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MCA: move the razor crossing bracket from both ends (Haboeck staircase + far-CA floor) - #1162

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MCA: move the razor crossing bracket from both ends (Haboeck staircase + far-CA floor)#1162
AllenGrahamHart wants to merge 1 commit into
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AllenGrahamHart:band-razor-bracket-export

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What changed

Five sha256-pinned certificate packets under experimental/data/certificates/, moving the official rate-half MCA crossing bracket from both ends. Every claim is machine-verified in the public campaign repository (AllenGrahamHart/rs-mca-prize-dag @ 4e77e95b3acf); the packets pin the exact files and record replay commands.

The safe side moves below 3n/4 for the first time

  • mca-haboeck-quadratic-johnson-import-v1 — imports Haboeck, A note on mutual correlated agreement for Reed-Solomon codes, IACR ePrint 2025/2110, Theorem 2 (this repo's own [Hab25]): the proved quadratic Johnson-range support-wise MCA bound. The unproved BCHKS25 linear refinement is explicitly excluded. The audit chain closes through this repository's own audit_bchks25_thm46_conditional_johnson_import.md (whose "resolved one level further" section carries the independent 2025/2110 Thm 2 proof audit, external trail at latifkasuli/mca), plus a 28-attack adversarial certification in the campaign repo — including the check with teeth: under the wrong rate convention the specialized thresholds would be unsafe by exactly 1.
  • mca-razor-haboeck-johnson-staircase-v1 — the exact official-row specialization: for admissible q >= Q_9*2^128 (log2 q >= 232.650530), a_RH(q) <= a_{m(q)} along an 87-member staircase; on every razor row q > 2^255.9, a_RH(q) <= a_94 = 1,563,215,236,073 (vs 3n/4 = 1,649,267,441,664 — a gain of 86,139,268,540 agreement steps), upgrading to a_95 above an exact threshold; m = 96 is unaffordable under q < 2^256. Safe side only; no status claim.
  • mca-unique-decoding-ca-mca-scope-fence-v1 — why a direct import was necessary: the published unique-decoding CA-to-MCA transfer has gate 2r <= n-k, which at rate 1/2 is exactly a >= 3n/4; the whole live interval fails it by >= 2.

The far-CA side gains its first floor

  • mca-razor-farca-floor-lb1-v1LB1: an explicit maximal-core pencil gives, at every posed row and every bracket-interior agreement, column-far pairs with B_ca^far(a) >= n-a+1. Consequences: the first lower bound at the safe index (2^39.9773, 88 bits under the 2^128 budget); the banked tall-regime bound T <= r+1 is tight on its whole domain; and B_ca^far(3n/4) >= 2^39+1 — residual budget 2^39 is unattainable at the bracket top. Exhaustive at the validation cell (all 46,656 witness assignments), sampled at six more cells over three scales.
  • rate-half-type2-fr-incidence-fence-v1 — the type-2 route fence with its proved complement: incidence axioms cannot bound |S ^ W| for arbitrary W (explicit m=64 witness), while at every canonical pair-union W* the bound is a two-line identity (exhaustive over all 32,896 pair unions of the fence's own blocks).

Net effect

On razor rows the crossing window is now [k + 2^34, a_94] with a two-sided far-CA window at the safe index. Complements (does not overlap) #1160's near-rational repair and the K3 lane (#1152/#1157-#1159): this is the band lane's first upstream entry.

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