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A registered result in its source context

Original ledger classification: Open (research contract; canonical geometric identification of the raw seam collar with F2[y,z]/(y^2,z^4) unproven; Milnor algebra + exponents classical)

Recorded statement: THE MILNOR LOCAL-RING IDENTIFICATION CONTRACT [O] (registered 2026-08-30, review wave 6, v1004). REQUIRED: a CANONICAL identification between the raw seam collar / E8 transition bus and the reduced Milnor algebra F2[y,z]/(y^2,z^4)…

Statement, assumptions and sources

Paper context: TFPT — Introduction and reading guide

The exact identifier, original classification and full claim are available below.

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SEAM.MILNOR.LOCALRING.01

Original ledger classification: Open (research contract; canonical geometric identification of the raw seam collar with F2[y,z]/(y^2,z^4) unproven; Milnor algebra + exponents classical)

Original claim text

THE MILNOR LOCAL-RING IDENTIFICATION CONTRACT [O] (registered 2026-08-30, review wave 6, v1004). REQUIRED: a CANONICAL identification between the raw seam collar / E8 transition bus and the reduced Milnor algebra F2[y,z]/(y^2,z^4) preserving simultaneously the dual-number action, Frobenius pairing, Gray torsor, deck action and CP. ACCEPTANCE: the identification must be geometric/mechanical (not basis-chosen), must produce the rank clock and socle-CP as OUTPUTS. KILL: any second inequivalent identification with the same invariants, or failure of mu4-equivariance. NOTE: would reduce P2 / alignment-bit / Gauss-code / Brieskorn origin to one local ring. Currently [O] because the Milnor algebra + E8 exponents are CLASSICAL (cite, no claim) and the corpus map is unproven. Executed finite algebra (v1004): rank clock (2-a)(4-b) sums to h(E8)=30; S=pqr*mu/8; self-clock iff mu=8; (2,3,5) unique among ordered spherical triples; Galois-Gray 11/7/-1; CP = socle/Frobenius; integral D^4 bridge basis-dependent. PG(3,2)=AG(3,2) sqcup PG(2,2) interpretive [C]. Status: Open [O].

Original classification detail

Open [O]: required canonical identification (dual-number + Frobenius + Gray torsor + deck + CP) geometric/mechanical, not basis-chosen; rank clock and socle-CP as outputs. Kill: second inequivalent identification, or mu4-equivariance failure. Classical cite vs new-in-corpus [E-finite] vs interpretive [C] typed on v1004. WAVE-6 2026-08-30. | AFTERNOON (2026-08-30 v1010): SHARPENED -- strong all-structure identification finitely obstructed at F2 (clock order 2 vs 4, CP Jordan rank 2 vs 4) and at all upstairs homes (Z/4: J^2=-I vs Gray P^2!=-I, D8 vs C4xC2; Gaussian k=2 order collapse, k=3 rank/relation clash; affine cannot repair linear parts). Only the coarse D-module+pairing bridge exists (witness constructed; |Aut(X)|=36864, |Aut(Y)|=8). Ring-internal identities (rank clock, socle CP, self-clock) of v1004 UNAFFECTED. Display stays [O].

Dependencies as recorded

SEAM.EQUIV.01; AX.P2.01

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Registered verification modules

  • v1004_milnor_frobenius_gray.pyRegistered verification module · frontier
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    SEAM.MILNOR.LOCALRING.01 [O] (Review-Welle 6, 2026-08-30; endliche Algebra; Korpus-Identifikation bleibt offen): KLASSISCH (zitiert, kein Claim) Milnor-Algebra von x^2+y^3+z^5 congruent Q[y,z]/(y^2,z^4) dim 8, Spektralzahlen = E8-Exponenten {1,7,11,13,17,19,23,29}. NEU-IM-KORPUS EXAKT [E-finite]: Rang-Uhr (2-a)(4-b), Summe 30=h(E8); S=pqr*mu/8; Selbst-Uhr iff mu=8; (2,3,5) einziges geordnetes sphaerisches Tripel; Galois-Gray 11/7/-1; CP=Sozkel/Frobenius; integrale D^4-Bruecke basisabhaengig. [C] PG(3,2)=AG(3,2) sqcup PG(2,2) nur interpretativ. Vertrag bleibt [O]. Python-only / Wolfram-Spiegel zurueckgestellt.

  • v1010_simplicity_bridge_census.pyRegistered verification module · frontier
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    Simplicity-Zensus + W/Q-Kanonizitaet + Milnor-Doppelobstruktion (Nachmittag 2026-08-30): Ableitungsmatrix; Restminimum S4=2; Anker (1,1,2) nicht unter 3 deklarierten Milnor-Karten; phi0 vier neu NULL. Bruecke Q KANONISCH: Leiter erzwingt Summen (9,5,1); C's 5 von R geerbt -- v1005-Zirkularitaetsflag als erzwungene Provenienz korrigiert. Bruecke W CHOICE aber bedingt eindeutig (1078 -> 1). Milnor-Starkbruecke NICHT existent bei F2 und allen upstairs homes; grobe D+Paarung existiert; |Aut(X)|=36864, |Aut(Y)|=8. SEAM.MILNOR.LOCALRING.01 bleibt [O]; AX.P2.01 bleibt Axiom. Python-only / Wolfram zurueckgestellt.

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