exact, Wolfram-mirrored) + [C] (the identification with the E8 Coxeter clock, as v223/v314) + [O] (the flip-atlas intertwiner COX.FLIP.INTERTWINER; Stage B metrization)

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=150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)

TFPT — Introduction and reading guide

Original identifier and classification

E8.DEGREE.MODULAR.01Identity [E, audit-only] (exact integer/q-series arithmetic incl. the j-series recomputation and all controls -- sympy exact, Wolfram-mirrored); explicitly NON-exclusive (D16 control passes); the fingerprint feeds no derivation (no-free-pattern rule honoured)

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=150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)

TFPT — Introduction and reading guide

Original identifier and classification

FTR.DISC7.NORM.01Identity [E] (exact norm/integrality/translation/discriminant arithmetic + negative controls -- sympy exact, Wolfram-mirrored) + [E, audit] (split prime 2, Heegner class number) + [C]/[O] (the arithmetic F_transfer frame: common Moebius action of the four solvers = preregistered next test; GATE.FTRANSFER unchanged)

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Red-team audit

Red-team audit

Original identifier and classification

CP.CHANNEL.IDENT.01Identity [E] (exact identities and certified numerics with mutation controls -- the hexagonal channel identity sum rho^{d_k} = 4 rho / sum rho^{m_k} = 4 sympy-exact with the sheet-even/odd parity typing, arg(prod c) = 0 exactly on both magnitude sectors with the branch-order law, Tier-1 emptiness by the conjugation-commutation theorem, the frame removal Im(rho det)/det = Im rho exact with the degree +1 account, the two inequivalent Tier-2 characters as verified homomorphisms, and the Jarlskog anchor J = 3.327021e-5 = v88 at unitarity 1.1e-41) -- NARROWINGS of four existing ledger readings only; no marker moves; R1/R2 typed OPEN

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=150 2026-08-01 (XVI) (the joint embedding lands ( v600 promoted): the compiler pair [formula in source] is REALIZED on the [formula in source] -cover — a [formula in source] -even degree-2 pair, [formula in source] -integral, seven-word rank [formula in source] , simultaneous conjugation to the compiler pair solved exactly, integer restrictions on the saturated [formula in source] lattice, and saturation index [formula in source] with the exact v566 divisor pattern; canonicity typed open, the gate does not move)

TFPT — Introduction and reading guide

Original identifier and classification

DIAMOND.PARA.SELFCODE.01Identity [E] (exact integer/symbolic algebra with mutation controls -- parabolic closure, double self-code, uniqueness enumeration + divisor argument, saturated Smith form, A2 quiver, trace code, cross-ratio identities, Lorentz/pencil identities) + [C] (the TFPT readings of the invariants; the bit-carrier and CR-test interpretations) + [O] (the No-Carrier-Reconstruction audit, the mark-local 81 mechanism, the CR-test execution); NO marker moves

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=150 2026-08-01 (IV) (the sheet involution exists unconditionally ( v590 promoted): the integral [formula in source] -commuting involutions are exactly [formula in source] (rigidity, both twins); the v574 type theorem [formula in source] seam reversal [formula in source] zero-mode fixing single out the explicit [formula in source] with exact [formula in source] -signature uniquely — GATE.QGEO.01's involution-existence input relocates to DERIVED)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.WINDING.SELF.01Identity [E] + typed gate [C] (rank theorem symbolic; enumerations at declared bound; the remaining gate named)

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Group-theoretic audits (optional)

E8 audit and bootstrap

Original identifier and classification

QGEO.DUALFORMS.01Exact [E] duality/dictionary/positivity identities + [X/O] quantified negatives and typed opens (exact sympy; two numeric inertia counts of exact matrices) + Lean certificate FORM.QGEO.04

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