A registered result in its source context
Original ledger classification: E8 degree-ladder structure theorem [E]/[I] + [P] functorial residual (degrees = 6*spine U det-ladder, forced by 2,3,5; reclassifies v354/v355 overhead)
Recorded statement: THE REVERSE-AUDIT 'UNMAPPED' E8 CASIMIR DEGREES ARE THE FORCED TWO-FAMILY DECOMPOSITION (2026-06-27, v431): the structural complement of v354/v355/v430. The reverse audit found FIVE 'unmapped' degrees {12,14,18,20,24} ('hull overhead');…
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Paper context: Red-team audit
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E8.DEGREE.LADDER.01
Original ledger classification: E8 degree-ladder structure theorem [E]/[I] + [P] functorial residual (degrees = 6*spine U det-ladder, forced by 2,3,5; reclassifies v354/v355 overhead)
Original claim text
THE REVERSE-AUDIT 'UNMAPPED' E8 CASIMIR DEGREES ARE THE FORCED TWO-FAMILY DECOMPOSITION (2026-06-27, v431): the structural complement of v354/v355/v430. The reverse audit found FIVE 'unmapped' degrees {12,14,18,20,24} ('hull overhead'); this module shows they are NOT diffuse overhead but the forced two-family decomposition deg(E8) = 6*spine{2,3,4,5} U ({2} U flavor-det-ladder{8,14,20}). [E] TWO-FAMILY SPLIT FORCED BY 30=2*3*5: the E8 exponents are the phi(30)=8 totatives of h=30=2*N_fam*g_car (coprime to 6 => +-1 mod 6), so the degrees occupy ONLY the residue classes {0,2} mod 6. [I] 6k family {12,18,24,30}/6 = {2,3,4,5} = the v91 spine {e3,e1,e2,p0}(a=(1,1,2)). [I] 6k+2 family {2,8,14,20}: {8,14,20}=(det R,det C,det L)=the winding line det M(s,0)=6s+8 of the flavor diamond (v135), C=R+Q diag(1,0,0); 2=the matched quadratic/metric Casimir (8=det R also = rank E8). [E] '18'=6*N_fam is NOT a holdout (spine family, not on the det-ladder; 6s+8=18 has no integer s). [E] SPECIAL TO E8 among the simply-laced exceptionals (E6/E7/D5 fail the clean {0,2}-mod-6 split; F4/G2 share the split but not the spine+det content). [P] HONEST v355 LINE: the arithmetic decomposition is exact [E]/[I], but the FUNCTORIAL claim '6k+2 Casimir stratum = flavor sheet operators' needs a representation-theoretic map and stays [P]; 12,24 admit two canonical readings each (6*spine vs |R(A3)|=12 / |W(A3)|=24), so this is a STRUCTURE theorem, not a forced functorial flavor map. CONCLUSION: reclassifies v354's overhead to ZERO orphan degrees, the functorial flavor identification honestly kept [P]; closes no gate.
Original classification detail
[E]/[I] the forced two-family decomposition (the {0,2}-mod-6 split from h=30=2*3*5, 6k=6*spine, 6k+2={2} U det-ladder) and the '18'=6*N_fam + E8-specialness facts; [P] the functorial flavor-sheet identification (rep-theoretic map open, 12/24 multiplicity). Reclassifies the v354/v355 overhead to zero orphan degrees; closes nothing.
Dependencies as recorded
E8.REVERSE.AUDIT.01; E8.UNMAPPED.BANDWIDTH.01; E8.OTHERSIDE.AUDIT.01; E8.CAS.01; v91; v135
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- Red-team audit
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-27 ( v431, v432 — the ``unmapped'' [formula in source] degrees are forced spine [formula in source] flavor structure; the unconditional over-determination floor)Research changelog; TFPT — Introduction and reading guide
Navigation through a shared verification script
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- 2026-06-29 (discoverability — an SEO/GEO pass on the public website: a generated /llms.txt, explicit AI-crawler robots.txt, query-targeted metadata, and the first real backlinks from the README and the Zenodo deposit)Research changelog; TFPT — Introduction and reading guide
- Layer 2 — no free pattern, and the reverse auditVerification safeguards
- OutcomeRed-team audit
- Summary — the layered defenseVerification safeguards
Registered verification modules
- v431_e8_degree_ladder.pyRegistered verification module · registry
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E8.DEGREE.LADDER.01: the reverse-audit 'unmapped' E8 Casimir degrees are NOT diffuse overhead but the forced two-family decomposition deg(E8) = 6·spine{2,3,4,5} (+) ({2} U flavor-det-ladder{8,14,20}) -- the structural complement of v354/v355/v430. [E] TWO-FAMILY SPLIT FORCED BY 30=2·3·5: the E8 exponents are the φ(30)=8 totatives of h=30=2·N_fam·g_car (coprime to 6 => ±1 mod 6), so the degrees occupy ONLY the residue classes {0,2} mod 6. [I] 6k family {12,18,24,30}/6 = {2,3,4,5} = the v91 spine {e3,e1,e2,p0}(a=(1,1,2)). [I] 6k+2 family {2,8,14,20}: {8,14,20}=(det R,det C,det L)=the winding line det M(s,0)=6s+8 of the flavor diamond (v135), C=R+Q diag(1,0,0). [E] '18'=6·N_fam is NOT a holdout (spine family, not on the det-ladder). [E] SPECIAL TO E8 among the simply-laced exceptionals (E6/E7/D5 fail the clean {0,2}-mod-6 split). [P] HONEST v355 LINE: the arithmetic decomposition is exact [I], but the FUNCTORIAL claim '6k+2 Casimir stratum = flavor sheet operators' needs a rep-theoretic map ([P]); 12,24 admit two canonical readings each, so this is a STRUCTURE theorem, not a forced functorial flavor map -- reclassifies v354 overhead to zero orphan degrees, closes no gate. Wolfram-mirrored, Python (sympy).
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