A registered result in its source context
Original ledger classification: Identity [I] (exact census on frozen selectors) + Physical [P] (selector establishment)
Recorded statement: THE MARGINS ARE THEOREMS (the FLAV.H2.04 residue closed: the established frozen selectors pin R uniquely - the atom margins lose their input status): THREE ESTABLISHED SELECTORS, all frozen pre-v120 - (S1) the D4 annihilator n = (5,-9,6)…
Statement, assumptions and sources
Paper context: Research contracts
The exact identifier, original classification and full claim are available below.
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FLAV.H2.05
Original ledger classification: Identity [I] (exact census on frozen selectors) + Physical [P] (selector establishment)
Original claim text
THE MARGINS ARE THEOREMS (the FLAV.H2.04 residue closed: the established frozen selectors pin R uniquely - the atom margins lose their input status): THREE ESTABLISHED SELECTORS, all frozen pre-v120 - (S1) the D4 annihilator n = (5,-9,6) with n^T R = (8,0,0) (FLAV.DIAMOND.01/tfpt_2: n kills the unchanged (c2,c3) plane; n.a = 8); (S2) det R = 8 = rank E8 (v71 determinant quartet (3,4,8,20), product 1920 = |W(D5)|); (S3) det K = 4 = |mu_4| with K = R + Q Sigma (the diamond); plus the definitional hexagon range {0..5}. (1) CENSUS [I]: hexagon columns with n.col = 8: exactly 4, with n.col = 0: exactly 4 => 64 (S1)-candidates; (S2) leaves 12; (S3) leaves EXACTLY ONE - and it is R. (2) COROLLARY [I]: the atom margins (4,8,10)/(4,13,5), the anchor column R e_1 = a = (1,1,2), and all FLAV.H2.03/04 sum rules (16, 10, 14, 24, 40) are CONSEQUENCES of (S1)-(S3) - input status revoked. (3) BONUS LEMMA [I]: on the (S1)+(S2) locus det(M + 2U) = 20 = det L holds for ALL 12 candidates - the fourth quartet determinant is NOT an independent selector but a consequence: the quartet (3,4,8,20) carries redundancy, the compiler's overdetermination pattern. (4) RESIDUE [P] (recorded): H2 reduces to the establishment of the selectors themselves (n and the diamond determinants - pre-existing inventoried objects); the address question introduces NO new residual class. FIREWALL: n, quartet, R, L, words frozen in v4/v18/v20/v71/v94 - nothing fitted
Original classification detail
Theorem: established selectors (n-annihilator + det R = 8 + det K = 4) pin R uniquely; margins + anchor column + sum rules = consequences; det L = 20 automatic
Dependencies as recorded
FLAV.H2.04; FLAV.DIAMOND.01-02; v71 (quartet); v94 (annihilator); CONTRACT.U.01
Open the original ledger source, row 206Location recorded in the ledger
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- Research contracts
Navigation through a shared verification script
These sections cite a script associated with the claim. This is a source navigation join, rather than an explicit citation of the claim or a theorem equivalence.
- What this changes, and what stays openE8 audit and bootstrap
- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Front matter / supportResearch contracts
- 2026-06-12 (external review integrated: [formula in source] typing, marker migration, website parity)Research changelog; TFPT — Introduction and reading guide
- Status summary and open audit pointsArchitecture, E8 and the electromagnetic fixed point
- Research Contract 1 — [formula in source]tfpt research contracts
- Status summary and open audit pointstfpt 1 architecture e8
- Front matter / supportResearch contracts
Registered verification modules
- v122_margin_theorem.pyRegistered verification module · registry
Read the description recorded in the module registry
THE MARGINS ARE THEOREMS (the established frozen selectors pin R uniquely — the v121 atom margins lose their input status): three selectors, all frozen BEFORE the address question was posed — (S1) the D₄ annihilator n = (5,−9,6) with nᵀR = (8,0,0) (v94: kills the (c₂,c₃) plane, n·a = 8), (S2) det R = 8 = rank E8 (v71 quartet (3,4,8,20)), (S3) det K = 4 = |μ₄| with K = R + QΣ (the diamond), plus the definitional hexagon range {0..5}; CENSUS [I]: 4×4×4 = 64 (S1)-candidates, (S2) leaves 12, (S3) leaves EXACTLY ONE — and it is R; COROLLARY [I]: the atom margins (4,8,10)/(4,13,5), the anchor column Re₁ = a, and ALL v120/v121 sum rules (16,10,14,24,40) are CONSEQUENCES — input status revoked; BONUS LEMMA [I]: on the (S1)+(S2) locus det(M+2U) = 20 = det L for ALL 12 candidates — the fourth quartet determinant is redundant (the compiler's overdetermination pattern); residue [P]: H2 reduces to the establishment of the selectors themselves (pre-existing inventoried objects) — the address question introduces NO new residual class
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