A registered result in its source context
Original ledger classification: Identity [I] (exact surface/wall/budget identities) + Physical [P] (reading)
Recorded statement: THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume walls at the discrete atoms; external review 2026-06-12, validated): (1) SURFACE + WALLS [I]: on the established diamond M(s,t) = R + Q diag(s,t,t)…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
The exact identifier, original classification and full claim are available below.
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Read the exact registered claim and its dependencies
FLAV.SURF.01
Original ledger classification: Identity [I] (exact surface/wall/budget identities) + Physical [P] (reading)
Original claim text
THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume walls at the discrete atoms; external review 2026-06-12, validated): (1) SURFACE + WALLS [I]: on the established diamond M(s,t) = R + Q diag(s,t,t) (FLAV.DIAMOND.01/02), det M(s,t) = 3s(t+1)(t+2) + t^2 + 5t + 8; two iso-volume WALLS independent of s: t = -2 => det = 2 = |Z2| (the Z2 wall), t = -1 => det = 4 = |mu_4| (the mu_4 wall; K = M(1,-1) lies on it - det K = 4 is a LAYER, not an isolated hit); the WINDING LINE t = 0 has det = 6s + 8 => (det R, det C, det L) = (8, 14, 20); the fourth canonical point closes the pattern: det F = det M(1,1) = 32 = 2^{g_car}. (2) ANCHOR BLOCK [I]: det B_{M(s,t)} = 6s(t+2) + 3t^2 + 15t + 16; on the winding line det B(s,0) = 2 det M(s,0) EXACTLY; own Z2 wall det B(s,-2) = -2 (s-independent); t = -1 is NOT a B-wall (6s+4, recorded honestly). (3) ROW-BUDGET AXES [I]: rowsum(C) = (7, 11, 13), rowsum(U) = (3,3,3) (democratic winding), rowsum(V) = (1,2,3) = Spec(Q_+) verbatim; audit: the centre budget (7, 11, 13) reads (scalaron, ||Pl(K)||_1, Delta_Q) - the three quark constants (audit, not load-bearing). (4) TWO ANCHOR MICRO-IDENTITIES [I]: e1^2 + e2^2 = 16 + 25 = 41 = 10 b1 (the anchor Pythagoras for the abelian coefficient, companion to Delta_Y = 25 = 9 + 16); p1^2 + p2^2 = 16 + 36 = 52 = the carrier coset root count (40 + 12, E8.GRADE.01). (5) READING [P] (recorded): the flavor algebra lives on a 2d surface whose walls are the discrete atoms and whose axes are democratic winding and the Q_+ progression - compiler semantics replacing the matrix list; no gate status changes
Original classification detail
Identity: det M = 3s(t+1)(t+2)+t^2+5t+8; walls 2 and 4 (s-independent); winding line (8 14 20); det F = 32; det B = 2 det M on t = 0; V-rowsum = Spec(Q+); 41 and 52 micro-identities
Dependencies as recorded
FLAV.DIAMOND.01-02; FLAV.H2.04; ARCH.TRIAD.01; E8.GRADE.01 (52); FLAV.KQ.01 (11 13)
Open the original ledger source, row 220Location recorded in the ledger
These document locations are recorded directly on the ledger row. They are document level navigation, rather than a newly inferred section citation.
- Standard Model and flavor structure
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.
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- 2026-06-24 (The sheet generator [formula in source] as a binary internal compiler: v410– v414)Research changelog; TFPT — Introduction and reading guide
- Front matter / supportStandard Model and flavor structure
- Research Contract 1 — [formula in source]tfpt research contracts
- OutcomeRed-team audit
- Front matter / supportResearch contracts
- Front matter / supportStandard Model and flavor structure
- 2026-06-12Research changelog; TFPT — Introduction and reading guide
Registered verification modules
- v135_det_surface.pyRegistered verification module · registry
Read the description recorded in the module registry
THE DETERMINANT SURFACE (the sheet diamond is a 2d surface with iso-volume WALLS at the discrete atoms): det M(s,t) = 3s(t+1)(t+2) + t² + 5t + 8 on the established diamond M(s,t) = R + Q·diag(s,t,t) (v94/v95) — two iso-volume walls INDEPENDENT of s: t = −2 ⇒ det = 2 = |Z₂| (the Z₂ wall) and t = −1 ⇒ det = 4 = |μ₄| (the μ₄ wall; K = M(1,−1) lies on it, so det K = 4 is a LAYER, not an isolated hit); the winding line t = 0 carries det = 6s + 8 ⇒ (det R, det C, det L) = (8, 14, 20), and det F = det M(1,1) = 32 = 2^g_car closes the four canonical points [I]; ANCHOR BLOCK: det B = 6s(t+2) + 3t² + 15t + 16 with det B(s,0) = 2·det M(s,0) EXACTLY on the winding line, its own Z₂ wall det B(s,−2) = −2, and t = −1 is NOT a B-wall (6s+4, recorded honestly) [I]; ROW-BUDGET AXES: rowsum(C) = (7,11,13), rowsum(U) = (3,3,3) (democratic winding), rowsum(V) = (1,2,3) = Spec(Q₊) verbatim; audit: the centre budget (7,11,13) = (scalaron, ‖Pl(K)‖₁, Δ_Q) [I]; TWO ANCHOR MICRO-IDENTITIES: e₁² + e₂² = 41 = 10·b₁ (the anchor Pythagoras for the abelian coefficient, companion to Δ_Y = 25 = 9+16) and p₁² + p₂² = 52 = the carrier coset root count (40+12, v128) [I]; reading [P]: the flavor algebra lives on a 2d surface whose walls are the discrete atoms and whose axes are democratic winding and the Q₊ progression — compiler semantics replacing the matrix list; no gate status changes
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