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A registered result in its source context

Original ledger classification: F1=KILL / F2=KILL / F3=ERFOLG ([E] exact Fraction/Clifford + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

Recorded statement: THE MINIMAL INTERACTING FIDKOWSKI-KITAEV SEAM TOY (2026-07-23; one module, 24 checks, ~97 s; triple-verdicted -- the FIRST firing Kill-Test-2 shadow). F1 = KILL, F2 = KILL, F3 = ERFOLG. (1) F1 = KILL (THE MOST IMPORTANT PART): Theta exists…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

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SEAM.INT.FKTOY.01

Original ledger classification: F1=KILL / F2=KILL / F3=ERFOLG ([E] exact Fraction/Clifford + float-track certificates; [C] flat-band parent / one interaction class fence); WOIT.OS.TWISTOR.01 stays Open; NO marker moves

Original claim text

THE MINIMAL INTERACTING FIDKOWSKI-KITAEV SEAM TOY (2026-07-23; one module, 24 checks, ~97 s; triple-verdicted -- the FIRST firing Kill-Test-2 shadow). F1 = KILL, F2 = KILL, F3 = ERFOLG. (1) F1 = KILL (THE MOST IMPORTANT PART): Theta exists exactly on the interacting model (U_r^2=2^8, Theta^2=+1, clock-tower inversion conj_V·V=4096, [Theta,H_g]=0 exact, Theta Omega_g = Omega_g) -- Kill-Test 1 does NOT fire; BUT Kill-Test 2 FIRES AT TOY LEVEL: RP breaks in the interacting ground state for every g>0 -- inertia ladder (37,0,0) at g=0 -> (33,4,0) at g=1/4,1/2 -> (31,6,0) at g=1 -> (29,8,0) at g=2 (most negative EW -4.5e-2, seven orders above threshold); Gibbs beta=2 exact same ladder; g=-1: (19,18,0). MECHANISM: interference (neither crossing nor half-local alone breaks -- each (37,0,0)); STRADDLE LAW (24/24): RP fails exactly on quartet-straddled cuts, stays PD on quartet-avoiding. MANDATORY FENCE: ONE toy, ONE interaction class, [C] flat-band parent -- narrows the Woit route (every A_hol must protect RP against exactly this mechanism), does not close it; WOIT.OS.TWISTOR.01 stays Open, but the contract MUST document the firing toy shadow as a named threat (Kill-Test-2 paragraph + the straddle law as a concrete hurdle for beta3/gamma). (2) F2 = KILL: the TENTH side-blind test (9->10), the first with genuinely non-Wick-computable dynamics -- the interaction sees delta massively (spectral spread 1.32, gaps 0.31-1.66, overlaps 0.869-0.962), but the mark-axis mirror Theta_15 maps H(m)->H(8-m) EXACTLY (Fraction identity); all side data mirror-equal (8e-15/7e-16/5e-15); Theta_7 for m=1<->7 obstructed by exactly two NS wrap signs; counterwitness anchors to identical dynamics as m=2. Door narrows: only dynamics that break mirror covariance in BOTH torsor orbits. (3) F3 = ERFOLG: grading exact ([H_q,(-1)^F]=0, <Gamma>=+1 incl. g=100); Z8 backbone: Utilde^2=256 Gamma=(-1)^F nonsplit, V^2=256 Utilde (the clock tower IS the root of the deck), Theta inverts the tower; FK anchor single quartet {-1,+1}x128, m=4 at g->inf binomial ladder {16,64,96,64,16}; OS quotient at g>0 constructive on the pi/2 model (Gram (37,0,0), tau_4 PD (11,0,0), vacuum fixed). (4) CONTROLS: Theta-incompatible quartic makes Gram non-Hermitian (0.46 vs 1e-16); site (3,3,1). Discovery provenance: seam_interacting_toy_fk_probe.py (24/24). NO marker moves. UPDATED 2026-08-27 (v972): the straddle law is REFINED to the ODD-SPLIT LAW -- the Jaffe-Pedrocchi sufficient condition, made decidable in v972 (unique crossing matrix B; 'B Hermitian AND -B PSD' a finite check), predicted RP survival on CENTER-straddled cuts (m = 4 model, axes 7/15, 2+2 mirror split) and direct measurement CONFIRMED it ((37,0,0) at g = 0.5/1/2); a straddled cut kills RP iff the split is odd (1+3). The confusion matrix vs measured RP is perfect over 35 cells (23/12/0/0) and the mu4-covariant quartic class (dim 464) is EMPTY on the basis (SEAM.INT.ODDSPLIT.01). The fence (one toy, one interaction class, [C] flat-band parent) is unchanged and inherited by the refinement.

Original classification detail

F1=KILL (Kill-Test-2 fires at toy level: RP breaks for every g>0; straddle law 24/24; Kill-Test-1 does NOT fire); F2=KILL (tenth side-blind test 9->10); F3=ERFOLG (grading+Z8+FK+OS quotient); [C] fence one toy/one class -- narrows WOIT route, does not close it; no marker moves

Dependencies as recorded

WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; SEAM.BIT.TWISTBLIND.01; SEAM.BIT.TWISTCLASS.01; SEAM.TAU.FLAG.01; SEAM.EQUIV.TWISTOR.01; v510; v512; v519; v524; v525

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Registered verification modules

  • v529_seam_interacting_toy_fk.pyRegistered verification module · frontier
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    SEAM.INT.FKTOY.01: the minimal interacting Fidkowski-Kitaev seam toy -- the FIRST firing Kill-Test-2 shadow (triple-verdicted; 24 checks, ~97 s). F1=KILL: Theta exists (U_r^2=2^8, Theta^2=+1, conj_V V=4096, [Theta,H_g]=0) so Kill-Test 1 does NOT fire; BUT Kill-Test 2 FIRES at toy level -- RP breaks for every g>0: inertia ladder (37,0,0)->(33,4,0)->(31,6,0)->(29,8,0); Gibbs beta=2 same ladder; mechanism = interference; STRADDLE LAW (24/24): RP fails exactly on quartet-straddled cuts. F2=KILL: the TENTH side-blind test (9->10) -- Theta_15 maps H(m)->H(8-m) EXACTLY despite delta-seeing spectra (spread 1.32). F3=ERFOLG: grading + Z8 tower (Utilde^2=256 Gamma, V^2=256 Utilde) + FK anchor + constructive OS quotient at pi/2. [C] fence: one toy, one interaction class, flat-band parent -- narrows WOIT route, does NOT close it; WOIT.OS.TWISTOR.01 stays Open. Discovery provenance: experiments/tfpt-discovery/seam_interacting_toy_fk_probe.py (24/24, 2026-07-23). NO marker moves.

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