Original ledger status
FLAV.SHEET.01
BRANCH-KERNEL SELECTION (next.txt P1 unblocked): at each branch point of the anchor-block cover the 2x2 anchor block is RANK 1 with canonical INTEGER kernels (Koide -2/3: right w=11*1-9a=(2,2,-7), left v=7*1-5a=(2,2,-3); carrier -5/3: right kernel = the democratic vector 1, left v=8*1-7a=(1,1,-6)). COLLAPSE LEMMA [L]: rank-1 forces P(x0).w perp span{1,a} => proportional to the antisymmetric direction (-1,1,0) of the anchor's two equal slots, on BOTH sides: sectors (up=-down, lepton pairing=0 - leptons sit ON the ramification; Koide is leptonic) and generations (gen1=-gen2, gen3=0). SECTOR ZERO LADDER [I]: lepton pairings ARE the det-B factors (zeros = the two branch points); up zeros = -3/2=-N_fam/|Z2| doubly (the v85 GL(2) rung; the whole up-row of P(-3/2) IS the odd direction); down zeros = 0 (=K itself) and -9/5=-N_fam^2/g_car. ORIENTATION: deck translation flips (up,down)=(+,-)->(-,+), magnitude ratio 10=A_Lambda; convention-free invariant f_up*f_down<0. CONTROLS: anchor (2,1,1) moves the collapse to (0,1,-1); (1,2,1) disc 40 non-split, no rational kernels (v82 trichotomy). The sector->sheet map is now DEFINED by the cover's own kernels - the P1 blocker (no independently motivated definition) is removed; the physical identification with the v92 chirality swap stays [P] (FLAV.SHEET.02)
Recorded status: Identity/Lattice [I]/[L] (kernels, collapse, ladder, controls) + [P] (sector-sheet physics)
Dependencies, status detail and source
Canonical status: Identity/Lattice: the cover defines the sector map; physics [P]
Dependencies: FLAV.PENCIL.03; FLAV.PENCIL.05; FLAV.DIAMOND.02; FLAV.MASSVOL.01 (sector rows)
Scripts: v96_branch_kernel_selection.py
Location: tfpt_2
Original CSV, line 174Original ledger status
CAR.PAIR.01
SHEET-PAIRING LEMMA (the first exact representation-theoretic anchor of the QBL programme; connects red-team Target B to the sheet Z2): character-exact weight-multiset results from the D5 spinor weights (+-1/2)^5 alone - (1) NO SCALAR WITHIN A SHEET: zero-weight multiplicity of S+xS+ (and S-xS-) is 0, because the odd slot count g=5 flips the sign parity of -w (a parity theorem of the five-slot code): there is no invariant bilinear pairing inside one chirality. (2) THE SCALAR LIVES ACROSS THE SHEETS: S+xS- has zero-weight multiplicity 16 = 1+5+10 (the Pascal triple) and equals exactly, as a weight multiset, the even-form tower Lambda^0 + Lambda^2 + Lambda^4 (256 = 1+45+210) with zero-mode grading (1,5,10) = the carrier code (Lambda^0,Lambda^1,Lambda^2)(C^5). (3) SHEET-DIAGONAL = ODD FORMS: (S+xS+) u (S-xS-) = 2Lambda^1 + 2Lambda^3 + Lambda^5 exactly (512 = 20+240+252): within-sheet pairings are odd-form-valued, never scalar. (4) the scalar-bearing tower tops at Lambda^{2K} with K=2 - bilinear seam data reach exactly the Pascal-ladder degree (CAR.LADDER.01). (5) QBL READING [P] (recorded, not claimed): the seam's single scalar two-point kernel is necessarily a SHEET PAIRING (chirality-off-diagonal, the same Z2 as GATE.METRIC.07 / FLAV.SHEET.01-03); the remaining step is to show the Calderon kernel supplies exactly this pairing and nothing beyond - then QBL => K=2 <=> g=5 closes the carrier choice
Recorded status: Identity [I] (character-exact multiset identities) + Physical [P] (QBL reading)
Dependencies, status detail and source
Canonical status: Identity: scalar pairing only across sheets; even tower tops at 2K; QBL anchored
Dependencies: CAR.LADDER.01; ARCH.QUAD.01 (QBL); GATE.METRIC.07 (sheet Z2); FLAV.SHEET.01-03; CAR.PASCAL.01
Scripts: v109_sheet_pairing.py
Location: tfpt_1
Original CSV, line 193