Original ledger status
FLAV.PENCIL.02
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
Recorded status: Identity/Lattice [I]/[L] + audit [P]
Dependencies, status detail and source
Canonical status: Identity/Lattice [I]/[L] (anchor singularity, type checker) + [P] (atlas/F4xG2 shadow audit)
Dependencies: FLAV.PENCIL.01; FLAV.KQ.01; v37; v52; v74
Scripts: v80_operator_pencil_geometry.py
Location: tfpt_2
Original CSV, line 147Original ledger status
FR.KOIDE.07
OPERATOR ORIGIN OF THE KOIDE SOURCE->POLE FACTOR 53/54 (external-review proposal 2026-06-14, validated; upgrades the FR.KOIDE.03 conjecture from a bare arithmetic guess 1-1/(2 N_fam^3) to an exact operator identity on the carrier): u_pole/u_source = a^T (R+Q) 1 / (2 * 1^T R a) = 53/(2*27) = 53/54. (1) THE CUBIC FAMILY BLOCK [I]: 1^T R a = 27, the E6xA2 flavor-shadow split 248 = dim E6 + det R + 2(1^T R a)N_fam = 78 + 8 + 2*27*3, so 2*27 = 54 is the sheet-doubled denominator. (2) THE MISSING CORNER [I]: the Sheet Diamond has present corners R=M(0,0), K=M(1,-1), L=M(2,0) and the ABSENT corner F=R+Q=M(1,1) with anchor-block determinant det B_F = 52 = dim F4 (FLAV.PENCIL.02/v80); its anchor response a^T(R+Q)1 = 53 = 52+1 (F4 shadow + singlet). (3) THE RATIO [I]: a^T(R+Q)1/(2*1^T R a) = 53/54 = 1-1/(2 N_fam^3) exactly (54 = 2 N_fam^3 = 2*27), so the two readings coincide but this one is structural, not fitted. (4) NEGATIVE CONTROL [I]: only the missing corner F gives 53 -- a^T M 1 for M in {R,Q,K,L} = {32,21,35,56}, none = 53 (specific, not generic). PHYSICAL STATUS [C]: the FACTOR is now sourced exactly; the MECHANISM (the leptonic pole-mass transfer evaluates the F corner) stays a conjecture, an F_transfer special case (F_pole: source->pole). Koide thus moves from 'near miss + conjecture' to 'operator-sourced source->pole transfer'; the prediction itself stays [C]. Cross-ref HOR.TRISECT.01 (the same Sheet-Diamond double-cover grammar carries the gravity clock, exponent ratio |Z2|)
Recorded status: Identity [I] (exact operator factor + negative control) + Physical [C] (the transfer mechanism)
Dependencies, status detail and source
Canonical status: Identity [I]: 53/54 = a^T(R+Q)1/(2*1^T R a) sourced from the missing Sheet-Diamond corner F (det B_F=52); mechanism stays [C]
Dependencies: FR.KOIDE.03; FLAV.PENCIL.02; FLAV.PLUCKER.02; v80_operator_pencil_geometry.py
Scripts: v183_koide_f_corner_transfer.py
Location: tfpt_4_frontier
Original CSV, line 178