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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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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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=150 2026-08-01 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.TRANSLATOR.01Exact [E] translator/bridge/chain/duality identities + [C] typed opens (exact sympy; Smith transforms over Z; Lean addendum green)

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=150 2026-08-01 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.MODESEP.01Exact [E] torsion/separation identities + [C] typed frame caveat + [X] honest arithmetic negative (exact sympy; Smith transforms over Z)

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=150 2026-08-01 (XXIV) (the selection rule lands ( v607 promoted): the infinity torsion is a genuine [formula in source] space, the deck rotation acts with char [formula in source] mod [formula in source] — EXACTLY ONE projective eigenline, and it IS the top mode; the three modes carry mutually exclusive canonical labels (seam [formula in source] [formula in source] -real, top [formula in source] deck-eigen, zero [formula in source] the only unlabeled) and [formula in source] flips exactly the labeled pair: BOTH v590 demands expressed through cover structure (typed reading; the gate residual is the continuum derivation))

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.SELRULE.01Exact [E] F_3/rigidity/labeling identities + [C] typed selection reading (exact sympy / F_3 arithmetic; Smith transforms over Z)

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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 (XXVI) (the translator factorization lands ( v609 promoted): the geometric identity of [formula in source] is CLOSED — the mirror intertwiner [formula in source] ( [formula in source] ) is unique, unimodular ( [formula in source] ), [formula in source] -integral and [formula in source] -involutive ( [formula in source] exactly), and the v605 element factorizes exactly as [formula in source] with [formula in source] : [formula in source] — all three v605 residuals are now resolved (seam reversal v603, zero-mode rule v607, [formula in source] -identity v609))

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.CFACTOR.01Exact [E] uniqueness/unimodularity/integrality/involutivity/factorization identities + [C] the closed-identity reading (exact sympy)

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=150 2026-08-01 (XXVIII) (the periods round lands ( v611 promoted): the analytic layer of the cover is CLASSICAL — all five basic period integrals are exact Beta values with Gamma denominators on the [formula in source] grid ( [formula in source] ); the [formula in source] rotation acts on periods with the exact characters [formula in source] ; [formula in source] exactly; and the cross-factor period ratio admits no low-degree integer relation (PSLQ null) — the two CM factors are period-independent, as the v610 splitting demands)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.LANDSCAPE.01Exact [E] characters/point-counts/census + [C] CM-theory reading and named resources (deterministic integer computations; no floats beyond the census prefilter)

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=150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.PERIODS.01Exact [E] symbolic Beta identities + 40-digit certificates + PSLQ-null consistency + [C] the period-dictionary reading

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=150 2026-08-01 (XXX) (the canonical period normalization lands ( v613 promoted) — THE ANALYTIC BRIDGE CLOSES: the quarter rotation acts DECK-FREE on the four branch segments (all [formula in source] wrap factors exactly [formula in source] ), and the exact dictionary is [formula in source] — [formula in source] EXACTLY, explaining [formula in source] structurally, with the deck power unique; the period rows (hol [formula in source] , hol [formula in source] , antihol [formula in source] ) realize the rotation eigenframe; the Hodge weights are explicit Gamma monomials ( [formula in source] , complex Beta formula); and [formula in source] PER CHARACTER: the compiler polarization is MINUS the analytic Hodge form — Riemann–Hodge positivity realized, v612's named step B5 executed)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.POLFRAME.01Exact [E] spectrum/diagonalization/signature identities + [C] the bridge reading (exact sympy)

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=150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.PERNORM.01Exact [E] dictionary/uniqueness identities + 40-digit certificates + Gamma-monomial closed forms + [C] the fork-basis residue (sympy + mpmath)

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=150 2026-08-01 (XXXI) (the Gauss–Manin transport round lands ( v614 promoted) — THE DECK STEP IS THE BOUNDARY MONODROMY: transporting the segment cycles along the rigid quarter-rotation loop, the discriminant [formula in source] winds ONCE around [formula in source] and the transported periods factorize EXACTLY, [formula in source] ; at [formula in source] the deck factor is [formula in source] on EVERY sheet (the exponent [formula in source] forced by the puncture count); the canonical transport matrix in the segment basis is EXACTLY [formula in source] — the v613 dictionary [formula in source] is CANONICAL, no conjugator freedom left, and [formula in source] re-derives [formula in source] ; v613's residue F1 closed at the transport level)

TFPT — Introduction and reading guide

Original identifier and classification

QGEO.TRANSPORT.01Exact [E] factorization/deck/uniqueness identities + 25-digit transport certificates + [C] the boundary-monodromy reading (sympy + mpmath)

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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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