Six conjunctive-query containment questions decided by homomorphism and by counterexample database, agreeing across three independent routes

Ran 2026-08-15 in 0.11 s warm. Four genuinely independent routes, not four names for one. The backtracking search proposes a map; `check_homomorphism` applies it to each atom and looks the image up in the frozen database, then checks the image of the head is the frozen head -- no search, no backtracking, no Chandra-Merlin. The solver decides the SAME question on a one-hot Boolean encoding (totality, functionality, one disjunction per body atom over the matching facts), its model is replayed against that encoding by the IR ground evaluator, and the decoded map is then put through the same `check_homomorphism`. Search and solver disagreeing is reported as a FAILURE. Largest certificate: four variable-to-element pairs.

16, 16 and 27 variable assignments enumerated with NO pruning and no early exit -- the point being that an exhausted search space and an unsearched one are the same output unless the count is reported, and that a space over the cap is an ERROR here rather than a silent `no`. The counterexample databases are 1 and 2 facts. Note what this does NOT use: the negative direction never appeals to Chandra-Merlin's converse (containment implies a homomorphism), which needs an infinite domain, because a concrete finite database separating the two queries refutes the containment on its own.

22 assertions, 2.1 s warm. 13 committed instance files each pin exactly ONE false answer -- an unimplied dependency declared implied, a candidate-key list with a key missing, a list with a non-key added, a BCNF verdict flipped, a 3NF verdict flipped (which a checker conflating the two normal forms would accept), a lossy split declared lossless and the reverse, a preserved dependency set declared lost and the reverse, and a query containment in each direction -- and every one must exit non-zero. Four more assertions cover the shape of the gate itself: a wrong --expect-checks count, an instance run through the wrong checker, a --verify-formal script whose negation is SATISFIABLE, and a --verify-formal target that asserts nothing. One further control, no-expectations.dbd, pins nothing at all and must be REFUSED rather than swept -- the `40 of 162 checker runs exit 0 on completion alone` failure this ledger measured on 2026-08-15. Finally three assertions require the TRUE instances to still be accepted, without which a checker that rejected everything would pass the whole sweep. Measured this run: 22 of 22.