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A registered result in its source context

Original ledger classification: Identity/Lattice [I]/[L] (kernels, collapse, ladder, controls) + [P] (sector-sheet physics)

Recorded statement: 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:…

Statement, assumptions and sources

Paper context: Standard Model and flavor structure

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FLAV.SHEET.01

Original ledger classification: Identity/Lattice [I]/[L] (kernels, collapse, ladder, controls) + [P] (sector-sheet physics)

Original claim text

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)

Original classification detail

Identity/Lattice: the cover defines the sector map; physics [P]

Dependencies as recorded

FLAV.PENCIL.03; FLAV.PENCIL.05; FLAV.DIAMOND.02; FLAV.MASSVOL.01 (sector rows)

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Location recorded in the ledger

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Registered verification modules

  • v96_branch_kernel_selection.pyRegistered verification module · registry
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    Branch-kernel selection (P1 unblocked): at each branch point the anchor block is RANK 1 with canonical integer kernels (Koide: w=(2,2,−7), v=(2,2,−3); carrier: w = the democratic vector 1, v=(1,1,−6)); collapse lemma — rank 1 forces P(x₀)·w ⊥ span{1,a} ⇒ ∝(−1,1,0): up = −down (the deck-odd pair), LEPTON pairing = 0 (leptons sit ON the ramification; Koide is leptonic); sector zero ladder: lepton zeros = the two branch points, up = −3/2 doubly (the v85 GL(2) rung), down = 0 (=K) and −9/5; anchor-placement controls (2,1,1)/(1,2,1)

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