A registered result in its source context
Original ledger classification: Exact [E] sector/spectrum/incidence statements on the explicit v524 net + [C] the gamma reading (free slice; A_hol untouched)
Recorded statement: The free gamma slice of the WOIT roadmap (one module, 9 checks, ~1 s; discovery probe gamma_free_slice_probe.py 9/9, verdict GAMMA-FREE-SLICE-LANDED; the v524 machinery imported read-only). THE BASELINE [E]: the chiral N = 8 OS Gram is PD…
Statement, assumptions and sources
Paper context: TFPT — Introduction and reading guide
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WOIT.GAMMA.FREE.01
Original ledger classification: Exact [E] sector/spectrum/incidence statements on the explicit v524 net + [C] the gamma reading (free slice; A_hol untouched)
Original claim text
The free gamma slice of the WOIT roadmap (one module, 9 checks, ~1 s; discovery probe gamma_free_slice_probe.py 9/9, verdict GAMMA-FREE-SLICE-LANDED; the v524 machinery imported read-only). THE BASELINE [E]: the chiral N = 8 OS Gram is PD (16,0,0) -- H_phys exists (v524 Q1.3 reproduced). THE FLIP LOCALIZES [E]: the anti-chiral (mirror) state's Gram has inertia (8,8,0) and the split is SECTOR-EXACT: even (8,0,0) PD, odd (0,8,0) STRICTLY NEGATIVE DEFINITE -- the v519 odd-sector definiteness flip stated sector-exactly on the full N = 8 half algebra. MIRROR EXCLUSION [E, the gamma-A statement at the free level]: every nonzero mirror fermion vector has strictly negative OS norm; hence in the doubled (vector-like) system any OS-positive subspace meets the mirror odd sector in {0}: NO mirror fermion mode survives OS reconstruction -- kill test (3) ('the reconstruction produces a vector-like mirror generation') CANNOT fire at the free level, upgraded from the v519 state-level shadow to the SECTOR level. ONE GENERATION, MULTIPLICITY-FREE [E]: the compressed clock spectrum on the odd (fermion) transfer domain is EXACTLY {1, sqrt(2)-1} -- two distinct eigenvalues, no degeneracy. MARK INCIDENCE AT THE FREE LEVEL [E]: the two positive-half mark algebras (monomials on {4,5} and {6,7}) have PD OS Grams (4,0,0) each (dim 4 = |mu4|); their monomial products generate the FULL 16-dim H_phys basis (the marks jointly generate the net, meeting in the vacuum line); and the quarter-turn transfer tau_2 IS the mark-A -> mark-B transport (alpha_2: {4,5} -> {6,7}), Hermitian PD on the mark algebra -- the incidence-compatible extension exists at the free level, kill test (7) does not fire there. FIREWALL: the FREE slice only -- the gamma milestone itself (A_hol, the interacting net, the spacetime extension) stays OPEN; all seven contract kill tests stay formally live on A_hol; WOIT.OS.TWISTOR.01 does not move; no marker changes. [2026-08-01 XXXIV: the interacting gamma slice lands at toy level -- v615: on the RP-surviving interaction class (the alignment bit, v534) the mirror odd sector is strictly ND on every cut and every coupling (kill test (3) cannot fire on the surviving class), the mark transport is Hermitian PD at every g (kill test (7) does not fire), and the odd transfer spectrum stays multiplicity-free; the dead member has no RP home -- bit selection and chirality data co-locate; see WOIT.GAMMA.TOY.01.]
Original classification detail
GAMMA-FREE-SLICE-LANDED: chiral (16,0,0); anti-chiral (8,8,0) sector-exact (odd strictly ND -- mirror exclusion); clock spectrum {1, sqrt2-1} multiplicity-free; mark algebras PD dim 4, products generate, tau_2 = mark transport PD; gamma open on A_hol; 9/9 checks
Dependencies as recorded
WOIT.OS.TWISTOR.01; WOIT.BETA2.OS.01; WOIT.THETA.FREE.01; v519; v524; v565
Open the original ledger source, row 626Location recorded in the ledger
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- E8 audit and bootstrap
- Research contracts
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- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- =150 2026-08-01 (XXXII) (the interacting gamma slice lands at toy level ( v615 promoted): the gamma battery executed ON the RP-surviving interaction class (the alignment bit [formula in source] , positive coupling, v534) — THE INTERACTING MIRROR FLIP: at the forced twist [formula in source] the mirror state's odd sector is STRICTLY NEGATIVE DEFINITE on every cut and every coupling [formula in source] (bounded away from zero: kill test (3) cannot fire on the surviving class — v608 upgraded from [formula in source] to the full grid); the mark transport exists interacting (kill test (7) does not fire); the odd transfer spectrum stays multiplicity-free; and the dead member has no RP home — the dynamical bit selection and the chirality data CO-LOCATE on the same member)Research changelog; TFPT — Introduction and reading guide
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- =150 2026-08-01 (XXV) (the free gamma slice lands ( v608 promoted) — the first executed step of the WOIT [formula in source] milestone: mirror modes are STRICTLY OS-negative sector-exactly (every mirror fermion vector has negative OS norm — no mirror survives reconstruction, kill test (3) cannot fire at the free level), the chiral generation is multiplicity-free (clock spectrum exactly [formula in source] ), and the mark transport exists ( [formula in source] is the mark-A [formula in source] B transport, PD — kill test (7) does not fire free); [formula in source] itself stays open on [formula in source] ; side finding: [formula in source] is unipotent mod [formula in source] )Research changelog; TFPT — Introduction and reading guide
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- Front matter / supportResearch 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
Registered verification modules
- v608_gamma_free_slice.pyRegistered verification module · core
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WOIT.GAMMA.FREE.01: die freie γ-Scheibe der WOIT-Roadmap — SPIEGEL-MODEN SIND STRIKT OS-NEGATIV: der Anti-chirale Zustand hat Inertia (8,8,0) mit SEKTOR-EXAKTEM Split (gerade (8,0,0) PD, ungerade (0,8,0) strikt ND) — jeder Spiegel-Fermion-Vektor hat strikt negative OS-Norm, KEIN Spiegel-Mode überlebt die OS-Rekonstruktion (Kill-Test 3 kann auf freiem Niveau nicht feuern; Sektor-Upgrade des v519-Schattens); das komprimierte Clock-Spektrum auf dem Fermion-Bereich ist EXAKT {1, √2−1} — multiplizitätsfrei, EINE Generation; MARK-INZIDENZ frei: beide Mark-Algebren PD (4,0,0) mit dim 4 = |μ₄|, Produkte erzeugen die volle 16-dim Basis, und τ₂ IST der Mark-A→Mark-B-Transport (α₂: {4,5}→{6,7}, hermitesch PD) — Kill-Test 7 feuert frei nicht; FIREWALL: nur die freie Scheibe, γ selbst bleibt auf A_hol offen (9 checks, ~1 s)
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