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
The exact identifier, original classification and full claim are available below.
The source wording and classification below are preserved as recorded. A paper link, shared script or authored topic relation does not upgrade the claim or report a new proof run. Read later reviewed findings separately.
Read the exact registered claim and its dependencies
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
Open the original ledger source, row 596Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- TFPT — Introduction and reading guide
- E8 audit and bootstrap
- Research contracts
Sections that explicitly cite this claim
A literal claim identifier is present in these paper sections. The section and its premises determine what the citation supports.
- Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)Research contracts
- Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)tfpt research contracts
- Sharper still: one anchor [formula in source] , and [formula in source] as a compiler hull ( )TFPT — Introduction and reading guide
- Research Contract 1 — [formula in source]tfpt research contracts
- Front matter / supportResearch contracts
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)tfpt research contracts
- Research Contract 1 — [formula in source]tfpt research contracts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- How to read this documenttfpt 1 architecture e8
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- Honest statusinput 4 origin theory
- Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)tfpt research contracts
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)tfpt research contracts
- Target G — the alignment bit and the interacting seam (the first shot that lands)Red-team audit
- The whole integer skeleton from one pair [formula in source]input 4 origin theory
- -1.2cm TFPT — [formula in source] Audit, Cascade Bridge and Bootstrap\\[2mm] The seven [formula in source] slices as an audit raster, the old cascade as the same even-integer spine, the M\"obius self-consistency loop — and the thirty-two-step celestial/twistor route with the measure chain derivedinput 5 tfpt 3 e8 audit bootstrap
All 38 linked sections
- Theorem 7 — the [formula in source] lift of the [formula in source] atlas
- Honest status
- -1.2cm TFPT — [formula in source] Audit, Cascade Bridge and Bootstrap\\[2mm] The seven [formula in source] slices as an audit raster, the old cascade as the same even-integer spine, the M\"obius self-consistency loop — and the thirty-two-step celestial/twistor route with the measure chain derived
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)
- =150 2026-07-24 (I) ( v534 — the straddle cone executed: THE FIRST DYNAMICAL SELECTION OF THE ALIGNMENT BIT — reflection positivity keeps exactly ONE member of the interacting mark family alive, [formula in source] with positive coupling; the literal leading-order cone formalization dies; NO marker moves)
- Front matter / support
- Global computation: the anchor multiset is derived
- Outcome
- The celestial and twistor continuum route
- -1.2cm TFPT — Research Contracts for the Remaining Interfaces:\\v_ geo [formula in source] G_ net [formula in source] F_ transfer [formula in source] (U_ wall) [formula in source] (G_ metric) [formula in source] [formula in source] / _1/ _2/ _3 [formula in source] next)
- Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)
- How to read this document
- Honest status
- =150 2026-07-23 (VIII) (prominence pass — the v519–v529 breakthroughs lifted into the FRAME texts of the papers and the website data layer; purely editorial, NO new modules, NO marker moves — (1) tfpt_5_redteam gains the seam round Target G: the ten-test side-blind scoreboard on the alignment bit ( v512/ v521/ v525/ v529) and the first firing kill test of the programme — the interacting straddle law ( v529), documented as a named threat AND the first hard selection principle for [formula in source] , fenced at toy level; (2) the bit-reduction statements in tfpt_1, tfpt_2 and origin_theory extended from the v512 state to the current state (ten side-blind tests, the twist-class definition with gauge-robust order parameter, ``in principle interferometrically readable'', v528 — the bit stays formal input); (3) the thermal seam lifted into the origin_theory horizon chapter (new keybox: [formula in source] measured, temperature the third leg of [formula in source] , v526) and into the tfpt_horizon_readouts head keybox; (4) tfpt_3 title/keybox now carry the thirty-step story and ``the measure chain is derived'' ( v520/ v523) prominently; (5) tfpt_research_contracts title/intro keybox now show the executed stages of CELEST.SEAM.01 (M1–M3, [formula in source] -chains decided, [formula in source] derived) and WOIT.OS.TWISTOR.01 ( [formula in source] executed, [formula in source] next under the straddle constraint); both contracts stay Open)
- Front matter / support
- Research Contract — CELEST.SEAM.01 (the celestial and twistor continuum route)
- Front matter / support
- Honest status
- =150 2026-07-23 (X) ( v530– v533 — the external review round promoted: center quotient compiler, Coxeter Stage A tensor clock, dual-degree modular checksum [formula in source] , sheet-transfer disc [formula in source] norm line; every identity machine-confirmed exactly before promotion (probe [formula in source] ); NO marker moves)
- -1.2cm TFPT — Research Contracts for the Remaining Interfaces:\\v_ geo [formula in source] G_ net [formula in source] F_ transfer [formula in source] (U_ wall) [formula in source] (G_ metric) [formula in source] [formula in source] / _1/ _2/ _3 [formula in source] next)
- Front matter / support
- The celestial and twistor continuum route
- =150 2026-07-23 (IX) (website entry redesign: narrative home, honesty band, proof strip, guided-tour route — editorial only, NO new modules, NO marker moves)
- Front matter / support
- The whole integer skeleton from one pair [formula in source]
- Front matter / support
- Research Contract — CCC.SEAM.CROSSOVER.01 (the conformal-cyclic crossover on the seam geometry)
- Theorem 7 — the [formula in source] lift of the [formula in source] atlas
- Global computation: the anchor multiset is derived
- Theorem 7 — the [formula in source] lift of the [formula in source] atlas
Registered verification modules
- v529_seam_interacting_toy_fk.pyRegistered verification module · frontier
Read the description recorded in the module registry
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.
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.