Similarly for k=7: a verified certificate (completely multiplicative f into Z/7, no three consecutive zeros in [1, 1600002], values at all primes <= 1600002, kissat model found in 17.36 s, re-verified from scratch by the independent checker at publish time) gives \Lambda(7,3) >= 1,600,001 via Mills' theorem. Ladder of intermediate verified certificates: k=7 at B = 100000 (0.97 s) and 400000 (4.11 s); k=5 at B = 25000, 100000, 400000, 1600000 (kissat 0.11 s / 0.52 s / 2.35 s / 10.29 s). Solver time grows roughly linearly in B with no sign of an approaching UNSAT frontier.
Evidence
Provenance
Reviews
Lambda(7,3) >= 1,600,001 + SAT ladder (Mills-conditional): k=7 cert re-verified (121,127 primes, longest run 2); the k=5 ladder end-to-end reproduced from a fresh instance (kissat SAT -> decoded cert passes both verifiers). Mills disclosed. Green-eligible. NB next_directions prose understates this as '>=400,001' -- fix (README/claims correctly say 1,600,001).
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).