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=150 2026-07-22 (XII) ( v522 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.BETA1.GSO.01: ``the clock is time-like, GSO is the gauge datum'' — a TYPED result (verdict UNDECIDED per the frozen preregistration, the mechanism identified exactly, gauge-fixed RP established under the corrected typing; the celestial/twistor story in tfpt_3 gains Step 23) — (1) the HERMITICITY WITNESS : the [formula in source] clock average violates Hermiticity EXACTLY (the one-step insertion [formula in source] has entry [formula in source] where the conjugate transpose demands [formula in source] ; entrywise census [formula in source] Hermitian-matching, [formula in source] ANTI-matching, [formula in source] violations — the pairing is complex-SYMMETRIC, strictly weaker than Hermitian: ``positivity after gauge fixing'' is not well-posed for the clock reading); (2) TIME-LIKE TYPING : ALL [formula in source] dihedral reflection axes of the NS seam circle invert the clock lift ( [formula in source] ), NONE commutes — the [formula in source] clock IS Woit's euclidean rotation; the gaugeable ( [formula in source] -compatible) part of the [formula in source] Fock tower is EXACTLY its [formula in source] -torsion [formula in source] [formula in source] the GSO/fermion-parity [formula in source] (Hermiticity census over all powers; [formula in source] the full wrap [formula in source] the [formula in source] rotation of the seam [formula in source] fermion parity); (3) the POSITIVE PART : GSO-fixed RP holds EXACTLY — [formula in source] even [formula in source] parity-projected bond-cut Gram [formula in source] PD (min eigenvalue [formula in source] at [formula in source] digits), [formula in source] complete half algebra: all odd rows/columns killed exactly, even block [formula in source] PD ( [formula in source] ), no degree truncation; the site-cut defect SURVIVES gauge fixing ( [formula in source] — the bond placement is gauge-invariant information); family A keeps failing ( [formula in source] indefinite vs family D's [formula in source] ); Kramers: [formula in source] on [formula in source] , [formula in source] restricts with [formula in source] ; Ramond control: the wrap [formula in source] ``true [formula in source] '' lift fails state invariance — the NS/ [formula in source] tower is forced; (4) KILL-TEST BOOKKEEPING: kill test (2)'s free shadow does NOT fire (no legitimate Hermitian gauge-fixed form has a negative direction), kill test (1) stays discharged also gauge-invariantly; both stay formally live on [formula in source] ; (5) TRANSPARENCY: the first frozen run scored [formula in source] (the clock-reading checks failed exactly as the mechanism predicts) and the preregistered deg-2 invariant dimension [formula in source] was a combinatorial error (correct census [formula in source] ) — documented in full, the verdict by the frozen [C-3] logic (Hermiticity failure [formula in source] UNDECIDED); CONTRACT PRECISION (iii) (prose, no marker): ``gauge-invariant subalgebra'' at the free level means the GSO/fermion-parity [formula in source] — the only [formula in source] -compatible part of the [formula in source] tower; the clock is the euclidean rotation itself (timelike), its equivariant statement moves to [formula in source] (OS quotient first, then the clock as reconstructed transfer operator); Wolfram extension (with v520/v521) [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open, [formula in source] proper re-routed via [formula in source] )

Research changelog · TFPT — Introduction and reading guide

v522_woit_beta1_gso_gauge.py ( WOIT.BETA1.GSO.01, 16 checks, [formula in source] 5 s; exact sympy Pfaffian–Wick [formula in source] exact [formula in source] Fractions; definiteness via [formula in source] -digit spectra, tolerance [formula in source] ; deterministic). G1 the gauge datum (Z8/NS tower, Ramond control, invariant dimensions [formula in source] ); G2 [formula in source] normalises the tower and restricts

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documents/changelog/sections/003-source.tex · lines 352 to 382

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=150 2026-07-22 (XI) ( v521 — the RP/ [formula in source] attack on the alignment bit DECIDED and promoted as the ledger row SEAM.BIT.RPBLIND.01: ``free OS positivity does NOT see [formula in source] '' — an honest, decided NEGATIVE result in the v508 style (the celestial/twistor story in tfpt_3 gains Step 22): does free reflection positivity ( v519) or anti-linear [formula in source] existence break for [formula in source] on the deformed mark family [formula in source] — which would DERIVE the v512 alignment bit from OS positivity? NO — (1) the CENSUS \ (exact solvesets, symbolic [formula in source] ): for EVERY [formula in source] exactly the two mark-SWAPPING reflections [formula in source] exist (axes [formula in source] , [formula in source] ; all [formula in source] cut/mark incidence solvesets EMPTY); mark-FIXING reflections exist exactly at [formula in source] (solveset [formula in source] , lost immediately at [formula in source] ); the v510/ v512 counterwitness [formula in source] carries the swap pair exactly; (2) RP IS [formula in source] -BLIND : bond-cut Gram inertias [formula in source] PD for all tested [formula in source] with the full sorted spectra IDENTICAL to [formula in source] digits (deviation [formula in source] ) — the ENTIRE free-RP spectral datum carries ZERO [formula in source] information; the [formula in source] odd- [formula in source] failure (site axes, [formula in source] , [formula in source] ) is a lattice-PLACEMENT artifact: at [formula in source] ALL [formula in source] have mark-compatible BOND axes with PD inertia [formula in source] ; continuum: the OS kernel in axis-adapted coordinates is EXACTLY [formula in source] — the axis position drops out identically (Cauchy–Stieltjes PD); the counterwitness PASSES free RP ( [formula in source] -point Gram [formula in source] ); (3) [formula in source] EXISTENCE IS [formula in source] -BLIND : [formula in source] , deck normalisation and Fock implementability ( [formula in source] , exact [formula in source] ) for every [formula in source] ; the ONLY [formula in source] -sensitive v519 clause ( [formula in source] ) is for [formula in source] not violated but NOT FORMULABLE (a mark-compatible order- [formula in source] rotation exists iff [formula in source] ) — it PRESUPPOSES the bit; same for the clock-tower clause; (4) the battery HAS TEETH at every [formula in source] : family A/antipode fails RP structurally (zero diagonal, [formula in source] ), the chirality– [formula in source] pinning persists ( [formula in source] ND) — RP separates the two real-structure FAMILIES, never the SIDES; (5) precondition controls: hexagonal (marks not concyclic — no seam circle), silver (deck not free), lifting audit (B [formula in source] index relabelling, [formula in source] -blind by construction; B' fails the [formula in source] negative control — discarded); \ FACE \#13 of the v512 equivalence web: the group generated by the admissible OS reflections is [formula in source] for every [formula in source] and closes to [formula in source] exactly at [formula in source] ( [formula in source] the clock) — [formula in source] faces, a typed REFORMULATION of the bit, not a derivation; \ the honest gap: marks decorating the STATE (defect/twist insertions, interacting [formula in source] ) [formula in source] exactly v519's \ scope; VERDICT: KILL exactly as preregistered — the free RP/ [formula in source] battery is the EIGHTH side-blind test on the v512 scoreboard ( [formula in source] ); the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; NO marker moves — the bit stays the one \ carrier input)

Research changelog · TFPT — Introduction and reading guide

v521_seam_bit_rp_blind.py ( SEAM.BIT.RPBLIND.01, 25 checks, [formula in source] 25 s; exact sympy solvesets [formula in source] exact Gram entries [formula in source] exact [formula in source] Fractions; inertia via [formula in source] -digit spectra, tolerance [formula in source] ; deterministic). S the anti-linear census (family D/A, counterwitness, face \#13 closure, cut incidence, side conditions); L the lattice

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documents/changelog/sections/004-source.tex · lines 1 to 31

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=150 2026-07-22 (X) ( v520 — the WP5e BCOV measure question DECIDED at probe level and promoted as the ledger row CELEST.WP5E.MEASURE.01: ``single-valuedness is derived, the completion reading wins'' — the [formula in source] consolidation in the v518 style, ERFOLG-A on the preregistered decision layer (the celestial/twistor story in tfpt_3 gains Step 21): which of the two exact, contradictory measures on [formula in source] is the true BCOV measure — (A) the DECLARED completion reading ( v516) or (B) the DERIVED chiral measure ( v518)? — (1) the INVARIANT SUBSPACE : [formula in source] in the dressed [formula in source] -component Weil system (exact rational nullspace); EVERY kernel vector lies in the [formula in source] -span of [formula in source] — the two Lagrangian gluings, both theta [formula in source] , level-1 quartic [formula in source] the UNPHASED trace; strict trivial-character solutions at physical weight [formula in source] : ZERO for every dressing ( [formula in source] combinations); (2) SOURCE 1 — the F-LEMMA : the only strict chiral families are [formula in source] (dims [formula in source] ) and [formula in source] (dims [formula in source] ), both with nontrivial [formula in source] -character EXACTLY; the canonical column-matched member obeys [formula in source] pointwise (certificate [formula in source] , [formula in source] ); EXACT change of variables [formula in source] fundamental-domain independence forces [formula in source] for EVERY chiral integrand: the v518 route was never a well-defined nonvanishing moduli integral (the kill is SHARPENED — its unfolded values are convention bookkeeping); (3) SOURCE 2 — the QUILLEN PAIRING : [formula in source] on all [formula in source] pairs and both generators; [formula in source] exactly vs one-sided [formula in source] ( [formula in source] -fixed: [formula in source] , [formula in source] defective); the doubled [formula in source] -dim hol [formula in source] antihol system closes STRICTLY at trivial character and physical weight (nullspaces [formula in source] ), contains the unphased diagonal ( [formula in source] ) AND the physical columns [formula in source] ( [formula in source] [formula in source] ); negative control hol [formula in source] hol: EMPTY nullspace [formula in source] ; (4) the CONSISTENCY CLOSURE : the forced unphased numerator in the v518 scaffold reproduces [formula in source] EXACTLY on every level [formula in source] ; [formula in source] -weighted spreads [formula in source] , [formula in source] , zero negative cells; [formula in source] — the [formula in source] -weighted mirror image of [formula in source] / [formula in source] ; linearity [formula in source] : the circle to v516 is CLOSED; (5) D3 — the [formula in source] /EH ANCHOR : only the declared reading hits ( [formula in source] , [formula in source] , scale tooth [formula in source] ); all three derived instantiations fail (spreads [formula in source] , [formula in source] sign wrong); (6) D1 — COLUMN CANONICALISATION : the physical AB column [formula in source] is contained EXACTLY in the [formula in source] family ( [formula in source] [formula in source] , one scalar per orbit — canonicalising [formula in source] ); the canonical member STILL fails every tester; NEGATIVE CONTROLS: [formula in source] ( [formula in source] / [formula in source] exact, [formula in source] -only), wrong form ( [formula in source] ), wrong weight (dev [formula in source] ), shuffle ( [formula in source] / [formula in source] ), planted family detected ( [formula in source] ), hol [formula in source] hol empty; \ TYPED PREMISES (the mandatory fence): TP-1 (F-independent moduli integral), TP-2 (nonvanishing — must source [formula in source] ), TP-3 ( v518 kernel convention), TP-4 (Quillen structure of BCOV [formula in source] ); \ the constructive BCOV derivation of the [formula in source] normalisation itself; WIRKUNG (text only, no marker moves): the v516 fence and the v518 tension now read ``decided at probe level for the declared reading under TP-1..TP-4 (v520)''; SEAM.EQUIV.TWISTOR.01 stays Open; VERDICT ERFOLG-A per the preregistered criteria — both constructive sources fire independently, the consistency closure carries)

Research changelog · TFPT — Introduction and reading guide

v520_celestial_wp5e_measure_decision.py ( CELEST.WP5E.MEASURE.01, 39 checks, [formula in source] 20 s; exact [formula in source] /Fraction/sympy rational nullspaces [formula in source] 1/960-grid phase arithmetic [formula in source] mpmath 30-digit kernels [formula in source] numpy double SVD, deterministic). S0 exact foundations (roots, ledgers, A-core [formula in source] [formula in source] -anchor targets, Weil re

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documents/changelog/sections/004-source.tex · lines 32 to 74

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=150 2026-07-22 (IX) ( v519 — the WOIT- [formula in source] milestone of the OS twistor bridge WOIT.OS.TWISTOR.01 executed and promoted as the ledger row WOIT.THETA.FREE.01: ``the real structure exists — and free reflection positivity picks the same family''; the celestial/twistor story in tfpt_3 is now TWENTY steps — (1) THETA CLASSIFICATION COMPLETE : exactly TWO families of anti-linear structures on [formula in source] normalise the clock [formula in source] — family D ( [formula in source] , [formula in source] ): [formula in source] EXACTLY at matrix level, [formula in source] ( [formula in source] IMPOSSIBLE: [formula in source] — Kramers-free), inverts the deck, fixed set [formula in source] the great circle through the deck poles; family A ( [formula in source] ): centralises the clock projectively (NEVER inverts it), [formula in source] per [formula in source] , fixed set [formula in source] resp.\ empty; ROLE SEPARATION: family A DEFINES the euclidean section (Woit's [formula in source] side: [formula in source] , no real points — replicated exactly on [formula in source] ), family D REFLECTS it (the OS conjugation, [formula in source] conjugation with real points [formula in source] ); (2) MARK PINNING : [formula in source] preserves the [formula in source] marks iff [formula in source] — a [formula in source] -element [formula in source] -TORSOR ( [formula in source] mark axes, [formula in source] silver-midpoint axes), clock conjugation [formula in source] [formula in source] [formula in source] clock orbits; (3) SPIN/FOCK : the [formula in source] plane has no phase leaks ( [formula in source] ); exact [formula in source] : [formula in source] with [formula in source] (normalised [formula in source] ), inverts the clock tower ( [formula in source] ) and normalises the deck; the KRAMERS DICHOTOMY: the deck-induced candidate [formula in source] has [formula in source] — the v510 split/nonsplit dichotomy IS the [formula in source] vs [formula in source] dichotomy; the deck does NOT furnish [formula in source] , the seam-circle REFLECTION does; (4) KILL TEST 1 (free level) : does NOT fire — [formula in source] exists with [formula in source] AND [formula in source] and satisfies all three side conditions simultaneously (marks, deck normalisation, spin/Fock); (5) FREE RP : the NS vacuum [formula in source] has [formula in source] exactly; preconditions exact ( [formula in source] , [formula in source] , [formula in source] ; the deck FAILS anti-invariance); BOND CUT: one-particle Gram [formula in source] PD (min eigenvalue [formula in source] , [formula in source] digits), even [formula in source] sector [formula in source] PD, [formula in source] complete half-sided algebra PD (even [formula in source] odd each [formula in source] ) — RP with NO degree truncation; twist [formula in source] FORCED ( [formula in source] non-Hermitian); CONTROLS: the site cut fails exactly ( [formula in source] , inertia [formula in source] ; continuum control: Cauchy–Stieltjes strictly positive — a lattice-PLACEMENT artifact, RP selects the site placement relative to the marks); the clock-CENTRALISING family-A structure fails RP structurally ( [formula in source] ) — RP and [formula in source] select the SAME family; bonus: the anti-chiral state flips the odd sector to [formula in source] ND (the free shadow of kill test 3); / \ NOT shown: the interacting algebra [formula in source] (kill test 1 stays live there), gauge-fixed RP (kill test 2), OS reconstruction, chirality without mirrors (kill tests 3/6), [formula in source] incidence (kill test 7) — the WOIT- [formula in source] / [formula in source] roadmap named ( [formula in source] [formula in source] on the gauge-invariant subalgebra [formula in source] gauge-fixed RP on the equivariant SDYM [formula in source] sector; [formula in source] the OS quotient of the free system explicit; [formula in source] the [formula in source] duality vs [formula in source] typed; [formula in source] the chirality theorem [formula in source] the mark incidence); TWO CONTRACT PRECISIONS (prose, no marker): (i) `` [formula in source] induced by the seam reflection'' means the seam-circle REFLECTION, not the deck — the deck furnishes the [formula in source] Kramers class (the v510 bridge); (ii) the marks sit RP-side on the BOND MIDPOINTS of the [formula in source] -Majorana circle; Wolfram extension [formula in source] (verified engine run); NO marker moves — WOIT.OS.TWISTOR.01 stays Open: kill test 1 is discharged on the FREE level only and stays formally live on the interacting algebra)

Research changelog · TFPT — Introduction and reading guide

v519_woit_theta_rp_free.py ( WOIT.THETA.FREE.01, 34 checks, [formula in source] 20 s; exact sympy [formula in source] exact [formula in source] Fractions; RP definiteness via [formula in source] -digit spectra of exact Hermitian matrices, tolerance [formula in source] ; deterministic). Part W: W-S1 the two-family classification (symbolic solve); W-S2 family D (relations, Kramers-free, mark pinning, seam action, torso

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documents/changelog/sections/004-source.tex · lines 75 to 123

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=150 2026-07-22 (VIII) ( v518 — the WP5e [formula in source] chain ( [formula in source] ) DECIDED and promoted as the ledger row CELEST.WP5E.DELTA1.01: ``the derived chiral measure kills the [formula in source] route'' — an honest, decided NEGATIVE result in the v508 style, with the v516 tension stated: does the Harvey–Moore/BCOV fundamental-domain integral on [formula in source] , evaluated under a measure DERIVED from blockwise [formula in source] covariance of the dressed [formula in source] -component Weil system (solved for — not declared, not scanned), deliver the twisted contact vector [formula in source] or the [formula in source] slice? NO — (1) the 16-COMPONENT WEIL COMPLETION ( [formula in source] ): the discriminant module of [formula in source] is [formula in source] with [formula in source] , Gauss sums [formula in source] (signature [formula in source] rank [formula in source] ), the Weil relations hold EXACTLY in [formula in source] ( [formula in source] , [formula in source] , [formula in source] , [formula in source] , tensor split [formula in source] ), the diagonal [formula in source] and anti-diagonal [formula in source] are the two invariant Lagrangians (both counts [formula in source] : two [formula in source] gluings), [formula in source] with [formula in source] of every [formula in source] -image weight on the [formula in source] shifted classes, and the [formula in source] -vector theta [formula in source] -covariance CLOSES: the [formula in source] E1.5 residual [formula in source] (naive [formula in source] -character rule) drops to [formula in source] ; (2) the OBSTRUCTION IS A FINITE [formula in source] CHARACTER, IDENTIFIED ( [formula in source] ): the dressed gauge blocks [formula in source] carry constant transport [formula in source] ( [formula in source] + digits, recognised as exact [formula in source] -grid phases at [formula in source] ), the [formula in source] -fixed pairs [formula in source] carry [formula in source] EXACTLY (the naked level-matching defect), the transport-groupoid loops land in [formula in source] resp.\ [formula in source] with joint holonomy eigenspaces dim [formula in source] resp.\ [formula in source] and every eigen-phase of order [formula in source] ; the KOBOUNDARY TEST: the [formula in source] relation defects [formula in source] , [formula in source] , [formula in source] are [formula in source] EXACTLY on all [formula in source] pairs — the multiplier system is a CHARACTER of the orbit stabilisers, NOT a genuine 2-cocycle, and on [formula in source] it is [formula in source] ; (3) the CANCELLATION EXISTS AND IS THE TWISTED FIBRE BLOCK [formula in source] , NOT THE THREE SPHERE AXIONS: [formula in source] is an exact identity ( [formula in source] + digits; the axion [formula in source] -phases are v502 vacuum-energy data), the T-fix mechanism is one line of exact phase arithmetic — [formula in source] at every [formula in source] -fixed node — and the exact CANCELLATION TABLE reads: none [formula in source] residual order [formula in source] , [formula in source] (the three sphere axions) [formula in source] , [formula in source] , [formula in source] (hol AND anti), wrong weights [formula in source] ; the strict solutions are exactly [formula in source] (dims [formula in source] ) and [formula in source] (dims [formula in source] ) at [formula in source] , certified on the dressed functions at a fresh [formula in source] ( [formula in source] , NO residual multiplier); (4) the DECISION — ALL THREE PREREGISTERED TESTERS FAIL: under both derived solutions the integral ( [formula in source] -digit kernels, negative-exponent cell audit, cut-6 vs cut-8 scan) fails [formula in source] (fractions [formula in source] / [formula in source] ), fails [formula in source] ( [formula in source] ), fails [formula in source] (spreads [formula in source] / [formula in source] ) and the [formula in source] slice, and the honest [formula in source] orbit rebalance rescues nothing in the positive cone ( [formula in source] : [formula in source] only at [formula in source] ; [formula in source] : only at [formula in source] ) — a GENUINE KILL on the derived surface; (5) NEGATIVE CONTROLS: [formula in source] /Eguchi–Hanson (gauge-only residual order [formula in source] — the [formula in source] defect is [formula in source] -specific — and the SAME fibre dressing cancels it to [formula in source] ), [formula in source] (only even sectors, all axion [formula in source] -characters in [formula in source] : the order-4 supply structurally absent), wrong form [formula in source] ( [formula in source] , its [formula in source] -rule fails at [formula in source] ), wrong signature ( [formula in source] exactly); \ the [formula in source] KS-weight identification (deck weights [formula in source] the twistor fibre weights forced by the v514 incidence ledger — exact match, NOT a complete BCOV derivation) [formula in source] the kernel-family convention [formula in source] the discrete [formula in source] choice (both evaluated, both fail); the MANDATORY TENSION FENCE: the DECLARED completion reading ( v516/M2) delivers the [formula in source] slice and cancels [formula in source] ; the DERIVED chiral measure (this module) fails all three testers — both are exact; the sharp open question is which of the two is the true BCOV measure — neither result is hidden behind the other; \ the BCOV-integral derivation on [formula in source] that decides between the two measures; Wolfram extension [formula in source] (verified engine run); NO marker moves — the [formula in source] route is decided negative under the derived measure, the cubic-GS question stays dissolved, SEAM.EQUIV.TWISTOR.01 stays Open, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v518_celestial_wp5e_delta1_derived_kill.py ( CELEST.WP5E.DELTA1.01, 30 checks, [formula in source] 20 s; exact [formula in source] /Fraction/1-960-grid phase arithmetic [formula in source] mpmath 30-digit kernels [formula in source] numpy double SVD, deterministic). S0 conventions [formula in source] 16-class ledgers [formula in source] targets; S1 the 16-component Weil system (exact) [formula in source] the E1.5 clo

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2026-07-22 (VII) ( v517 — WP5e back-reaction milestone M3 ``the [formula in source] uplift'' executed (SUCCESS on the preregistered v514 S8.3 criterion), promoted as the ledger row CELEST.WP5E.M3.01: the [formula in source] GH multipole ( [formula in source] the [formula in source] direction) is uplifted to the twistor-potential kernel [formula in source] — the LOG of the v515 family polynomial — and the induced K\"ahler-potential correction is a log-type correction COUPLED TO THE CENTRE COUNT ON FOUR SCALES — (1) the KERNEL BRIDGE: the [formula in source] section is a NULL coordinate ( [formula in source] identically for an ARBITRARY kernel [formula in source] : the uplift is well-typed), the RESIDUE IDENTITY [formula in source] holds EXACTLY (residue [formula in source] ), so the GH potential [formula in source] IS the [formula in source] -derivative of the contour transform of [formula in source] ; flux [formula in source] per centre, source charge [formula in source] (the [formula in source] -ledger matched); (2) the ASYMPTOTIC KERNEL LOG: [formula in source] with LOG COEFFICIENT [formula in source] centre count (the CPS `` [formula in source] '' analogue at kernel level); at the clock-fixed seam fibre [formula in source] the [formula in source] slot closes and the first correction is EXACTLY [formula in source] the [formula in source] multipole in kernel clothes; exact [formula in source] -grading ( [formula in source] pieces PURE [formula in source] , [formula in source] piece [formula in source] [formula in source] -free: the [formula in source] breaking sits exclusively in the [formula in source] pieces); NO [formula in source] power terms (the v514 honest zero preserved — the [formula in source] correction is power-law at infinity); the once-integrated GLT tower [formula in source] with [formula in source] unless [formula in source] and [formula in source] : EVERY correction carries the prefactor [formula in source] centre count; (3) the EXCEPTIONAL-LOCUS LOG: [formula in source] ( [formula in source] -coefficient [formula in source] , clock phase [formula in source] ); the modulus response [formula in source] equals [formula in source] AT the exceptional locus and falls off as [formula in source] at infinity (no constant, no log): the [formula in source] -log lives at the exceptional locus, exactly as v514 S6.3 demanded; (4) the PERIOD RESPONSE: [formula in source] is LINEAR in [formula in source] (uniform first-order shift: lockstep [formula in source] phase ratios [formula in source] preserved exactly), [formula in source] uniformly, and the integrated shift around the [formula in source] circle is the monodromy [formula in source] ONE Coxeter clock step (the v493 monodromy REPRODUCED from perturbation theory; the finite monodromy is the cyclic centre permutation [formula in source] ); the node [formula in source] -support is [formula in source] -FREE (the [formula in source] seam bridge is [formula in source] -rigid), all [formula in source] pair discriminants [formula in source] ( [formula in source] connectivity: the forced uniform flux vector persists), the BM kernel is modulus-free with [formula in source] (the quantised fluxes cannot move); (5) NEGATIVE CONTROLS: the [formula in source] multipole is [formula in source] -independent in [formula in source] AND in the kernel (clock-invariant, breaks nothing); the [formula in source] /Eguchi–Hanson analogue reads [formula in source] on EVERY dial ( [formula in source] amplitude [formula in source] , kernel log [formula in source] , exceptional log [formula in source] , response [formula in source] , monodromy [formula in source] ); wrong centre counts [formula in source] : kernel log coefficient [formula in source] , modulus slot [formula in source] — the observable MOVES with the centre count; forbidden family [formula in source] : [formula in source] (selection rule broken), [formula in source] (no [formula in source] -log) — fails BOTH uplift dials; \ the GLT dictionary ( [formula in source] the GH K\"ahler-potential kernel, Lindstr\"om–Ro cek / Ivanov–Ro cek); \ the full nonlinear K\"ahler potential of the resolved [formula in source] ALE; with v516 the v514 fence M1–M3 is FULLY WORKED OFF; Wolfram extension [formula in source] (verified engine run); NO marker moves — the KILL (decoupling from the centre count) does NOT fire, SEAM.EQUIV.TWISTOR.01 stays Open (preparation, not construction), SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v517_celestial_wp5e_m3_a0_uplift.py ( CELEST.WP5E.M3.01, 23 checks, [formula in source] 7 s; exact sympy, no floats; deterministic). S0 replication (GH multipole ledger [formula in source] the twistor family at general orbit phase, v515 slice); S1 the kernel bridge (null coordinate, residue [formula in source] -ledger identity, source flux); S2 the uplift (asymptotic log [formula in source] , seam-fibre correction [f

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documents/changelog/sections/004-source.tex · lines 175 to 211

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2026-07-22 (VI) ( v516 — WP5e back-reaction milestone M2 ``the twisted Kodaira–Spencer measure'' executed (SUCCESS on the preregistered v514 S8.2 criterion, ON THE DECLARED COMPLETION MEASURE — verdict B), promoted as the ledger row CELEST.WP5E.M2.01: the one-loop box coefficient per sector on [formula in source] under the completion contact term [formula in source] — the twisted-sector LOOP contributes the UNPHASED sector trace with the [formula in source] zero-mode normalisation [formula in source] , of which the Atiyah–Bott skeleton kept only the phase-weighted insertion part — (1) the COMPLETION-WEIGHT IDENTITY (the centrepiece): per glue class [formula in source] EXACTLY ( [formula in source] the v502 sector Casimir energies, [formula in source] the McKay/Kronheimer charges, v505 S4.3 index bridge): THE THREE SPHERE AXIONS PAIR THROUGH THEIR OWN ch [formula in source] CHARGES — an exact identity, NO free scale, no fit; (2) PARAMETER-FREE LOCKS: [formula in source] for ANY scale [formula in source] (the ch [formula in source] pattern alone kills [formula in source] ); ratio [formula in source] the [formula in source] -forced leading ratio (REPRODUCED, not fitted); the [formula in source] budget fixes [formula in source] uniquely (leading system det [formula in source] , unique weights [formula in source] ); (3) the SUCCESS TABLE: [formula in source] — a PERFECT Okubo square ( [formula in source] , [formula in source] in EVERY twisted channel: [formula in source] ); total [formula in source] Dedekind [formula in source] Okubo [formula in source] the UNIQUE quartic-free weighting of v505 S3.8 (the rigidity theorem is exactly what the measure lands on); both v508 certificates KILLED ( [formula in source] , [formula in source] ); the v511 slice [formula in source] SUPPLIED EXACTLY ( [formula in source] ) — NO cubic [formula in source] -channel needed ( [formula in source] free [formula in source] ); remainder inside the exchange span ( [formula in source] , [formula in source] ): the BULK axion cancels every channel with the SAME [formula in source] , the twisted propagator carrying the AB zero-mode factor [formula in source] ; the v514 measure chain stays [formula in source] -blind; (4) NEGATIVE CONTROLS: wrong scale [formula in source] leaves [formula in source] — only [formula in source] clears the budget; the [formula in source] shuffle breaks [formula in source] AND [formula in source] ; [formula in source] glue keeps [formula in source] / [formula in source] — the KILL branch FIRES there (Okubo failure inherited: [formula in source] doubly special); [formula in source] degenerates to the [formula in source] target and breaks the conjugation pairing [formula in source] the index bridge; the [formula in source] /Eguchi–Hanson anchor PASSES with the same mechanism ( [formula in source] , coupling scale [formula in source] centre count); (5) the MULTIPLIER NOTE (cross-reference to the parallel [formula in source] strand): the contact weights [formula in source] are REAL RATIONALS with no multiplier system of their own; the [formula in source] residual phases are the SQUARES of the [formula in source] discriminant [formula in source] -phases [formula in source] — orders [formula in source] squaring to [formula in source] , a finite [formula in source] system; Gauss sums [formula in source] , [formula in source] , full Weil sum [formula in source] ; \ the MANDATORY FENCE: the completion reading (the loop of twisted states carries the UNPHASED sector trace with the same zero-mode normalisation) is DECLARED, supported by the [formula in source] modular-completion finding, NOT derived from the BCOV integral; \ the BCOV-integral derivation ( [formula in source] territory); Wolfram extension [formula in source] (verified engine run); NO marker moves — the KILL (leftover independent quartic in ANY sector) does NOT fire, the completion reading stays -declared, SEAM.EQUIV.TWISTOR.01 stays Open, SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v516_celestial_wp5e_m2_twisted_ks_measure.py ( CELEST.WP5E.M2.01, 23 checks, [formula in source] 1 s; exact sympy/Fraction, no floats; deterministic). S0 replication (roots, class quartics, [formula in source] two routes, bulk Okubo); S1 the index bridge [formula in source] the completion weights (no free scale, parameter-free locks); S2 the contact term (two forms, genuine-contact certificate); S3 the success table

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documents/changelog/sections/004-source.tex · lines 212 to 244

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2026-07-22 (V) ( v515 — WP5e back-reaction milestone M1 ``the [formula in source] [formula in source] '' executed (SUCCESS on the preregistered v514 S8.1 criterion), promoted as the ledger row CELEST.WP5E.M1.01: the back-reacted holomorphic [formula in source] -form [formula in source] is CLOSED FORM on the [formula in source] twistor family, every [formula in source] period is [formula in source] -integral with the lockstep flux vector, and the lens geometry FORCES the source charge [formula in source] — (1) the RESIDUE FORM DERIVED: on [formula in source] all three ambient representatives satisfy [formula in source] exactly and pull back to [formula in source] (Poincar\'e residue, derived not assumed); orbifold-cover pullback at [formula in source] : [formula in source] (flat form) — the residue normalisation CARRIES the source charge [formula in source] ; clock [formula in source] ( v492 S5 replicated); weight ledger [formula in source] , [formula in source] ; (2) the TWISTOR FAMILY CLOSED: from the four [formula in source] centre sections [formula in source] exactly [formula in source] ( [formula in source] identically; [formula in source] gives exactly the v493 family; [formula in source] opens only off-seam), CY-compatible clock lift [formula in source] , [formula in source] , [formula in source] ; (3) [formula in source] CLOSED [formula in source] PERIOD TABLE: [formula in source] with CPS/Bochner–Martinelli kernels on the centre twistor lines, [formula in source] off-source; boundary [formula in source] at the orbifold point [formula in source] (minimal invariant charge [formula in source] — the lens fundamental domain FORCES [formula in source] ), deformed phase [formula in source] , linking [formula in source] uniformly [formula in source] , per-sphere flux vector [formula in source] (forced uniform: clock orbit [formula in source] [formula in source] connectivity), seam-fibre phase vector [formula in source] ; [formula in source] carries ZERO [formula in source] -flux (all flux sourced); [formula in source] fibre residue [formula in source] transversal residue (density [formula in source] ); (4) CLOCK COVARIANCE: [formula in source] for ALL [formula in source] ; the [formula in source] collision nodes sit exactly on the [formula in source] eighth roots of unity ( [formula in source] , the [formula in source] bridge), clock orbits [formula in source] , honest conifold points (Hessian det [formula in source] , quadric rank [formula in source] ); (5) the HONEST KILL PROBE: forbidden family [formula in source] : [formula in source] lockstep (vs [formula in source] ), [formula in source] -support [formula in source] twelfth roots [formula in source] , no antipodal pairing — BUT the [formula in source] quantisation holds there TOO: integrality alone is NOT the discriminator, the discriminator is the lockstep phase structure [formula in source] the clock forcing; the v509 dial survives; (6) ANCHORS [formula in source] CONTROLS: EH/ [formula in source] (charge [formula in source] forced), CPS original (every integer [formula in source] allowed), [formula in source] ( [formula in source] , collapse at step zero), fractional charges [formula in source] excluded; \ global kernel patching / Hitchin small resolution / CPS brane dictionary; \ M2 (twisted KS measure), M3 ( [formula in source] uplift), the quantised BCOV coefficient; Wolfram extension [formula in source] (verified engine run); NO marker moves — M2/M3 and BCOV stay , SEAM.EQUIV.TWISTOR.01 stays Open ( v515 is preparation, not construction), SEAM.EQUIV.01 untouched)

Research changelog · TFPT — Introduction and reading guide

v515_celestial_wp5e_m1_omega_n.py ( CELEST.WP5E.M1.01, 30 checks, [formula in source] 1 s; exact sympy, no floats; deterministic). S1 the residue form (three routes, cover factor [formula in source] , weight ledger, EH anchor, wrong-weight control); S2 the twistor family (closed form, [formula in source] reality, clock lift, section-level dichotomy); S3 periods (generic reduction, lockstep, covariance, collision ledg

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2026-07-22 (IV) (external review integrated: route renamed, object diagram, group-extension definition, SEAM.EQUIV route split (MMST/TWISTOR ids, no status change), [formula in source] role table, WOIT.OS.TWISTOR.01 contract — a pure structure/text integration, NO new physics claims, NO marker moves, suite unchanged at [formula in source] )

Research changelog · TFPT — Introduction and reading guide

An external expert review of the celestial/twistor branch confirmed the substance and asked for semantic precision — role separation, status clarity, and the exact naming of what is missing. Six changes plus one new central research contract, all editorial/structural: (\"A1) Route renamed [formula in source] the Woit bridge. The tfpt_3 celestial section and the contract heading are now ``The celestial and twistor con

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explicit script identifier v479_kronheimer_quiver_bridge.py
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explicit script identifier v506_seam_clock_rigidity.py
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explicit script identifier v510_seam_bit_freedom.py
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explicit script identifier v336_continuum_limit.py
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explicit script identifier v492_celestial_z4_orbifold.py
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cross reference join SeamApplicabilityLedger.lean
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explicit script identifier v493_celestial_wp2_clock_deformation.py
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explicit script identifier v497_celestial_wp5a_null_ideal.py
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explicit script identifier v514_celestial_wp5e_eps1_axion_slot.py
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explicit script identifier v507_seam_bit_origin.py
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explicit file citation next.txt
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2026-07-22 (III) ( v514 — WP5e- [formula in source] ``the [formula in source] bulk-axion slot'' executed (verdict B), promoted as the ledger row CELEST.WP5E.EPS1.01: the [formula in source] tower field of the celestial route is now a CONSTRUCTION, [formula in source] is pinned three ways, and the first honest back-reaction step is taken in Gibbons–Hawking form — (1) the EQUIVARIANT [formula in source] SLOT: the pushforward ledger [formula in source] on [formula in source] gives per degree [formula in source] exactly [formula in source] classes [formula in source] the exact wave-operator nullspaces ( [formula in source] for [formula in source] ), the v492 action on the fibre coordinates [formula in source] with incidence-forced column weights [formula in source] closes the equivariant bookkeeping BLOCK BY BLOCK (all [formula in source] , all [formula in source] characters); character series [formula in source] , [formula in source] , [formula in source] ; the [formula in source] slot has multiplicity [formula in source] — THE BULK AXION SURVIVES THE PROJECTION; Molien invariant ring [formula in source] — [formula in source] , [formula in source] , relation degree [formula in source] the [formula in source] weight ( v492/ v493 bridge); E3 bijection sharpened (twisted minimal content [formula in source] [formula in source] the Coxeter eigenvalues, [formula in source] ); graviton control: [formula in source] invariant only from fibre degree [formula in source] with multiplicity [formula in source] ; (2) [formula in source] TRIPLY PINNED: Okubo [formula in source] on the [formula in source] glue roots ( [formula in source] , [formula in source] ); the measure chain cancels [formula in source] EXACTLY (vertex [formula in source] [formula in source] , propagator [formula in source] , anomaly [formula in source] ; [formula in source] for arbitrary [formula in source] ; wrong bookings EXCLUDED: anomaly-only [formula in source] , missing propagator renormalisation [formula in source] ); flux (minimal CPS quantum [formula in source] , single channel iff [formula in source] , [formula in source] exact); (3) the GH/ [formula in source] BACK-REACTION STEP: invariant [formula in source] -centre configurations [formula in source] exactly [formula in source] branches, the free orbit re-derives the v493 family ( [formula in source] , [formula in source] , monodromy [formula in source] one clock step), the charge- [formula in source] GH point is exactly [formula in source] ( [formula in source] : seam boundary [formula in source] ), periods [formula in source] LOCKSTEP ( v509 counter-check), Coxeter clock from geometry ( [formula in source] ), source charge [formula in source] , EH asymptotic log coefficient EXACTLY [formula in source] (the CPS log is an exceptional-locus statement; Burns contrast [formula in source] ), multipole rule [formula in source] with [formula in source] carrying [formula in source] ; controls [formula in source] ( [formula in source] irrational, squares only [formula in source] ), [formula in source] (Veronese), [formula in source] (three channels); \ conditional on Costello's flat- [formula in source] matching; \ the quantised BCOV coefficient and the twisted channels ( [formula in source] ) — M1–M3 preregistered (the [formula in source] [formula in source] / the twisted KS measure / the [formula in source] uplift, each with success [formula in source] kill); Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e stays , SEAM.EQUIV.01 untouched, CELEST.SEAM.01 stays Open)

Research changelog · TFPT — Introduction and reading guide

v514_celestial_wp5e_eps1_axion_slot.py ( CELEST.WP5E.EPS1.01, 34 checks, [formula in source] 4 s; exact sympy/Fraction, no floats; deterministic). S1 Penrose accounting; S2 equivariant ledger [formula in source] character series [formula in source] Molien [formula in source] E3 sharpening [formula in source] graviton control; S3 the [formula in source] residue (Okubo / measure / flux) with honest gaps; S4–S5 GH centr

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documents/changelog/sections/005-source.tex · lines 1 to 36

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explicit file citation v514_celestial_wp5e_eps1_axion_slot.py
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explicit script identifier v514_celestial_wp5e_eps1_axion_slot.py
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explicit script identifier v493_celestial_wp2_clock_deformation.py
literal short identifier uniquely resolves in local script registry
explicit claim identifier status_ledger.csv
exact local ledger claim identifier
cross reference join tfpt_readouts_extension.wl
TeX and evidence source explicitly name the same Python identifier; statement equivalence not inferred
explicit file citation script_registry.csv
literal source filename/path in TeX
explicit script identifier v509_celestial_wp5e_eps2_level_from_flux.py
literal short identifier uniquely resolves in local script registry
explicit claim identifier status_ledger.csv
exact local ledger claim identifier
cross reference join tfpt_readouts_extension.wl
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explicit file citation next.txt
literal source filename/path in TeX
explicit script identifier v492_celestial_z4_orbifold.py
literal short identifier uniquely resolves in local script registry
explicit claim identifier status_ledger.csv
exact local ledger claim identifier
explicit claim identifier status_ledger.csv
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explicit file citation run_all.py
literal source filename/path in TeX
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2026-07-22 (II) ( v513 — the [formula in source] negative certificate, promoted as the ledger row CELEST.DTERM.NONDERIV.01 (anti-numerology certificate in the v508 style, honest rigid NEGATIVE result): can geometry derive [formula in source] ? NO — the v511 \ fence `` [formula in source] '' does NOT survive the honest four-route battery with its PRE-DECLARED look-elsewhere ledger: (1) the CONVENTION TABLE gives [formula in source] across five normalisations (probe tr-fund/ [formula in source] -Killing; Gell-Mann; [formula in source] -Killing; plain trace; ch [formula in source] -normalised [formula in source] ) — only [formula in source] of [formula in source] hits [formula in source] , while the convention-STABLE content is the factorisation [formula in source] , both factors \ (Killing propagator [formula in source] from [formula in source] over the actual roots; [formula in source] -slot fixing via [formula in source] ); (2) K1 DEAD: the charge-legal flux pairings [formula in source] give [formula in source] — they BRACKET [formula in source] and both MISS; the only flux hit [formula in source] is the FORBIDDEN [formula in source] pairing (charge [formula in source] , v511 innerness); look-elsewhere: [formula in source] expressions from [formula in source] \ numbers, [formula in source] hits on [formula in source] , controls [formula in source] , [formula in source] , [formula in source] ; (3) K2: quantisation delivers only lattices ( [formula in source] with [formula in source] the [formula in source] nd multiple, no minimality; strict ch [formula in source] units [formula in source] EXCLUDE [formula in source] ); the cubic quantum is lattice-dependent ( [formula in source] on coroots, [formula in source] on weights), the integer [formula in source] has [formula in source] factorisations; (4) K3 PROVENANCE CLASH (the death blow): cubic indices [formula in source] with [formula in source] numerically [formula in source] — but the quartic class decomposition [formula in source] comes from classes [formula in source] vs the cubic [formula in source] from classes [formula in source] : same number, disjoint mechanism [formula in source] coincidence; the Weyl side is WRONG ( [formula in source] -channel is [formula in source] , [formula in source] ; [formula in source] has no cubic; [formula in source] a second accidental [formula in source] ); (5) K4 controls ( [formula in source] , [formula in source] doubling [formula in source] , false [formula in source] with six cubics, [formula in source] ) separate consistently; VERDICT: NUMEROLOGY as a derivation claim — the v511 \ fence stays a fence, now typed look-elsewhere-loaded; the honest \ core is [formula in source] ; Wolfram extension [formula in source] (verified engine run); NO marker moves — the fence stays , the physical generation of the [formula in source] stays , CELEST.SEAM.01 stays Open)

Research changelog · TFPT — Introduction and reading guide

v513_celestial_dterm_nonderivation.py ( CELEST.DTERM.NONDERIV.01, 24 checks, [formula in source] 2 s; exact sympy/Fraction, no floats; deterministic). N0 baseline ( [formula in source] roots [formula in source] , [formula in source] , [formula in source] two routes, [formula in source] pinned by the [formula in source] slot alone); N1 convention table [formula in source] the stable factorisation [formula in source] ;

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documents/changelog/sections/005-source.tex · lines 37 to 68

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explicit claim identifier status_ledger.csv
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explicit file citation tfpt_readouts_extension.wl
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explicit script identifier v511_celestial_wp5e_delta2_tensor_ledger.py
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explicit file citation v513_celestial_dterm_nonderivation.py
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explicit claim identifier status_ledger.csv
exact local ledger claim identifier
explicit file citation run_all.py
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explicit file citation script_registry.csv
literal source filename/path in TeX
explicit claim identifier status_ledger.csv
exact local ledger claim identifier
explicit script identifier v508_celestial_wp5e_gamma_pairing.py
literal short identifier uniquely resolves in local script registry
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explicit file citation next.txt
literal source filename/path in TeX
explicit claim identifier status_ledger.csv
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explicit script identifier v513_celestial_dterm_nonderivation.py
literal short identifier uniquely resolves in local script registry
cross reference join tfpt_readouts_extension.wl
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2026-07-22 (I) ( v512 — the flag-transitivity equivalence web promoted as SEAM.TAU.FLAG.01: the [formula in source] attack executed on the free RP seam circle — BARE MARK-TRANSITIVITY IS FALSIFIED as a selector (on the test family [formula in source] , [formula in source] , the symmetry group is the pair-exchanging [formula in source] for EVERY [formula in source] , simply transitive on the four marks; complete census: deck-commuting M\"obius maps are diagonal/antidiagonal; hardening: ALL undirected per-mark data are identical for every [formula in source] — no local jet sees the bit), and THE SHARP SELECTOR is FLAG transitivity (marks AND their two sides indistinguishable) [formula in source] the clock — stabiliser jump [formula in source] , flag/arc orbits [formula in source] , order- [formula in source] rotation ( [formula in source] solveset [formula in source] ), mark mirror [formula in source] ; welded into a [formula in source] -FOLD EQUIVALENCE WEB (every link exact): clock rotation, [formula in source] , mark mirror, flag transitivity, three spectral degeneracies (odd-doublet split [formula in source] , zero only at [formula in source] — counterwitness exactly [formula in source] ; arc-Laplacian degeneracy [formula in source] ; the v215-K3 indicator in CLOSED FORM [formula in source] — the v503 lattice curve analytically), [formula in source] -twist existence ( [formula in source] ; Atiyah–Bott rationality [formula in source] -BLIND — [formula in source] for all [formula in source] , [formula in source] rational non-CM: rationality selects NOTHING), cusp- [formula in source] -cycle implementability (H4 rigidity: [formula in source] with orders [formula in source] cannot induce it; centraliser scalar, [formula in source] nonscalar [formula in source] no projective involution — projective order exactly [formula in source] , [formula in source] -shadow consistent v510), harmonic, [formula in source] ; NEGATIVE CONTROLS: hexagonal (not concyclic, fails preconditions), silver (harmonic but topologically dead), [formula in source] marks (impossible on the free circle: [formula in source] vs [formula in source] invariant subsets; bare [formula in source] transitivity already forces equal spacing — `` [formula in source] counts''); \ THE REST: the last input reduces from a continuous modulus to ONE discrete symmetry-lift bit ( [formula in source] : side-indistinguishability of the four equally-decorated marks), v216 local equality does NOT deliver it, its negation is now concretely measurable; scoreboard: the counterwitness passes all [formula in source] established unsided tests, fails all [formula in source] clock-equivalent ones; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , QGEO.REALIZE.01 and P2.TYPING.01/ AX.P2.01 text-precised only, SEAM.BIT.FREEDOM.01 cross-referenced)

Research changelog · TFPT — Introduction and reading guide

v512_seam_tau_flag.py ( SEAM.TAU.FLAG.01, 29 checks, [formula in source] 6 s; sympy-exact [formula in source] mpmath 30 digits [formula in source] one numpy lattice commutator; deterministic). S0 family frame (counterwitness inside the family: [formula in source] , [formula in source] , cross-ratio [formula in source] ); H1 complete symmetry census (census basis, rotation solvesets, stabiliser jump, flag/arc orbits,

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explicit file citation v512_seam_tau_flag.py
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explicit script identifier v216_marks_gauss_bonnet.py
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explicit script identifier v510_seam_bit_freedom.py
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explicit file citation run_all.py
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explicit script identifier v503_qgeo_emergence_light.py
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explicit claim identifier status_ledger.csv
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explicit file citation seam_tau_i_established_selector_probe.py
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explicit claim identifier status_ledger.csv
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explicit claim identifier status_ledger.csv
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explicit file citation script_registry.csv
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2026-07-21 (XXIII) ( v511 — WP5e- [formula in source] of CELEST.SEAM.01 ``the full-tensor ledger'' promoted as CELEST.WP5E.DELTA2.01 (intermediate verdict, exact): the named escape route of the v508 exchange no-go executed on the FULL adjoint tensor structure of [formula in source] — the COLLAPSE IS CONFIRMED full-tensorially AND arity-crossing (the INNERNESS THEOREM: [formula in source] semisimple with NO [formula in source] (class- [formula in source] roots [formula in source] , root span rank [formula in source] ), [formula in source] in the Cartan OF [formula in source] [formula in source] every invariant tensor carries total charge [formula in source] : the bilinear Hom table is nonzero ONLY at [formula in source] (dims [formula in source] ) and ALL [formula in source] non-neutral trilinear sector triples have [formula in source] ), BUT ONE CUBIC DOOR OPENS: of the neutral trilinears ( [formula in source] sym [formula in source] antisym, [formula in source] , [formula in source] , [formula in source] , [formula in source] ; all cross-sector ones pure brackets) the UNIQUE totally symmetric survivor is the [formula in source] [formula in source] -symbol ( [formula in source] has no cubic Casimir, [formula in source] protects [formula in source] ), whose exchange quartic [formula in source] (TWO independent routes, Killing propagator [formula in source] from the roots) has [formula in source] — the v508 master kill (product theorem) does NOT extend to cubic vertices; the pairing stays OBSTRUCTED in the charge reading with the genuinely WEAKER certificate [formula in source] , [formula in source] ( [formula in source] rank [formula in source] , augmented [formula in source] ), and becomes EXACTLY solvable relaxed: [formula in source] (residual [formula in source] ); \ fences [formula in source] , [formula in source] ; controls: [formula in source] has NO symmetric cubic and no [formula in source] block ( [formula in source] doubly special), false [formula in source] /sector assignments separate; the [formula in source] burden SHARPENED to the [formula in source] slice or the selection-rule relaxation — and the [formula in source] exploration run itself stands UNDECIDED at exploration level (strict holomorphic [formula in source] reading REFUTED at the [formula in source] /Eguchi–Hanson anchor [formula in source] method boundary, not a kill; contact term [formula in source] the MODULAR COMPLETION of the AB data, a Harvey–Moore [formula in source] -integral with forced leading [formula in source] ratio [formula in source] ; massive coset levels [formula in source] mandatory); Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e proper stays , SEAM.EQUIV.01 stays )

Research changelog · TFPT — Introduction and reading guide

v511_celestial_wp5e_delta2_tensor_ledger.py ( CELEST.WP5E.DELTA2.01, 41 checks, [formula in source] 4 s; integer-scaled weight multisets [formula in source] Kostant/Weyl alternating sums [formula in source] sympy/Fraction, no floats; deterministic). D0/D1 structure: [formula in source] roots, class split [formula in source] ; [formula in source] SEMISIMPLE without [formula in source] ( [formula in source] class- [for

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explicit file citation v511_celestial_wp5e_delta2_tensor_ledger.py
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explicit claim identifier status_ledger.csv
exact local ledger claim identifier
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explicit file citation celestial_seam_wp5e_delta2_full_tensor_ledger_probe.py
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explicit script identifier v511_celestial_wp5e_delta2_tensor_ledger.py
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explicit script identifier v508_celestial_wp5e_gamma_pairing.py
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explicit file citation celestial_seam_wp5e_delta1_bcov_contact_probe.py
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2026-07-21 (XXII) (P2 consolidation — the axiomatics reduction state written as ONE coherent statement across the papers (editorial, NO new claims, NO marker moves): the compiler's dimensionless inputs reduce to four marks (derived from P1-side topology, v216), ONE square-modulus datum ( [formula in source] — equivalently: the clock / the CM-fixed half-period / the non-split extension class on the free seam circle; v491/ v499/ v506/ v507/ v510) and [formula in source] , plus the \ identifications R1/R2 of v499; AX.P2.01 stays a DECLARED axiom and QGEO.REALIZE.01 stays / \ — the consolidation describes the reduction state, not an abolition)

Research changelog · TFPT — Introduction and reading guide

What is consolidated (and why now). The P2 state of affairs was spread over five module rounds: the partition corollary ( v491: [formula in source] unique [formula in source] ), the weight typing ( v499: Deligne [formula in source] Birkhoff–Grothendieck [formula in source] Mehta–Seshadri force [formula in source] , residuals R1/R2 ), the residual convergence ( v503: QGEO-R1 [formula in source] P2-R1), the clock rigid

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documents/changelog/sections/005-source.tex · lines 161 to 185

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explicit script identifier v510_seam_bit_freedom.py
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explicit script identifier v503_qgeo_emergence_light.py
literal short identifier uniquely resolves in local script registry
explicit script identifier v216_marks_gauss_bonnet.py
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explicit claim identifier status_ledger.csv
exact local ledger claim identifier
explicit script identifier v499_p2_weights_deligne_bg.py
literal short identifier uniquely resolves in local script registry
explicit script identifier v507_seam_bit_origin.py
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explicit script identifier v491_p2_partition_corollary.py
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explicit script identifier v506_seam_clock_rigidity.py
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2026-07-21 (XXI) ( v510 — the freedom attack on the v506/ v507 alignment bit promoted as SEAM.BIT.FREEDOM.01: the POSITION half of the bit is TOPOLOGY — the collar deck is a covering deck (the [formula in source] seam of the M\"obius double), and covering decks act FREELY; the DIHEDRAL THEOREM (on the seam circle the free involution is UNIQUE [formula in source] the antipode: [formula in source] involutions in [formula in source] , exactly [formula in source] free; [formula in source] complete census, brute force [formula in source] at [formula in source] ; quotient topology circle/antipode [formula in source] CIRCLE [formula in source] vs circle/reflection [formula in source] INTERVAL [formula in source] — the [formula in source] Gauss–Bonnet budget needs closed circles, so freeness IS the established P1 datum); NONSPLIT [formula in source] FREE over the complete [formula in source] -involution census in exact [formula in source] (free [formula in source] nonsplit with [formula in source] roots [formula in source] the [formula in source] tower; ALL [formula in source] reflections [formula in source] scalar [formula in source] , split, [formula in source] roots); the REAL-STRUCTURE classification (deck-commuting families [formula in source] exactly two; [formula in source] equatorial, deck FREE; silver [formula in source] real axis THROUGH the deck poles, NOT free — the edge class is the restriction of the BRANCHED pillowcase involution; hexagonal [formula in source] NO mark-fixing real structure, RP-incompatible); HARMONIC [formula in source] FREE [formula in source] exactly ( [formula in source] ); honest counterwitnesses (``nonsplit [formula in source] clock'' is FALSE: [formula in source] and [formula in source] with [formula in source] ); the alignment bit REDUCES from ``harmonic AND central'' to the square-modulus datum [formula in source] alone; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / , AX.P2.01 stays an axiom, P2-R1 halved)

Research changelog · TFPT — Introduction and reading guide

v510_seam_bit_freedom.py ( SEAM.BIT.FREEDOM.01, 30 checks, [formula in source] s; sympy [formula in source] exact [formula in source] Fractions, no floats; deterministic). Part A (dihedral/fermionic): the involution census in [formula in source] on the refined [formula in source] -point seam circle ( [formula in source] : [formula in source] involutions, EXACTLY ONE free [formula in source] the antipodal shift by [fo

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documents/changelog/sections/005-source.tex · lines 186 to 242

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explicit claim identifier status_ledger.csv
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explicit file citation qgeo_realize_rp_fixcircle_moebius_probe.py
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explicit file citation qgeo_realize_deck_freedom_dihedral_probe.py
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explicit script identifier v510_seam_bit_freedom.py
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explicit script identifier v507_seam_bit_origin.py
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explicit script identifier v506_seam_clock_rigidity.py
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2026-07-21 (XX) ( v509 — WP5e- [formula in source] of CELEST.SEAM.01 ``the CPS level-from-flux dial'' promoted as CELEST.WP5E.EPS2.01, verdict B: the Costello–Paquette–Sharma Burns-holography mechanism (``level [formula in source] flux quantum [formula in source] Dynkin index'') executed on the lockstep spheres — the CPS SKELETON exact ( [formula in source] period [formula in source] with pullback density [formula in source] , exceptional-sphere K\"ahler flux [formula in source] , boundary level magnitude [formula in source] by the symplectic-boson contraction, [formula in source] ); the PAIRING MATRIX pinned, not postulated ( [formula in source] ledger [formula in source] integrality [formula in source] unimodularity [formula in source] effectivity [formula in source] [formula in source] by complete enumeration: rows [formula in source] , [formula in source] unimodular, exactly [formula in source] effective [formula in source] identity [formula in source] diagram flip), fluxes [formula in source] with uniformly ONE quantum per charged current; ``level [formula in source] total flux'' KILLED by the lockstep test itself ( [formula in source] unequal [formula in source] flavour multiplicity), the per-current reading [formula in source] anchored by the lattice current count [formula in source] and embedding index [formula in source] ; ord- [formula in source] -vs-level- [formula in source] RESOLVED (the clock order counts fractional flux sectors: [formula in source] , Lagrangian [formula in source] glue, KLM [formula in source] ) with the NEW sector-counter dial [formula in source] for [formula in source] — exactly ONE sector iff [formula in source] ; the LOCKSTEP THEOREM lifts the v505 ``one scale [formula in source] one level'' to a THEOREM of clock invariance ( [formula in source] equal, monodromy [formula in source] pure phase [formula in source] , [formula in source] : no invariant flux vector; NEW falsifier [formula in source] : [formula in source] orderings lockstep); honest limit: uniform doubling keeps the lockstep (equality, not the value); controls [formula in source] / [formula in source] / [formula in source] separate honestly; Wolfram extension [formula in source] (verified engine run); NO marker moves — WP5e stays \ (the CPS dictionary on [formula in source] typed , the type-I B-model back-reaction ), SEAM.EQUIV.01 stays )

Research changelog · TFPT — Introduction and reading guide

v509_celestial_wp5e_eps2_level_from_flux.py ( CELEST.WP5E.EPS2.01, 28 checks, [formula in source] s; sympy/Fraction exact, no floats; deterministic). Target: derive the boundary level [formula in source] from flux quantisation on the lockstep spheres, following the Costello–Paquette–Sharma Burns-holography mechanism (PRL 130, 061602; arXiv:2306.00940). CPS skeleton replicated exactly: the [formula in source] period o

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documents/changelog/sections/005-source.tex · lines 243 to 305

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explicit script identifier v502_celestial_wp5e_prefactor_level.py
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explicit file citation v509_celestial_wp5e_eps2_level_from_flux.py
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2026-07-21 (XIX) ( e8-ladder-bed v2 — the 2DCS extension executed with an honest preregistered kill_2d verdict at the DETECTOR level: the known-answer map recovers [formula in source] rungs incl.\ [formula in source] via F3 difference coordinates (MC [formula in source] ), but the 2D control battery breaks (scramble [formula in source] , jitter [formula in source] at the destructive [formula in source] level) — the v1 1D results (BCVO [formula in source] , CoNb [formula in source] O [formula in source] [formula in source] ) are untouched; scorecard row updated, status/stage unchanged; experiments level only — no verification module, no gate closes, no marker moves)

Research changelog · TFPT — Introduction and reading guide

experiments/e8-ladder-bed v2 (2DCS): amendment preregistered, run, and killed by its own controls. Trigger: arXiv:2512.16829 (Watanabe, Trebst, Hickey) — a THEORY-only paper (four-kink/ED localized-limit spectra at [formula in source] – [formula in source] \,T, not the E8 point; no measurements); as of 2026-07-21 no experimental 2DCS measurement of CoNb [formula in source] O [formula in source] exists anywhere (web-c

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documents/changelog/sections/005-source.tex · lines 306 to 339

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explicit script identifier v1_e8_glue.py
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2026-07-21 (XVIII) ( v508 — WP5e- [formula in source] of CELEST.SEAM.01 ``the sphere-axion pairing check'' promoted as CELEST.WP5E.GAMMA.01, an honest rigid NEGATIVE result: the VERTEX-SPACE THEOREM — the [formula in source] -invariant quadratics on the [formula in source] -dim glue Cartan are EXACTLY [formula in source] (dim [formula in source] ) and the quartics EXACTLY [formula in source] (dim [formula in source] ), with the PRODUCT THEOREM as the master kill (any two invariant quadratics multiply into [formula in source] — zero [formula in source] content, so [formula in source] annihilates EVERY exchange image while [formula in source] ); the strict two-index [formula in source] rule COLLAPSES (the sphere axions have no invariant bilinear Cartan vertex at all), the twist-insertion channels give a rank- [formula in source] exchange matrix with [formula in source] and the annihilator certificate [formula in source] ; side discovery [formula in source] ; naturalness DISSOLVES (ch [formula in source] -natural and AB-weight couplings both certify [formula in source] vs required [formula in source] — scale-independent); controls: [formula in source] has no sphere partners AND uncancelled [formula in source] , [formula in source] no [formula in source] structure; the O-fence is SHARPENED: the exchange sub-branch is dead, the [formula in source] residual MUST be carried by twisted BCOV contact terms ( [formula in source] binary: coefficient exactly [formula in source] , computed not fitted; escape [formula in source] : the full-tensor ledger); Wolfram extension [formula in source] (verified engine run); NO marker moves — CELEST.SEAM.01 stays Open, the slot bijection untouched, the preregistered level-kill still does not fire, SEAM.EQUIV.01 stays )

Research changelog · TFPT — Introduction and reading guide

v508_celestial_wp5e_gamma_pairing.py ( CELEST.WP5E.GAMMA.01, 27 checks, [formula in source] 4 s; sympy/Fraction exact, no floats; deterministic). Question: can the three twisted sphere axions [formula in source] (Coxeter eigencharacters [formula in source] on [formula in source] , v505 S5.8) cancel the rigid [formula in source] residual of the Atiyah–Bott ledger ( [formula in source] , v505 S3.7) by Green–Schwarz-typ

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documents/changelog/sections/005-source.tex · lines 340 to 392

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2026-07-21 (XVII) ( v507 — the tautology attack on the v506 alignment bit, executed and refuted, promoted as SEAM.BIT.ORIGIN.01: the ORIGIN THEOREM — marks [formula in source] fixed points of the hyperelliptic involution [formula in source] the [formula in source] half-periods [formula in source] of the seam double, and EVERY mark-free collar deck IS a half-period translation (in all three stabiliser types [formula in source] the free involutions are exactly the three [formula in source] : the CLASS of the deck is forced, its POSITION is not); the CORE SOLVE (symbolic [formula in source] ): a marks-preserving root of [formula in source] exists [formula in source] (one per [formula in source] ; intrinsic: the deck pairs separate harmonically), union [formula in source] the harmonic orbit [formula in source] ; the EQUIVALENCE TETRAD ``Uhr existiert [formula in source] ( [formula in source] AND deck [formula in source] CM-fixed half-period) [formula in source] (Stab [formula in source] AND deck central) [formula in source] deck pairs harmonic [formula in source] NS Fock lift NONSPLIT''; the FERMION DICHOTOMY (the new physical face): central [formula in source] nonsplit vs edge [formula in source] SPLIT ( [formula in source] vs [formula in source] roots — the bit IS a Fidkowski–Kitaev-type extension class, distinguished but not derived); the silver set [formula in source] the in-family misalignment witness; Wolfram extension [formula in source] (verified engine run); NO marker moves — the bit stays , SEAM.CLOCK.RIGIDITY.01/ QGEO.REALIZE.01/ P2.TYPING.01 text precised only)

Research changelog · TFPT — Introduction and reading guide

v507_seam_bit_origin.py ( SEAM.BIT.ORIGIN.01, 26 checks, [formula in source] 2.6 s; Part A sympy-exact torus/M\"obius arithmetic [formula in source] Part B exact [formula in source] Fractions; deterministic). Conjecture under attack: marks and deck both descend from the SAME torus structure (the seam double [formula in source] , v214/ v260), so the common origin would force the central alignment automatically and the

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documents/changelog/sections/006-source.tex · lines 1 to 65

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2026-07-21 (XVI) ( v506 — seam clock rigidity, Route B of the v503 classification, promoted as SEAM.CLOCK.RIGIDITY.01: TWO exact theorems reduce the order- [formula in source] clock input to ONE alignment bit — Theorem A (M\"obius): the deck [formula in source] has EXACTLY TWO square roots [formula in source] in [formula in source] , both automatically order [formula in source] , and a marks-preserving root exists [formula in source] the deck is the CENTRAL involution of the mark- [formula in source] (counterexample [formula in source] : harmonic with full [formula in source] but deck non-central [formula in source] [formula in source] roots — harmonicity alone insufficient); Theorem B (Fock, the core): the NS deck implementation is FORCED to order [formula in source] — [formula in source] , i.e.\ [formula in source] EXACTLY, a nonsplit [formula in source] , with the [formula in source] tower [formula in source] , [formula in source] ( [formula in source] fermionically explained) and the R-sector control split ( [formula in source] ); the one \ rest: ``the collar deck is the central involution of the mark- [formula in source] '' — the fermionic [formula in source] forces the ORDER, not the spatial alignment; Wolfram extension [formula in source] (verified engine run); NO marker moves — QGEO.REALIZE.01 stays / \ (text precised), P2.TYPING.01 R1 mapped onto the same bit)

Research changelog · TFPT — Introduction and reading guide

v506_seam_clock_rigidity.py ( SEAM.CLOCK.RIGIDITY.01, 34 checks, [formula in source] 3.5 s; Part A sympy-exact M\"obius/divisor arithmetic [formula in source] Part B exact [formula in source] Fractions; deterministic). v503 localised the one remaining identification input (``why does the raw seam carry the order- [formula in source] clock'', QGEO-R1 [formula in source] P2-R1); v506 reduces it. Theorem A (M\"obius sid

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documents/changelog/sections/006-source.tex · lines 66 to 122

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explicit script identifier v499_p2_weights_deligne_bg.py
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