A registered result in its source context

Original ledger classification: Measured [E] (toy level; v529 fence inherited); no marker moves

Recorded statement: OS VIABILITY ON THE QUARTET-AVOIDING FAMILY (measured 2026-08-27; promoted in v972): the v529 kill-test-2 counterweight -- (1) the straddle census 24/24 reproduced; (2) the clock-invariant m = 4 member's quartet-avoiding cut family…

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Paper context: Research contracts

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SEAM.INT.OSAVOID.01

Original ledger classification: Measured [E] (toy level; v529 fence inherited); no marker moves

Original claim text

OS VIABILITY ON THE QUARTET-AVOIDING FAMILY (measured 2026-08-27; promoted in v972): the v529 kill-test-2 counterweight -- (1) the straddle census 24/24 reproduced; (2) the clock-invariant m = 4 member's quartet-avoiding cut family generates the FULL even seam algebra (rank 15, dim 32768 = 2^15; the single-cut members m = 2/6 carry a typed deficit of EXACTLY 1); (3) OS/GNS on the avoiding cut k = 3 at g = 1 is POSITIVE (min eig +4.4338e-5, GNS 37/37, PD clock-transfer shadow, the low spectrum deforming continuously from g = 0, distances 1.044/1.386/1.650 monotone); (4) the straddled control GENUINELY FAILS (-6.936e-2) -- same machinery, honest negative; (5) the mu4 clock maps the avoiding pair {3, 11} onto itself EXACTLY at operator level. READING: the interacting toy state IS OS-positive on the cut family its own clock geometry selects -- the kill-test-2 threat is NARROWED (an OS-viable geometry exists), NOT removed (every A_hol must still protect RP against the odd-split mechanism). FENCE INHERITED: one toy, one interaction class, [C] flat-band parent; toy statement, not a reconstruction of an interacting continuum theory.

Original classification detail

[E] the avoiding family generates the full even algebra (rank 15) and carries a positive OS/GNS structure at g = 1 while the straddled control fails; kill-test-2 counterweight narrowed, not removed; toy level

Dependencies as recorded

SEAM.INT.FKTOY.01; SEAM.INT.ODDSPLIT.01; WOIT.OS.TWISTOR.01; v529

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E8 audit and bootstrap
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Research contracts
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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
Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Research Contract — WOIT.OS.TWISTOR.01 (the Osterwalder–Schrader twistor bridge)tfpt research contracts

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Target G — the alignment bit and the interacting seam (the first shot that lands)Red-team audit
Sharper still: one anchor [formula in source] , and [formula in source] as a compiler hull ( )TFPT — Introduction and reading guide
-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
Front matter / supportResearch contracts
-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
The celestial and twistor continuum routeinput 5 tfpt 3 e8 audit bootstrap
-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)tfpt research contracts
Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap

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Registered verification modules

v972_seam_interaction_front.pyRegistered verification module · core
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SEAM.INT.ODDSPLIT.01 [E] + SEAM.INT.OSAVOID.01 [E] + SEAM.STATE.RPMIXING.01 [E] (+ Updates an SEAM.INT.FKTOY.01 / WOIT.OS.TWISTOR.01 / SEAM.STATE.DERIVATION.01; Konsolidierung dreier Explorationsrunden vom 2026-08-27, alle drei Sonden byte-exakt eingebettet mit gepinnten Quell-SHA-256 und wörtlich ausgeführt, 20/20 + 18/18 + 25/25, Verdikte CLASS_EMPTY_ON_BASIS + OS_VIABLE_ON_AVOIDING + RP_ADMITS_MIXING): **DIE SEAM-INTERAKTIONSFRONT** — (1) Die hinreichende Jaffe–Pedrocchi-Bedingung für Majorana-Reflexionspositivität (arXiv:1406.1384; Wei–Li–Xiang arXiv:1601.01994) wird auf dem v529-FK-Toy ENTSCHEIDBAR gemacht: die Kreuzungs-Koeffizientenmatrix B ist EINDEUTIG (Links-Monom-Paare bijektiv auf Kreuzungsmonome), also ist „B hermitesch UND −B PSD" ein endlicher Check; der freie FK-Hamiltonian wird auf allen 8 Bond-Cuts zertifiziert (Twist η = −i erzwungen); die Konfusionsmatrix gegen gemessene RP über 35 Zellen ist PERFEKT (23 zert.&PD / 12 unzert.&fail / 0 FP / 0 FN); der μ4-kovariante Quartik-Raum (dim 464) ist auf der Basis LEER (und auf 64 geseedeten Kombinationen; der Träger-Ausschluss pinnt den vollen 1820-dim Raum) — DIE ENTDECKUNG: das v529-Straddle-Gesetz VERFEINERT sich zum ODD-SPLIT-GESETZ: JP sagte RP-Überleben auf ZENTRIERT gestraddelten Cuts voraus (m = 4-Modell, Achsen 7/15, 2+2-Spiegelsplit), die Direktmessung bestätigt ((37,0,0) bei g = 0.5/1/2); die v529-Ankerleiter exakt reproduziert. (2) Die quartett-MEIDENDE Cut-Familie des uhr-invarianten m = 4-Mitglieds erzeugt die VOLLE gerade Seam-Algebra (Rang 15, dim 32768 = 2¹⁵; Einzel-Cut-Mitglieder m = 2/6 mit typisiertem Defizit EXAKT 1), und OS/GNS auf dem meidenden Cut k = 3 bei g = 1 ist POSITIV (min +4.43e−5, GNS 37/37, Distanzen 1.044/1.386/1.650 monoton), während die gestraddelte Kontrolle ehrlich scheitert (−6.94e−2); die μ4-Uhr bildet das meidende Paar {3, 11} exakt auf sich ab — das Kill-Test-2-Gegengewicht VERENGT, hebt nicht auf. (3) Die v903-Exklusivität ist STRAHL- und SPIEGELUNGS-relativ, nicht slice-weit: auf dem vollen 33-dim C6-kovarianten Mixing-Slice sieht θ_abT genau EINE Koordinate (a_J, Kernwert −1/(1+c²) = −0.8240271368 bei c = tanh(1/2)), 32/33 unsichtbar ⇒ 32-dim MARGINALE RP-Hyperebene {a_J = 0}; die θ_S-Defektabbildung hat Rang 16 ⇒ 17-dim erstordnungs-neutraler Unterraum mit STRIKTEN finite-s-Zeugen (W_S bei s = 1/8, λ_min 0.1558 — genau die Richtung, die θ_abT tötet); der v903-Anker reproduziert (a_J = +0.04068013). Modul-eigene Exaktsektion S0 (sympy/GF(2), keine Sonden-Importe): JP-Entscheidbarkeits-Lemma am 4-Majorana-Toy (9 paarweise verschiedene Kreuzungsmasken ⇒ eindeutiges B; Falschvorzeichen-Toy SCHEITERT), Odd-Split-Arithmetik (zentriert ⇔ 2+2 exakt auf Z₁₆; der ungerade 1+3-Block [[0,b],[b*,0]] erzwingt b = 0 — die Obstruktion; Vorzeichen-Flip-Mutant CAUGHT), GF(2)-Erzeugungs-Buchhaltung (Paarrang 15, 2¹⁵ = 32768; Innerhalb-Hälften-Rang 14 — Defizit exakt 1), Fenster-Arithmetik (33 = 24 + 9, 32 + 1, 33 − 16 = 17; Kernwert symbolisch == −cosh(1/2)²/cosh(1)) plus 4 Verdikt-Bars mit Kipp-Mutanten. EHRLICH: KEINE Marker-Bewegung; SEAM.EQUIV.01 bleibt [O]; der v529-Pflichtzaun (EIN Toy, EINE Wechselwirkungsklasse, [C] Flachband-Parent) wird von allen drei Resultaten GEERBT; JP ist nur hinreichend; der S1-Zensus ist sektor-trunkiert. KEIN RH-Claim.

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