nx_eqsat_test.nx

nx_eqsat_test.nx -- proof-of-life + correctness GATE for the equality- saturation engine (the GENERATOR organ of the Sovereign Invention Engine). Case 1 -- EXTRACTOR correctness. (add (mul x x) 0): add_zero unions it with (mul x x); the add-class stays canonical (shallow cost 1 < mul's 3) with best_node = the add node, so the V1 CACHED extractor returns (add (mul x x) 0) [cost 4] -- a wasted +0. The REAL bottom-up extractor (nx_eqsat_recompute_best) returns (mul x x) [cost 3]. Known: before_op=ADD(2), cached_op=ADD(2) [the bug], real_op=MUL(4), real_cost=3. Case 2 -- a REAL optimization WIN. (mul x 8): the strength-reduction rule (mul x 2^k)->(shl x k) fires, and the real extractor picks (shl x 3) [cost 1] over (mul x 8) [cost 3] -- a genuine 3->1 win. The idempotent rule lets saturation CONVERGE (NX_EQSAT_SATURATED). Known: red_op=SHL(11), red_cost=1. Full known answer (FAIL LOUD): "2 2 4 3 11 1 ".