MCA: move the razor crossing bracket from both ends (Haboeck staircase + far-CA floor) - #1162
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…staircase + far-CA floor LB1)
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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 ownaudit_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 admissibleq >= Q_9*2^128(log2 q >= 232.650530),a_RH(q) <= a_{m(q)}along an 87-member staircase; on every razor rowq > 2^255.9,a_RH(q) <= a_94 = 1,563,215,236,073(vs3n/4 = 1,649,267,441,664— a gain of 86,139,268,540 agreement steps), upgrading toa_95above an exact threshold;m = 96is unaffordable underq < 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 gate2r <= n-k, which at rate 1/2 is exactlya >= 3n/4; the whole live interval fails it by >= 2.The far-CA side gains its first floor
mca-razor-farca-floor-lb1-v1— LB1: an explicit maximal-core pencil gives, at every posed row and every bracket-interior agreement, column-far pairs withB_ca^far(a) >= n-a+1. Consequences: the first lower bound at the safe index (2^39.9773, 88 bits under the2^128budget); the banked tall-regime boundT <= r+1is tight on its whole domain; andB_ca^far(3n/4) >= 2^39+1— residual budget2^39is 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 arbitraryW(explicitm=64witness), while at every canonical pair-unionW*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.🤖 Generated with Claude Code