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Original ledger classification: Exact [E] classification/pin/excision data + [C] typed premise remainder (resolved by v653) (Python-only per GATE.WOLFRAM.02).
Recorded statement: Arf/GSO hardening of the B-vs-C3 discriminator (one module, 15 checks, ~30 s; discovery probe orbifold_arf_probe.py 15/15, verdict ARF-B-STRUCTURAL). THE LADDER [E]: the mu6 defect ladder on the seam double measures the C3-excised states…
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Paper context: input 5 tfpt 3 e8 audit bootstrap
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QGEO.ORBARF.01
Original ledger classification: Exact [E] classification/pin/excision data + [C] typed premise remainder (resolved by v653) (Python-only per GATE.WOLFRAM.02).
Original claim text
Arf/GSO hardening of the B-vs-C3 discriminator (one module, 15 checks, ~30 s; discovery probe orbifold_arf_probe.py 15/15, verdict ARF-B-STRUCTURAL). THE LADDER [E]: the mu6 defect ladder on the seam double measures the C3-excised states DIRECTLY -- exponents 2 Delta = (1/18, 2/9, 1/2) at rel devs < 8e-4 (N = 96..1536 and within-ring), the half-twist (tau) Klein Gram exactly real symmetric and PSD, exact charge-resolved minima (0, 1, 4, 9, 4, 1)/36 = the measured sector grounds. THE EXCISION VERDICT [E, central]: the measured exponents hit B's c = 0 minima in every sector (< 3%); C3's odd-sector predictions 85/18 and 81/18 exceed the measurements by factors 85.0 and 9.0 -- the defect string is occupation-diagonal, hence exactly charge-neutral: C3 excises states that exist on the lattice seam with positive Klein norm and measured dimension. THE PIN [E]: the cover circle is NS (sympy closed form); among ALL 6^6 = 46656 sector-character wirings exactly {B, C3} survive the exact lattice degeneracies, and the single-Fock-space requirement forces B. HONEST: the earlier v639 2/9 read alone is B-vs-C3-BLIND (B and C3 coincide exactly on the even sectors); the new tau datum: OPE exponent 1/18 (rel 2.9e-3). TYPED [C]: the bond-defect premise (-> v653); GATE.QGEO does not move.
Original classification detail
ARF-B-STRUCTURAL: B vs C3 decided structurally -- the 6^6 classification leaves {B, C3}, the one-Fock-space pin forces B, and the mu6 ladder measures the C3-excised states directly (factors 85.0/9.0); the v639 2/9 read is B-vs-C3-blind; new tau datum 1/18; GATE.QGEO does not move.
Dependencies as recorded
QGEO.ORBASM.01; QGEO.ORBMOD.01; QGEO.KLEINRP.01; QGEO.TWISTOPE.01; v622; v623; v628; v639
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- E8 audit and bootstrap
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- Front matter / supportE8 audit and bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
- Group-theoretic audits (optional)input 5 tfpt 3 e8 audit bootstrap
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- =150 2026-08-27 (CXXXVI) (the transport-lift wave — the two external-review rounds on the quantum structure of the seam transport graduate from the experiments tree into the load-bearing suite as v976_seam_lift_birkhoff.py and v977_transfer_unistochastic_wilson.py (suite [formula in source] , ledger [formula in source] : new rows TRANSFER.HIDDEN.CIRCULATION.01 and TRANSFER.COHERENT.WILSON.01, both ``executed half [E] / selection open [O]''; the exploration probes transfer_ birkhoff_ circulation_ probe.py 42/42 and transfer_ coherent_ wilson_ probe.py 28/28 stay in experiments/tfpt-discovery/ as the discovery record). (1) v976 — the Birkhoff fibre and the entanglement-breaking no-go. The Birkhoff (random-permutation) fibre of the seam single step [formula in source] (exact sixth root of the v221 kernel, [formula in source] bit-exact) is exactly a one-parameter line [formula in source] ; the hidden coordinate is the sign-character Fourier coefficient [formula in source] , populations are exactly [formula in source] -free, and no fibre member is chiral ( [formula in source] forced). The one-step coherence spectrum is [formula in source] and the triangle loop current is an exact eigen-observable [formula in source] — one step plus one current readout measures [formula in source] without an ancilla. On the contrast qubit the Choi partial transpose has spectrum [formula in source] : the deployed sixth-root spectrum sits exactly on the entanglement-breaking boundary because [formula in source] (mutated spectra miss by [formula in source] ); at the full three-level the family stays NPT at every tested iteration with [formula in source] , [formula in source] -independent. The no-go that sharpens DYN.UNITARY.DILATION.01: the deployed Kraus dilation [formula in source] is measure-and-prepare, hence entanglement breaking with quantum capacity [formula in source] and [formula in source] exactly — any dilation closing that contract must be a genuinely different object. Shannon KKT certificates: [formula in source] is exactly capacity-achieving for both [formula in source] and [formula in source] ( [formula in source] bit, [formula in source] bit, ratio [formula in source] ) — the surviving classical message is binary on every scale. The defect–Birkhoff value coincidence (weights [formula in source] vs the v652 ladder [formula in source] ) is recorded typed [C] with its honest multiplicity audit; the forcing functor is the named open contract TRANSFER.DEFECT.BIRKHOFF.01. (2) v977 — the unistochastic [formula in source] lift and the 5-12-13 Wilson code. [formula in source] is unistochastic: an exact [formula in source] with [formula in source] entrywise, angles forced by [formula in source] ( [formula in source] , [formula in source] , [formula in source] ), [formula in source] unique, lift set [formula in source] up to rephasing; Jarlskog [formula in source] exactly, and the real part of every Wilson plaquette is fixed by [formula in source] through unitarity — the full rephasing-invariant Wilson data is classical up to the [formula in source] orientation bit [formula in source] . The main plaquette is [formula in source] , normalized [formula in source] with [formula in source] (atoms: [formula in source] , [formula in source] , [formula in source] ); all nine plaquettes close on four Gaussian phase types with norms exclusively [formula in source] . The center bridge: [formula in source] for the v530 atom matrix, [formula in source] , and the v530 sibling quotients fail the identity — the bridge selects the atom quotient. Rationality selection: [formula in source] is rational only at [formula in source] (the deployed step hits [formula in source] exactly, so [formula in source] ); census over 238 valid family points: exactly one full-code point [formula in source] the deployed [formula in source] ( [formula in source] the preregistered [formula in source] kill). No fixed microstep: [formula in source] and a Dirichlet recurrence witness ( [formula in source] ) shows no single closed unitary generates the relaxing sequence — repeated steps require dephasing between steps, the six-step macro-gate [formula in source] (the coherent sharpening of clock-vs-walk). The PMNS near-miss stays a negative control ( [formula in source] vs [formula in source] ; [formula in source] ; no PMNS derivation). Surfaces. Research-contracts document: the DYN.UNITARY.DILATION.01 section gains the executed lift-structure sharpening, the CCC reduced-channel prose and the two former ``exploration-only'' citations of rounds DCXCVI/DCXCVII are upgraded to veri citations; origin_theory gains the honest ``what the classical transport does not determine'' paragraph next to the v221 recoverability code; tfpt_2 gains the [formula in source] bridge corollary in the v530 center-quotient block. No status marker moves; both contracts stay open; no PMNS/CP/flavor claim.)Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v652_orbifold_arf.pyRegistered verification module · core
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QGEO.ORBARF.01: die Arf/GSO-Härtung des B-vs-C3-Diskriminators — **DIE 6⁶-KLASSIFIKATION ALLER SEKTOR-CHARAKTER-VERDRAHTUNGEN LÄSST GENAU {B, C3} ÜBRIG, DER EIN-FOCKRAUM-PIN ERZWINGT B, UND DIE μ₆-DEFEKT-LEITER MISST DIE VON C3 EXZIDIERTEN ZUSTÄNDE DIREKT** — Leiter-Exponenten 2Δ = (1/18, 2/9, 1/2) auf < 8e−4, exakte ladungsaufgelöste Minima (0,1,4,9,4,1)/36; **C3s Odd-Sektor-Vorhersagen 85/18 und 81/18 verfehlen die Messung um Faktor 85.0 und 9.0** (der Defekt-String ist exakt ladungsneutral: C3 exzidiert Zustände, die auf der Gitter-Naht mit positiver Klein-Norm existieren); der v639-2/9-Read allein ist B-vs-C3-BLIND (beide stimmen auf geraden Sektoren exakt überein) — das neue τ-Datum: OPE-Exponent 1/18 (rel 2.9e−3); Bond-Defekt-Prämisse → v653 (15 checks, ~30 s)
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