A registered result in its source context

Original ledger classification: Formal/Identity [E] (exact solveset censuses, exact Gram entries, exact Cl(16) implementers, 40-digit gap-certified inertia spectra, continuum axis elimination, precondition controls) + [C] (face #13 = a reformulation of the bit) + [O] (mark-decorated states / interacting A_hol); the bit stays the one [C] carrier input; NO marker moves

Recorded statement: THE RP/THETA ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-22; one module, 25 checks, ~25 s; an honest, decided NEGATIVE result in the v508 style): does free reflection positivity (v519 RP) or anti-linear Theta existence (with the v519 side…

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Paper context: TFPT — Introduction and reading guide

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SEAM.BIT.RPBLIND.01

Original claim text

THE RP/THETA ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-22; one module, 25 checks, ~25 s; an honest, decided NEGATIVE result in the v508 style): does free reflection positivity (v519 RP) or anti-linear Theta existence (with the v519 side conditions) BREAK for delta != pi/2 on the deformed mark family M(delta) = {+-1, +-e^(i delta)} -- which would DERIVE the v512 alignment bit from OS positivity? NO: the entire free RP/Theta battery is SIDE-BLIND, hereby documented as the EIGHTH side-blind test on the v512 scoreboard (7 -> 8); the bit REMAINS genuine discrete input. (1) CENSUS (exact solvesets, symbolic delta): for EVERY delta exactly the two mark-SWAPPING reflections Theta_(+-e^(i delta)) exist (axes delta/2, delta/2 + pi/2; all 20 cut/mark incidence solvesets EMPTY); mark-FIXING reflections exist exactly at delta = pi/2 (solveset cos delta = 0 = {pi/2}, lost immediately at pi/2 - eps); the v510/v512 counterwitness {+-1, +-(3+4i)/5} carries the swap pair exactly and is NOT excluded. (2) RP IS delta-BLIND: bond-cut Gram inertias (8, 0, 0) PD for all tested delta at N = 16, even deg <= 2 sector (29, 0, 0); the full sorted 40-digit spectra are IDENTICAL across all axes (deviation 0.0) -- the ENTIRE free-RP spectral datum carries ZERO delta information; the N = 16 odd-m failure (site axes, inertia (3,3,1), det = 0) is a lattice-PLACEMENT artifact: at N = 32 ALL m = 1..7 (delta = m pi/8) have mark-compatible BOND axes with PD inertia (16, 0, 0); continuum: the OS kernel in axis-adapted coordinates is EXACTLY 1/sin((s+t)/2) -- the axis position drops out identically (Cauchy-Stieltjes factorisation PD); the counterwitness PASSES free RP (6-point Gram (6, 0, 0)). (3) THETA EXISTENCE IS delta-BLIND: Theta^2 = +1, deck normalisation and Fock implementability (U^2 = +2^7/2^8 > 0, exact Cl(16)) hold for every delta; the ONLY delta-sensitive clause of the v519 battery (Theta rho Theta = rho^-1) is for delta != pi/2 not violated but NOT FORMULABLE (a mark-compatible order-4 rotation exists iff delta = pi/2) -- it PRESUPPOSES the bit instead of deriving it; same for the clock-tower clause. (4) THE BATTERY HAS TEETH AT EVERY delta: RP separates the two real-structure FAMILIES (family A/antipode: zero diagonal, indefinite (4, 4, 0); chirality-eta pinning: anti-chiral state (0, 8, 0) ND) -- but never the SIDES within family D. (5) PRECONDITION CONTROLS: hexagonal marks not concyclic (|b_hex| = 2 - sqrt(3) != 1, no seam circle -- rejected before positivity is asked); silver marks all real (deck not free -- excluded by topology); lifting audit: B (pullback) = index relabelling (delta-blind by construction), B' (stretched sampling) fails the pi/2 negative control (not the chiral vacuum -- discarded). [C] FACE #13 of the v512 equivalence web: the group generated by the admissible OS reflections is V4 for every delta < pi/2 and closes to D4 exactly at delta = pi/2 (Theta_i o Theta_1 = the clock) -- a typed REFORMULATION of the bit (12 -> 13 faces (since 13 -> 15 by v528 facets #14/#15)), not a derivation from positivity. [O] HONEST GAP: marks decorating the STATE (defect/twist insertions, interacting A_hol) are outside the free class = exactly v519's [O] scope -- there, and only there, could positivity still see the bit; since DECIDED by v525 (SEAM.BIT.TWISTBLIND.01): the mark-decorated free-plus-twist state class (sigma gauge, Kadanoff-Ceva 4-twist insertions, mu4/Bogoliubov defects -- everything Wick-computable) is side-blind too, the NINTH side-blind test (8 -> 9); the free-plus-twist class is EXHAUSTED, the remaining door is a genuinely interacting A_hol with non-Pfaffian-reducible OS data. VERDICT: KILL exactly as preregistered. Discovery provenance: seam_alignment_bit_rp_selector_probe.py (25/25) in experiments/tfpt-discovery/ (2026-07-22). NO marker moves.

Original classification detail

KILL (honest negative, preregistered): free RP and Theta existence are side-blind on the whole M(delta) family -- the eighth side-blind test on the v512 scoreboard (7 -> 8), face #13 added [C] (12 -> 13; since 13 -> 15 by v528); the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; [O] gap: mark-decorated/interacting states -- the mark-decorated (free-plus-twist) half since decided side-blind by v525 (the ninth side-blind test, 8 -> 9); what remains is the genuinely interacting A_hol

Dependencies as recorded

SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; SEAM.BIT.ORIGIN.01; SEAM.CLOCK.RIGIDITY.01; WOIT.THETA.FREE.01; v506; v507; v510; v512; v519

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E8 audit and bootstrap
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Research contracts
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Registered verification modules

v521_seam_bit_rp_blind.pyRegistered verification module · core
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SEAM.BIT.RPBLIND.01: the RP/Theta attack on the alignment bit DECIDED -- 'free OS positivity does NOT see delta', an honest, decided NEGATIVE result (v508 style; 25 checks, ~25 s): does free reflection positivity (v519) or anti-linear Theta existence break for delta != pi/2 on the deformed mark family M(delta) = {+-1, +-e^(i delta)}, which would derive the v512 alignment bit from OS positivity? NO -- the free RP/Theta battery is the EIGHTH side-blind test on the v512 scoreboard (7 -> 8); the bit remains genuine discrete input. [E] CENSUS (exact solvesets, symbolic delta): for every delta exactly the two mark-SWAPPING reflections Theta_(+-e^(i delta)) exist (axes delta/2, delta/2 + pi/2; all 20 cut/mark incidence solvesets empty); mark-FIXING reflections exist exactly at delta = pi/2 (solveset cos delta = 0, lost immediately at pi/2 - eps); the v510/v512 counterwitness {+-1, +-(3+4i)/5} carries the swap pair exactly. [E] RP IS delta-BLIND: bond-cut Gram inertias (8,0,0) PD for all tested delta, spectra IDENTICAL to 40 digits (deviation 0.0) -- the entire free-RP spectral datum carries ZERO delta information; the N = 16 odd-m failure (site axes, (3,3,1), det = 0) is a lattice-PLACEMENT artifact: at N = 32 all m = 1..7 have mark-compatible bond axes with PD inertia (16,0,0); continuum: the OS kernel in axis-adapted coordinates is exactly 1/sin((s+t)/2), the axis position drops out identically (Cauchy-Stieltjes PD); the counterwitness PASSES free RP (6-point Gram (6,0,0)). [E] THETA EXISTENCE delta-BLIND: Theta^2 = +1, deck normalisation and Fock implementability (U^2 = +2^7/2^8 > 0, exact Cl(16)) for every delta; the ONLY delta-sensitive v519 clause (Theta rho Theta = rho^-1) is for delta != pi/2 not violated but NOT FORMULABLE (mark-compatible order-4 rotation <=> delta = pi/2) -- it PRESUPPOSES the bit; same for the clock-tower clause. [E] the battery has teeth at every delta: family A/antipode fails RP structurally (zero diagonal, (4,4,0) indefinite), chirality-eta pinning persists ((0,8,0) ND) -- RP separates the two real-structure FAMILIES, never the SIDES. [E] precondition controls: hexagonal (marks not concyclic, no seam circle), silver (deck not free), lifting audit (B = index relabelling, delta-blind by construction; B' fails the pi/2 negative control -- discarded). [C] FACE #13 of the v512 equivalence web: the group generated by the admissible OS reflections is V4 for every delta < pi/2 and closes to D4 exactly at delta = pi/2 (Theta_i o Theta_1 = the clock) -- 12 -> 13 faces, a typed REFORMULATION of the bit, not a derivation. [O] honest gap: marks decorating the STATE (defect/twist insertions, interacting A_hol) = exactly v519's [O] scope -- there, and only there, could positivity still see the bit. VERDICT: KILL exactly as preregistered; the alignment bit is NOT derivable from OS positivity and remains genuine discrete input; no marker moves.

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