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A registered result in its source context

Original ledger classification: Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]

Recorded statement: THE TWO NAMED FACES OF ALPHA.QUILLEN.EXACT.01 CARRY COMPUTED WITNESSES (2026-08-27, seam/alpha promotion wave; probes seam_bfk_conical_det_probe 21/21 SPEC d06b3bbec70e7efc / laughlin_pump_em1_probe 20/20 SPEC f9b5cb0bf20d0293 /…

Statement, assumptions and sources

Paper context: Architecture, E8 and the electromagnetic fixed point

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ALPHA.QUILLEN.FACES.01

Original ledger classification: Exact/computed witnesses [E] + typed conditional [C]; the target row stays [O]

Original claim text

THE TWO NAMED FACES OF ALPHA.QUILLEN.EXACT.01 CARRY COMPUTED WITNESSES (2026-08-27, seam/alpha promotion wave; probes seam_bfk_conical_det_probe 21/21 SPEC d06b3bbec70e7efc / laughlin_pump_em1_probe 20/20 SPEC f9b5cb0bf20d0293 / quillen_rigidity_chain_probe 18/18 SPEC b4ee0dd0141da6ab, embedded byte-exact in v974). [E] BFK FACE EXECUTED: the Mayer-Vietoris determinant gluing on the seam circle at the four mu4 marks -- C_glue = 2^-N EXACT (N = 1..4 symbolic, general lengths), det'_zeta(Delta_S1) = l^2 reassembled, R(m) = (G_m|_marks)^-1; at KMS R_0 = 16 c3 circ(2,-1,0,-1), det'R_0 = 2^16 c3^3, glued product (2 pi)^2; vs v484 channel-wise EXACT (same mu4 eigenbasis, |spec| {0,2,2,4}, doublet ratio 4/ln2 with c3 cancelling, Tr B^k = 4^k + 2 2^k vs Tr C^k = 4^k + 2(-2)^k) but NOT globally proportional -- the kernel swap (gauge zero mode vs sign rep) is the sharpened diagonal-zeta face. [E] EM1 FACE COMPUTED: pumped charge == edge spectral flow == Streda == Chern == 1 on the v367 collar, single complex copy, sign-coherent conjugation mutant; 16-copy bookkeeping exact (c_- = 8, kY = 5/3, (1/kY) 41/6 = 41/10 = b1). [E] QUILLEN IDENTITY AT THE FINITE SHADOW: Berry integral == Poincare-Lelong divisor integral == +1 two-sided, difference an exact form, transition winding == Chern; anchor re-derived (alpha^-1 = 137.03599921684071, split residual 6.4e-58 at 50 digits, 8 b1 = 164/5 exact). [C] TYPED CONDITIONAL: IF the seam state is quasi-free (the rigidity premise, measured not forced in the strong form by SEAM.STATE.RPMIXING.01) THEN the identity applies literally to the seam det line. HONEST SCOPE: closes NOTHING on ALPHA.QUILLEN.EXACT.01 -- remaining content {rigidity premise} + {channel-swap question} + {continuum Bismut-Freed identification}; the BFK face is Delta = |D|^2, not a |D|-level operator identity; the pump is a single-copy statement.

Original classification detail

Exact witnesses for both faces; target stays open

Dependencies as recorded

ALPHA.QUILLEN.EXACT.01; SEAM.CONTACT.UNIT.01; SEAM.CONTACT.UNIT.02; EM.WARD.01; ALPHA.QUILLEN.INFLOW.01; SEAM.STATE.RPMIXING.01

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Registered verification modules

  • v974_alpha_faces_computed.pyRegistered verification module · core
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    ALPHA.QUILLEN.EXACT.01 [O-Update] + SEAM.CONTACT.UNIT.01/.02 + EM.WARD.01 / ALPHA.QUILLEN.INFLOW.01 + ALPHA.QUILLEN.FACES.01 [E, NEU] (Seam/Alpha-Promotionswelle 2026-08-27): **beide benannten Faces des Alpha-Targets tragen jetzt GERECHNETE Zeugen** — drei Probes byte-exakt eingebettet, sha256-gepinnt und wörtlich ausgeführt (21/21 MATCH_MODULO_LOCAL_FACTOR + 20/20 PUMP_QUANTIZED_MATCHES_CHERN + 18/18 CHAIN_SHADOW_OK) plus die modul-eigene Exaktsektion S0 (sympy/Fraction/mpmath, keine Probe-Importe). (1) Das BFK-Face AUSGEFÜHRT: die Burghelea–Friedlander–Kappeler-Klebekonstante ist EXAKT 2^−N (symbolisch hergeleitet N = 1..4, allgemeine Intervalllängen, Laurent-Polynom-Identität); masselose Reassemblierung det′_ζ(Δ_S¹) = l² = 2^−N·∏(2a_j)·(l/N)·det′(R₀) mit det′(R₀) = N·l/∏a_j; an der KMS-Skala l = 2π = 1/(4c₃): R₀ = 16c₃·circ(2,−1,0,−1) (16c₃ = |μ₄|·4c₃ pro Intervall), det′R₀ = 2¹⁶c₃³, Produkt (2π)²; Sprungmatrix R(m) = (G_m|_marks)⁻¹ exakt; gegen die v484-Markenmatrix G_marks = −4c₃ln2·circ(0,1,2,1) KEINE globale Proportionalität (Kerne in VERTAUSCHTEN μ₄-Kanälen: Eich-Nullmode vs. Vorzeichendarstellung), aber kanalweise EXAKT (gleiche μ₄-Fourier-Eigenbasis, |spec|-Multimengen {0,2,2,4}, Dublett-Verhältnis 4/ln2 mit KÜRZENDEM c₃, Tr B^k = 4^k + 2·2^k spiegelt Tr C^k = 4^k + 2(−2)^k — der Vorzeichen-Flip IST der Kern-Tausch); der v485-Skalenkanal EXAKT reproduziert über die KMS-Einheit (log det′-Differenz = (1/(4c₃))·G_reg(0;l)). (2) EM1 GERECHNET: gepumpte Ladung == Rand-Spektralfluss == Streda == Chern == 1 pro Flussquant auf dem v367-Kragenmodell (Wannier-Winding-Residuum 0.0; Streda ΔN = C·n_φ exakte Ganzzahlen; der Konjugations-Mutant kippt ALLE VIER Lesarten simultan, der Falschband-Projektor bricht die Quantisierung gitterinstabil); Buchhaltung exakt: 16 Majoranas = 8 komplexe Kopien, c₋ = 8 = g_car + N_fam, k_Y = 5/3, (1/k_Y)·41/6 = 41/10 = b₁. (3) Die endliche Quillen-Identität ZWEISEITIG: Berry-Integral == Poincaré–Lelong-Divisor-Integral == +1 über dem Twist-Torus (beide Referenzen, beide Größen), Differenz eine EXAKTE Form (3.3e−16), Übergangs-Winding == Chern (Dai–Freed); typisiert konditional auf die Quasi-frei-Rigiditäts-Prämisse (gemessen, nicht bewiesen — SEAM.STATE.RPMIXING.01). S0 leitet alles unabhängig her: die BFK-Geschlossenformen aus den ζ_R-Werten, den Alpha-Anker bei 50 Stellen (8b₁ = 164/5 exakt, EINDEUTIGE Wurzel im Scanfenster, α⁻¹ = 137.03599921684071, Split-Residuum 6.4e−58), die Inflow-Buchhaltung als exakte Brüche und ein probe-freies FHS-Chern-Zertifikat. Mutanten: Hash-Mutation vom sha256-Pin gefangen; die falsche KMS-Einheit (2π → 4π) bricht die Skalenidentität um EXAKT −2ln2; der b₁-Mutant gefangen. KEINE Marker-Bewegung: das Target bleibt [O] — Restinhalt typisiert als {Rigiditäts-Prämisse} + {Kanal-Tausch-Frage (das geschärfte Diagonal-Zeta-Face)} + {Kontinuums-Bismut–Freed-Identifikation}; α⁻¹ bleibt [E] unabhängig davon.

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