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Original ledger classification: Open (research contract)

Recorded statement: THE PRIME-COMPLETION CONTRACT [O] (registered 2026-09-04, v1020): replaces the "unique from seam data alone" reading of SEAM.BULK4D.RECON.01/B7 by uniqueness IN THE CATEGORY OF SEAM-GENERATED (PRIME) COMPLETIONS. DEMAND: (1) an explicit…

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BULK.PRIME_COMPLETION.01

Original ledger classification: Open (research contract)

Original claim text

THE PRIME-COMPLETION CONTRACT [O] (registered 2026-09-04, v1020): replaces the "unique from seam data alone" reading of SEAM.BULK4D.RECON.01/B7 by uniqueness IN THE CATEGORY OF SEAM-GENERATED (PRIME) COMPLETIONS. DEMAND: (1) an explicit family of seam-derived subalgebras A_i (seam CAR algebra, its time evolution, inclusions/intersections); (2) generatedness A_bulk = vN(v_i A_i); (3) NO-SPECTATOR: trivial relative commutant (v_i A_i)' ^ A_bulk = C.1, equivalently no decoupled tensor factor with trivial boundary map; (4) uniqueness ONLY within this category; (5) stability of (2)/(3) in the 3+1D limit. KILL: a seam-generated completion with nontrivial relative commutant, or two inequivalent prime completions. FINITE WITNESS (v1020, free fermions, 2+1D strip): stacking a trivial gapped sector leaves every seam datum unchanged (Chern, edge modes, seam-restricted covariance) and changes the bulk; Krylov generatedness + commutant test separate B from B (+) C by exactly dim C at every momentum; generatedness holds a.e. in p (fails only at p=0 by symmetry). Dimension typing: hypotheses 2+1D free-fermion, conclusion a re-scoped 4D demand (DIMENSION.UPLIFT.FIREWALL.01 F2). The 2D modular-invariant uniqueness of the holomorphic (E8)_1 net is untouched and is NOT a 4D no-spectator theorem.

Original classification detail

Open: the prime-completion contract (uniqueness in the category of seam-generated completions with trivial relative commutant); finite free-fermion witness in v1020 (B vs B (+) C separated by dim C at every momentum, generated a.e. in p); no closure; SEAM.BULK4D.RECON.01/B7 re-scoped, not superseded; DIMENSION.UPLIFT.FIREWALL.01 F2 dimension typing in force

Dependencies as recorded

SEAM.BULK4D.RECON.01; DIMENSION.UPLIFT.FIREWALL.01

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Registered verification modules

  • v1020_spectator_sector_obstruction.pyRegistered verification module · frontier
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    Spectator-Sektor-Hindernis (r644-Audit-Ernte 2026-09-04): endlicher freier-Fermion-Zeuge, neu abgeleitet (keine Proben-Importe). Aufschichten eines entkoppelten trivialen Gap-Sektors C (M=3, Chern 0) auf das Seam-Modell B (M=1, NY=8) laesst alle Seam-Daten identisch (Chern C_B=C_{B+C}=-1, C_C=0; Nullmoden 2/0/2 mit B-Träger 1.0; Randdispersion koinzident 1.4e-15; seam-restringierte Kovarianz 0.0; Randprofil-Ueberlapp 1.0) und aendert den Bulk (Dim 16 vs 32, E0(C)=-25.31, Rang 4 vs 8, HS 0.752536 vs 0.760202). Repariertes Kriterium: Krylov-Erzeugtheit spectator_dim(B+C)-spectator_dim(B)=16 an allen 128 Impulsen; Kommutant 1 vs 17, Pi_C im Kommutanten (Rest 0.0); Auswahl eindeutig (B ausgewaehlt, B+C verworfen). EHRLICH: spectator_dim(B)=10 nur bei p=0 -- Kriterium fast ueberall in p. SEAM.BULK4D.RECON.01 bleibt [O]; BULK.PRIME_COMPLETION.01 neu [O] registriert. KEIN MARKER-MOVE. KEIN RH-CLAIM. Python-only / Wolfram zurueckgestellt.

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