Five-Node Intervention Discovery

Question

Does smarter intervention acquisition — especially complex phase-aware targeting — beat matched controls on a fully enumerated five-node wave-causal oracle?

Context

Wave-Causal Circuit Search tests whether representing causal edges as complex transfer functions (gain + lag) improves search when paths cancel in phase. The acquisition hypothesis, motivated by Complex Phase Representation, says phase-aware disagreement should pick better interventions than phase-blind magnitude or observational baselines.

From Five-Node Exact Intervention Pilot and the sealed study:

• Causal edges are complex: magnitude = strength, phase = lag; loop phases and relative lags are physical, single-edge phase is gauge-dependent.
• Exact enumeration of 29,281 labeled five-node DAGs is a practical oracle at this scale — MAP recovery is not the same as high-certainty identification.
• A phase-cancelling generator can be real while acquisition policies still fail their gates; the pilot mostly failed to create the complex-vs-phase-blind intervention contrast.

Findings

• All four preregistered claims — intervention_value, coverage_value, adaptive_value, phase_value — failed their frozen effect-size gates (0 of 4 passed).
• Phase cancellation is real. With complex edge transfers $H_{XY}$ (direct) and $H_{XQ}H_{QY}$ (mediated), the interventional transfer is the head-to-tail sum, not the sum of magnitudes:

Interventional transfer, not raw wave power, is what the circuit delivers.

• Every policy recovered the true MAP graph (rank 1, SHD 0); median true-graph proposal mass stayed near 0.025%. Rank-one recovery ≠ concentrated belief.
• Effect-size gates here are descriptive pilot verdicts. Seed-level paired uncertainty belongs in the thirty-seed confirmatory study.
• In the RSI Lab map this is Club A intervene + verify: exact oracle, frozen gates, negative acquisition claims kept public.

Method

Oracle: 29,281 labeled five-node DAGs. Paired acquisition under seeds 7, 13, 23. Policies: sample-matched observational, random one-node, balanced round-robin, complex transfer disagreement, phase-blind magnitude disagreement. Circuit mass is a verifier Gibbs proposal (uniform base, sparsity penalty 0.035) — a search distribution, not a Bayesian posterior. Claims and kill gates were frozen before runs. Paired effects are computed within seed, then median-aggregated.

Limits

• Three seeds; linear, fully observed, acyclic synthetic family — no latent confounding, noise, feedback, or nonlinearity.
• Complex and phase-blind selectors chose different nodes only in seed 7; seeds 13 and 23 both chose S, so the phase comparison was mostly uninformative rather than a clean negative on phase.
• Gates were internal, not externally preregistered. “Killed” means the fixed effect-size gate failed; it does not prove the negation of the claim.
• Next claim needs a manipulation check that selectors diverge, uncertainty-sensitive outcomes, and ≥30 paired seeds — see Thirty-Seed Wave-Causal Uncertainty Study.

Artifact

Executed snapshot of committed study artifact wccs.five_node_intervention_study.v1. Numbers come from frozen JSON only; nothing recomputes live. Artifact hash and source commit are pinned above. Open the dedicated notebook route for the reading brief and claim scorecard: notebooks/five_node_intervention_discovery.py via uv run marimo edit --sandbox in wave-causal-circuit-search.