Finite handles
The local exact replay now reaches 61 and matches OEIS A398173 at 59 and 61. OEIS continues through 73; the first absent prime is 79.
| Leaf | Required evidence | State |
|---|---|---|
| Exact table at 67, 71, 73 | Witnesses and dual lower replay; compare with the published values | open |
| Extend the exact table at 79 through 199 | Witness and dual lower replay at a prime absent from the record | open |
| Shapes of extremal sets | Affine orbit data with direct arithmetic checks; not a table extension | open |
Completed: local (q5) and local (q6), both matching
the published terms. Neither is a dent. At 61 the 15-set is checked in two
languages; size at most 14 is excluded by AP5 (C and Rust) together with
28 AP4-but-not-AP5 named midpoint classes and 26 AP4-free classes, each
UNSAT in C and in Rust. See q5/CLAIM.md and q6/CLAIM.md.
The q5 engines stop at primes below 64, so 67 and later need a wider mask before the same ladder can run. The q3 replay through 53 also matches the existing record.