Heilbronn triangle problem (Erdős #507): exact-certified unit-disk configurations for n = 5..40 (DISK_TABLE v1.1)

Thirty-six exact-certified best-known configurations for n points in the unit-radius disk for the finite-n Heilbronn triangle problem (Erdős #507, erdosproblems.com/507), contiguous for n = 5..40. Every value is an exact rational recomputed from the bundled configuration (containment x²+y² ≤ 1 verified exactly per point; minimum over all C(n,3) triangle areas in Fraction arithmetic) — no float-only claims. These are constructions (lower bounds on α(n)), not optima. To our knowledge (four independent literature digs, latest re-verified 2026-08-01) this is the first public exact-certified table for the disk variant; rows not matching a closed-form baseline are marked "⚪ candidate best-known for disk", and rows n = 27/28 are honestly labeled below the transported square record. The bundle is self-contained: table, regime plot, 89 configuration files, and a standard-library-only verifier (~250 lines) that re-checks everything in seconds with one command (89/89 PASS). Developed with AI assistance under a machine-verification gate; see README for the production chain and honest labels. v1.1 extends v1.0 (n = 5..30/36 lineage) to n = 5..40 with the n = 31 row improved (+3.16%).