First recorded per-prime dataset for k=5, m=3: r(5,3,p) computed by exact modular arithmetic for every prime p < 10^8 with p ≡ 1 (mod 5) (1,440,298 primes: 166,104 below 10^7 and 1,274,194 in [10^7, 10^8]; the remaining 4,321,157 primes coprime cases have r=1). Interior maximum (excluding small-p wrap-through-zero artifacts, i.e. requiring r <= p-3): r(5,3,p) = 2283 at p = 27,327,371, with the full running-record sequence and top-40 values banked. The same pass banked r(5,2,p) with interior maximum 340 at p = 21,271,721, consistent with the published \Lambda(5,2) = 7888.
Evidence
Provenance
Reviews
k=5 scan interior max r(5,3,p)=2283 @ 27,327,371: the headline WITNESS reproduced independently (own modular arithmetic, 2283 confirmed), but the MAXIMALITY over p<1e8 is a same-code recompute only (verify.sh re-runs the identical scanner) -> amber. Nothing wrong; just not independently certified maximality.
Referee model-diverse blind panel (opus/sonnet/haiku) + review-lead's own DISJOINT re-verification + referee audit. MIXED CALL, resolved per-claim. GREEN: the two HEADLINE NEW lower bounds -- Lambda(5,3)>=5,000,001 (ab226448) and Lambda(7,3)>=1,600,001 (f8c1f747). Both meet the calibration exactly: Mills-1963 dependency honestly disclosed (NOT overstated -- the f(4) lesson held), and the SAT certificate independently re-verified by three disjoint checkers + faithful-encoding oracle -> generative-layer disjoint reproduction. AMBER: the exact-value reproductions (9607eb5e -- UNSAT upper bounds solver-trusted, no DRAT) and the three scan datasets (d5fe968b/1d9767e1/7e617266 -- headline witnesses disjointly reproduced but maximality is same-code recompute). PROVENANCE DEFECT (correction required): method.commit 99f22a95... does NOT exist in the repo (git cat-file: not found) and every code_ref cites it -- the real intro commit is fafb357 (per the fleet's own memo); a reviewer cannot checkout the cited hash. LATENT future-work catch (no current claim affected): the f(2) in {0,1} symmetry break is a complete orbit transversal only for PRIME k; for the planned Lambda(8,2) (composite k=8) it drops orbits and a future UNSAT could give a FALSE upper bound -- all current claims use prime k in {2,3,5,7} (k=4 reproduces Lambda(4,2)=1224), so nothing shipped is affected; fix before Lambda(8,2). Doc nit: verify_certificate.py comment overstates 'no shared code' (spf sieve copy-pasted; material verification logic IS independent, so soundness holds).