# DRCT v9 — Predict-Before-Reveal Causal Query Complexity

For a fixed input and output coordinate, an m-component intervention table is a
set function f: 2^[m] -> R with a unique Möbius expansion

    f(S) = sum_{T subseteq S} mu(T).

Without structural assumptions, an arbitrary set function has 2^m independent
values. Exact worst-case recovery therefore requires the complete 2^m factorial.

If it is known that mu(T)=0 for |T|>d, then all coefficients are recovered from
the subsets of size <=d, requiring

    sum_{k=0}^d C(m,k)

subset interventions.

In DRCT language, causal interaction order is an intervention closure depth.

The fresh experiment uses five macro transformer components. At stage d, only
terms through interaction order d are admitted. Predictions for higher-order
interventions are frozen and SHA-256 hashed before they are scored. Residual
error therefore quantifies omitted interaction structure rather than post-hoc
fit quality.

Anti-vacuity rule:
A mechanistic explanation must use a constrained hypothesis language and must
predict interventions not used to construct it. Exact post-hoc decomposition
alone is insufficient evidence of mechanistic understanding.