nx_mulchain_deep_test.nx

nx_mulchain_deep_test.nx -- GATE for the deepened, cost-bounded chain search (the escalation resolution). Proves three things, exit 0 only if ALL hold: (A) COST SELECTION is correct under a LATENCY model (cap=5, tie_thresh=3): constants with a <=3-op chain pick the chain; constants needing >3 ops (incl. the escalated 466/683/691) and primes with no short chain pick IMUL. This is the per-constant cost decision that replaces the blunt depth-4 "expensive -> escalate". (B) every chain the selector keeps is VERIFIED to compute c*x on a fresh held-out input (independent of the search's own check) -- verify, don't trust. (C) TRACTABLE: the run completes (the primes that hung at depth 6/12 fail-fast at the cap). Memory-backed verdict tally in small helpers (mitigates the non-deterministic compiler's fat-main register clobber). license_tier: ORIGINAL