A registered result in its source context
Original ledger classification: Identity/Lattice [I]/[L] + audit [P]
Recorded statement: Operator-pencil geometry of (K,Q,R,L) - the anchor plane as a small area in operator space (validated review block; all in admissible classes). STRONG: [2] ANCHOR SINGULARITY THEOREM det B(K+xQ)=9x^2+21x+10=(N_fam x+|Z2|)(N_fam…
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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FLAV.PENCIL.02
Original ledger classification: Identity/Lattice [I]/[L] + audit [P]
Original claim text
Operator-pencil geometry of (K,Q,R,L) - the anchor plane as a small area in operator space (validated review block; all in admissible classes). STRONG: [2] ANCHOR SINGULARITY THEOREM det B(K+xQ)=9x^2+21x+10=(N_fam x+|Z2|)(N_fam x+g_car)=(3x+2)(3x+5), oriented anchor area degenerates at x=-|Z2|/N_fam=-2/3 (Koide target/gap base (2/3)^6) and x=-g_car/N_fam=-5/3 (D5/A3 glue asymmetry) => 2/3 is the FIRST SINGULAR POINT of the mass<->transport anchor plane, not just a recurring fraction [I/L]; [4] buildup chain (3,7,6,4) partial sums (3,10,16,20)=(N_fam,A_Lambda,dim S+,det L), scalaron 7=A_Lambda-N_fam [I]; [6] type checker det B_Q=9=N_fam^2, det B_K=10=A_Lambda, det B_R=16=dim S+, det B_L=40=|R(D5)| [I/L]. AUDIT (exact values [I], reading decorative [P]): [3] differential spectrum D,D',D'' at -1,0,1,2 = (2,4,20,68),(1,6,29,70),(-4,14,32,50) (29=top E8 exp, 32=2^gcar, 50=A4xA4 block); [5] F4xG2 shadow det B_{R+Q}=52=dim F4, chi_[K,Q]=t^3+5t+14 (14=dim G2), |Pl_R(K)|_1=26, 248=52+14+26*7 = real E8->F4xG2 branching (52,1)+(1,14)+(26,7) - an operator shadow, not a Lie-theoretic embedding proof
Original classification detail
Identity/Lattice [I]/[L] (anchor singularity, type checker) + [P] (atlas/F4xG2 shadow audit)
Dependencies as recorded
FLAV.PENCIL.01; FLAV.KQ.01; v37; v52; v74
Open the original ledger source, row 147Location recorded in the ledger
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- 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
- Front matter / supportStandard Model and flavor structure
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- 2026-06-14 (operator origin of the Koide 53/54 factor: the missing Sheet-Diamond corner, v183)Research changelog; TFPT — Introduction and reading guide
- The Koide relation — near [formula in source] , computed exactlyFrontier and open physical interfaces
Registered verification modules
- v80_operator_pencil_geometry.pyRegistered verification module · frontier
Read the description recorded in the module registry
operator pencil: anchor singularity det B(K+xQ)=(3x+2)(3x+5); block-det type checker (9,10,16,40); F₄×G₂ shadow 52+14+26·7=248
A registered module is a source reference. Its presence does not assert that the module was executed in this snapshot.