Wave-Causal Circuit Search

Can programmable complex-wave networks execute structural causal mechanisms, expose circuit sensitivities, and support verifier-guided search without confusing wave energy or proposal weight with causal truth? Exact enumeration and held-out interventions remain authoritative; learned or derived representations may propose candidates but never decide whether a causal claim survives. Circuit mass is a verifier Gibbs proposal (uniform base measure, sparsity energy 0.035) — a search distribution, never a Bayesian posterior.

Two hash-pinned studies are public. The five-node pilot enumerates 29,281 labeled DAGs under seeds 7, 13, 23: the phase-cancelling circuit is real (direct X→Y magnitude 0.52 at −1.65 rad vs mediated 0.61 at 1.15 rad, summing to do(X)→Y transfer 0.21), yet 0 of 4 preregistered acquisition-superiority claims passed their effect-size gates. The thirty-seed confirmatory follow-up passed its manipulation check (complex vs phase-blind selectors diverged in 20/30 paired seeds across 9 ordered target pairs) and then killed all four eligible superiority claims at frozen gates — a primary negative kept beside the positive calibrations.

Public surfaces are the paper notebook and the two sealed study notebooks with artifact hashes. The Python package, Lean Tier-0 formalization (currently blocked on a correct semantics certificate; no theorem accepted), recursive-discovery archives, and raw experiment trees remain private until they clear their gates.