Bit selector ladder
v568_bit_selector_ladder.py · flavor
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DIAMOND.BIT.SELECT.01: the residual reconstruction bit located, separated and given a canonical witness — the two 81-twins of the v567 audit (q32 = 2 = |Z2| vs 0) generate DIFFERENT integral orders (equal index 81, different lattices: the bit is integrally visible where every classical invariant coincides); the dominant mode of the sheet direction is v(c) = (1, 2, 2c) identically, and the LADDER SELF-CONSISTENCY — the dominant mode reproduces its own eigenvalue as the geometric ladder (2⁰,2¹,2²) = (1,2,4) — picks c = 2 UNIQUELY on all 28 members of the carrier-free class (no 81-pin, no column budget needed); the witness is prior structure (AnchorLadder steps 2ⁿ, 2 = |Z2|, the v566 trace code), not a found number; the SPLIT geometry sits at q32 = 1 and is EXCLUDED by the demands already imposed (algebra collapses to dim 5 — the v566 A2 Ext arrow is nonzero on the whole class; neither twin splits: the bit toggles WHICH nonsplit order is realised, not split/nonsplit); Priority-2 candidates tested honestly: the mu4-grading fails (order not graded — 81 stays a fingerprint), left V-multiplication induces a canonical F3-action on the cokernel (Z/3)⁴ — computed: charpoly x(x−1)²(x+1) mod 3, eigenvalues {0,1,1,−1}, NOT the regular μ₄ pattern; U acts as zero; twins identical — after two candidates the 81 stays a fingerprint. The physical selection is NOT derived — why the ladder self-consistency should hold is the relocated open question, the same slot as the RP-selection of the alignment bit (11 checks, ~1 s)
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