Certified sum-difference lower-bound certificates for C_3a, C_3b, and C_3c

This record is a self-contained certificate archive for three Mosaic Intelligence lower-bound contributions merged into teorth/optimizationproblems on 2026-06-21: C_3a >= 1.1835129324218615..., C_3b >= 1.77898884, and C_3c >= 1.6747338950208249. It is a sibling certificate record to the Katz-Tao sum-difference paper record 10.5281/zenodo.20646385, which contains the paper and upper-bound ladder/wall material but not these MI2026 lower-bound certificate artifacts. The archive contains exact-count or exact-rational certificate data plus pure-Python verifier scripts using exact arithmetic and, where needed, interval arithmetic. The full C_3a recount is intentionally a long-running independent audit; the shipped quick checker verifies that the certified integers imply the quoted lower bound. Contact and updates: Mosaic Intelligence — https://x.com/111111 · https://github.com/463464q435q43