A registered result in its source context
Original ledger classification: Identity [I] (surface/winding/normal closures + negative controls) + Audit (F corner) + honest corrections
Recorded statement: SHEET DIAMOND & WINDING LINE (second review round 2026-06-11; arithmetic fully validated, interpretations corrected where needed) [I]: (1) all four flavor operators are distinguished points of ONE two-parameter surface M(s,t)=R+Q…
Statement, assumptions and sources
Paper context: Standard Model and flavor structure
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FLAV.DIAMOND.01
Original ledger classification: Identity [I] (surface/winding/normal closures + negative controls) + Audit (F corner) + honest corrections
Original claim text
SHEET DIAMOND & WINDING LINE (second review round 2026-06-11; arithmetic fully validated, interpretations corrected where needed) [I]: (1) all four flavor operators are distinguished points of ONE two-parameter surface M(s,t)=R+Q diag(s,t,t): R=M(0,0), K=M(1,-1), L=M(2,0), F=M(1,1), with the global invariants det M(s,t)=3st^2+9st+6s+t^2+5t+8 and det B_M(s,t)=6st+12s+3t^2+15t+16; the mass-transport pencil K+xQ is the cut (s,t)=(1+x,x-1), on which det B factorises as (3x+2)(3x+5) = the v81/v85 master cover. (2) BUILT-IN NEGATIVE CONTROLS: the factorisation is special to that cut - the diagonal cut t=s gives 9s^2+27s+16 with disc=153 NON-square, the SAME control discriminant as v85's R-direction (anchor-first coherence), and the R->L cut t=0 is linear/degenerate. (3) WINDING SYNCHRONISATION: on R_s=R+s*1e1^T, det B_{R_s}=2 det R_s for ALL s (8+2s vs 16+4s); the triple lock (tr=15=dim A3, det=20=det L, coxeter lift (R_s^T a)_1=30=h(E8)) fixes s=6=|R+(A3)| by each condition alone. (4) COFACTOR SEAM NORMAL (typed as repackaging - adjugate row by construction; content = integer readings): n=(5,-9,6) is the common first adjugate row of R and L, n.1=2=|Z2| is the per-winding determinant increment, n^T R=(8,0,0) and n^T L=(20,0,0): the normal annihilates the stable columns - only generation 1 is an open torsion channel. (5) REALITY CORRECTED (the review's 'Reality Selector' is wrong as a selection claim): disc(s)=17s^4-18s^3+709s^2+588s-7996 changes sign at s*~2.825, so the spectrum is real for all s>~2.83 and reality does NOT select s=6; at the physical s=6: disc=39200=2^5 5^2 7^2=2(10*14)^2, spectrum real positive. (6) F-CORNER AUDIT extending v80: det F=32=2^5, chi_F=(lam-2)(lam^2-13lam+16), B_F=[[37,43],[53,63]] with det 52=dim F4, sum 196=14^2=(dim G2)^2, tr 100, 43+53=96=2 Omega_adm - audit fingerprints, not load-bearing. (7) FIREWALL REJECTED as a hard rule: 'all small rational factors must be adjacent spine quotients' is FALSE - 16/7, 7/6 (lepton c), 5/6 (gamma_car), 8/7 are load-bearing non-members; the v74 quotient ladder remains an observation, not an admissibility filter
Original classification detail
Identity [I]: one surface carries R/K/L/F; winding synchronised; reality threshold corrected; firewall rejected
Dependencies as recorded
FLAV.KQ.01; FLAV.PENCIL.05; v74; v80; v81; v85
Open the original ledger source, row 171Location 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
- Verification reference catalog
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.
- 2026-06-15 (the diamond axis geometry — two axes + the transfer corner)Research changelog; TFPT — Introduction and reading guide
- Quarks: hierarchy from the same word-lengthsStandard Model and flavor structure
- The Sheet Diamond and the Winding Line: masses and transport from one surfacetfpt 2 standard model
- Quarks: hierarchy from the same word-lengthstfpt 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
- 2026-06-11Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
Registered verification modules
- v94_sheet_diamond.pyRegistered verification module · registry
Read the description recorded in the module registry
Sheet diamond: R, K, L, F are four points of ONE surface M(s,t) = R+Q·diag(s,t,t) (mass pencil = the cut (1+x,x−1); diagonal cut reproduces v85's non-square disc 153 — built-in negative control); winding line det B = 2·det for ALL s with the s=6 triple lock; cofactor normal (5,−9,6) selects generation 1; quark-ratio integers canonicalised as left/right Plücker norms of K (11, 26); reality threshold corrected to s*≈2.83; spine-quotient firewall rejected (16/7, 7/6, 5/6, 8/7 counterexamples)
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.