A registered result in its source context

SEAM.BIT.TWISTBLIND.01

Original ledger classification: Formal/Identity [E] (Pfaffian-exact insertion machinery cross-validated three ways, exact integer incidence frame, exact congruence mechanisms, 40-digit gap-certified inertia/spectrum/energy/parity certificates) + [C] (each lifting is a construction choice, all tested) + [O] (the genuinely interacting A_hol with non-Pfaffian-reducible OS data); the bit stays the one [C] carrier input; NO marker moves

Original claim text

THE TWIST-STATE ATTACK ON THE ALIGNMENT BIT DECIDED (2026-07-23; one module, 20 checks, ~80 s; an honest, decided NEGATIVE result in the v508 style -- the NINTH side-blind test on the v512 scoreboard, 8 -> 9): do mark-decorated STATES (Kadanoff-Ceva twist/defect insertions, sigma-gauge arc decorations, mu4/Bogoliubov bond defects -- the v521 [O] gap, everything Pfaffian/Wick-computable) make RP side-sensitive on M(delta) = {+-1, +-e^(i delta)}? NO. (1) ALL LIFTINGS WELL-DEFINED AND BLIND: (a) sigma-gauge (Z2): sigma o r = sigma on every swap axis makes the twisted Gram a diagonal unitary congruence D M D -- spectra IDENTICAL to untwisted (dev 0.0); (b) Kadanoff-Ceva 4-twist insertion omega(D .)/omega(D): well-defined on the whole N = 32 ladder (omega(D) real nonzero, deck-consistent; the N = 16 odd-m degeneration -- omega(D) = 0 at m = 1, imaginary at m = 3 -- is exactly the C(even) = 0 checkerboard artifact); its RP SPECTRA are the FIRST free-class data of the program that depend on delta (min shift 0.242, pairwise up to 1.05 -- the mark-anchored strings break the v521 rotation-equivalence mechanism), but the INERTIA is (16, 0, 0) PD with the SAME eta = +i for EVERY m = 1..7 incl. pi/2 +- pi/8, both swap axes, even sector (29, 0, 0) -- the decoration sees delta, the positivity does not; (c) the mu4 defect at beta = pi/2 is PURE PLANE GAUGE (one state up to gauge, signed permutation = extended monomial class, RP-invisible like (a)); (c') the genuine Bogoliubov defect at beta = pi/4: the sign pattern becomes a real datum and Theta-compatibility selects EXACTLY 2 of 16 patterns (the crossed pattern forced by the NS wrap signs; the naive alternating pattern FAILS), the winner is pure and genuinely non-monomial (|C(even)| up to 0.45) -- still PD everywhere, spectra again IDENTICAL. STRUCTURE THEOREM (empirical, mechanism exact): the defect planes never straddle a cut bond (marks avoid the cuts), so O block-decomposes across the cut and the Theta precondition turns every twisted Gram into an orthogonal congruence U M U^T -- EVERY Theta-compatible quasi-free mark decoration is RP-spectrally INVISIBLE: the quasi-free class cannot even carry delta into its RP datum; only the insertion FUNCTIONALS do, and there positivity stays blind. (2) SUB-RESULTS: the total defect energy E_def = 1.2752872 for EVERY m (40-digit spread 4e-40) -- delta-blind; the 4-twist Casimir ln|omega(D)| measures delta smoothly (-0.890 .. -1.348) but is EXACTLY mirror-symmetric under m <-> 8-m (dev 1.15e-40) -- the delta <-> pi-delta equivariance makes pi/2 the symmetric point of every invariant readout: a family gauge, never a side selector; the twisted parity <Gamma>_tw = +1 for every m (the (-1)^F/Kramers class untouched by every decoration). (3) TWO BIT-PRESUPPOSING pi/2 STRUCTURES (the harvest): the eta flip +i -> -i on the mark-fixing axes (sigma o r = -sigma, odd sector exactly negated, even sector unchanged); the twist frustration of the mark-fixing mirror (theta maps D_short <-> D_long; the theta-closed symmetrized insertion is Hermitian but INDEFINITE (4, 4, 0) for both eta -- the lattice shadow of the Ising twist field's mirror-oddness) -- both formulable ONLY on the fixing axes existing iff delta = pi/2: they PRESUPPOSE the bit (v512 facet class), no selector. (4) NEGATIVE CONTROLS: the twist-free limit reproduces v519/v521 exactly (dev 0.0); the site cut keeps failing in every decorated state; the v512 counterwitness delta_cw = atan(4/3) is ARC-EQUIVALENT at N = 16 to the blind member delta = pi/4 (identical decorated state, integer incidence) and carries no lattice mark-compatible reflection -- no decorated-state selector can exclude it without excluding a blind member; a single twist string is ODD, omega(D) = 0 identically (twists exist only in mark PAIRS); the deck-breaking two-twist decoration is defective -- the deck-paired FOUR-twist decoration is the minimal well-defined one. VERDICT: KILL exactly as preregistered -- the NINTH side-blind test (8 -> 9); the free-plus-twist class (everything Wick-computable) is EXHAUSTED: only a genuinely INTERACTING A_hol whose OS data are NOT Pfaffian-reducible to the chiral vacuum could still see the bit. The alignment bit remains genuine discrete input. Discovery provenance: seam_alignment_bit_twist_state_probe.py (20/20) in experiments/tfpt-discovery/ (2026-07-23). NO marker moves.

Original classification detail

KILL (honest negative, preregistered): every well-defined mark-decorated state functional in the free-plus-twist class keeps RP positive on the always-existing cuts along the whole M(delta) ladder -- the NINTH side-blind test on the v512 scoreboard (8 -> 9); quasi-free decorations are RP-spectrally invisible (exact congruence mechanism), insertion spectra and the 4-twist Casimir measure delta but never reach the positivity verdict, the only pi/2-exclusive structures presuppose the bit; the free-plus-twist class is EXHAUSTED -- the interacting half is since decided by v529 (SEAM.INT.FKTOY.01): the TENTH side-blind test (9 -> 10) on genuinely non-Wick dynamics, while Kill-Test-2 fires at toy level (RP breaks for every g > 0; straddle law); the alignment bit remains genuine discrete input

Dependencies as recorded

SEAM.BIT.RPBLIND.01; SEAM.TAU.FLAG.01; SEAM.BIT.FREEDOM.01; WOIT.THETA.FREE.01; v510; v512; v519; v521