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A registered result in its source context

Original ledger classification: Identity [I] (exact census/uniqueness theorem on frozen operators) + Physical [P] (margins)

Recorded statement: THE ADDRESS TABLE IS PINNED (the FLAV.H2.03 per-fermion item closed at the information level; exact census theorem): (1) THE WORD TABLE IS THE RESIDUE OPERATOR [I]: the established identity L = R + 2U (FLAV.DIAMOND.02, U = winding axis…

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FLAV.H2.04

Original ledger classification: Identity [I] (exact census/uniqueness theorem on frozen operators) + Physical [P] (margins)

Original claim text

THE ADDRESS TABLE IS PINNED (the FLAV.H2.03 per-fermion item closed at the information level; exact census theorem): (1) THE WORD TABLE IS THE RESIDUE OPERATOR [I]: the established identity L = R + 2U (FLAV.DIAMOND.02, U = winding axis N_fam 1 e_1^T) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 word lengths verbatim; the addresses are R's entries plus one hexagon turn for generation 1, and R's first column is THE ANCHOR a = (1,1,2) - the first-generation residues are the anchor components. (2) THE MARGINS ARE ATOMS [I]: row sums of R = (4, 8, 10) = (e1, rank E8, p3); column sums = (4, 13, 5) = (e1, Delta_Q, g_car); total 22 = 2x11 (ARCH.TRIAD.01). (3) PINNING THEOREM [I, exact census]: among ALL 3x3 matrices with entries in the hexagon {0..5}, exactly 17 have the atom margins, and exactly ONE has det = 8 = rank E8 - and it is R (the same one is the unique one with SNF (1,1,8); all 17 determinants are distinct, 8 occurs once - control computed explicitly). The per-fermion assignment table carries ZERO residual information beyond the atom margins and the rank determinant. (4) within-sector assignment = the established transport reading (m ~ lambda_Y^L, longer word = lighter fermion). (5) RESIDUE [P] (recorded): the open H2 item shrinks from 'derive 9 per-fermion integers' to 'derive the six atom margins + det = rank'. FIREWALL: R, L and all word lengths were frozen in v4/v18/v20/v71 long before today's census - no degrees of freedom spent

Original classification detail

Theorem: R = unique hexagon matrix with atom margins + det 8; address table = R + first-generation winding; H2 residue = the margins

Dependencies as recorded

FLAV.H2.03; FLAV.DIAMOND.02 (L = R + 2U); FLAV.H2.01; ARCH.TRIAD.01; v18; v20; v71

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Registered verification modules

  • v121_address_pinning.pyRegistered verification module · registry
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    THE ADDRESS TABLE IS PINNED (the per-fermion assignment closes at the information level; exact census theorem): THE WORD TABLE IS THE RESIDUE OPERATOR [I] — the established identity L = R + 2U (v95) says the word-length table IS L[sector][generation] with rows (up; down; lepton) = ((7,3,0); (7,5,2); (8,5,3)) = the v18/v20 words verbatim; addresses = R's entries + one hexagon turn for generation 1, and R's first column is THE ANCHOR a = (1,1,2); THE MARGINS ARE ATOMS [I]: row sums (4,8,10) = (e₁, rank E8, p₃), column sums (4,13,5) = (e₁, Δ_Q, g_car); PINNING THEOREM [I, exact census]: among ALL 3×3 matrices with entries in the hexagon {0..5}, exactly 17 have the atom margins and exactly ONE has det = 8 = rank E8 — and it is R (also unique with SNF (1,1,8); all 17 determinants distinct — control computed explicitly) ⇒ THE ASSIGNMENT TABLE CARRIES ZERO RESIDUAL INFORMATION beyond atom margins + rank determinant; within-sector ordering = established transport reading; residue [P]: H2 shrinks from 'derive 9 integers' to 'derive the six atom margins + det = rank'; firewall: R, L, words frozen in v4/v18/v20/v71

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