# DiscoCATE Validation Criteria

> Status: falsification contract for a **proposal_only** paper. No experiment has
> been executed or accepted as evidence yet.

## What the first experiment must decide

The first experiment is not “does DiscoCATE obtain a low PEHE on one benchmark?”
It must decide whether the **full belief measure** contributes information beyond
ordinary covariates and simpler compressions, under a matched causal estimand.

## Minimum regimes

### E0 — Null heterogeneity

Use constant treatment effect or a regime where \(Q_X\) contains no additional
effect information. DiscoCATE must not manufacture heterogeneity or systematic
advantage.

### E1 — Oracle belief geometry

Generate known \(u_i\), calibrated oracle \(Q_i\), treatment assignment, and
potential outcomes. Separate the value of the weighting principle from errors in
learning the abductor.

### E2 — Multimodal weak evidence

Construct response-relevant types that overlap in raw \(X\), have opposing
effects, and leave a genuinely multimodal \(Q_i\). This is the regime in which a
full distribution may beat posterior means or hard classes.

### E3 — Belief misspecification

Control calibration error, overconfidence, excessive diffusion, label
reparameterization, and distance distortion. AIPW robustness must not be used to
hide failures caused by learned-\(Q\) error.

### E4 — Causal identification stress

Separate randomized assignment, observed confounding with adequate overlap,
weak overlap, and hidden confounding. Hidden confounding is a required negative
control, not a regime in which Unit Abduction is expected to repair identification.

### E5 — Leakage falsification

Deliberately let a donor's realized \(Y_j\), treatment assignment, or query action
enter its similarity weight. Confirm that apparent gains can arise from changing
the estimand / outcome selection. The accepted V0 must use pretreatment-only,
honestly frozen application-time weights.

## Matched baselines

At minimum compare:

1. Causal Forest / GRF;
2. a standard DR-learner using \(X\);
3. an \(X\)-space kernel with the same bandwidth / effective sample size;
4. hard latent subgroup assignment;
5. posterior point / mean embedding distance;
6. posterior-similarity weighting using the full \(Q_i\);
7. oracle-\(Q\) weighting where simulation permits it.

All methods must share treatment/outcome nuisance folds where appropriate, use
the same admissible evidence, and be evaluated against the same estimand. A
method is not allowed to win by using a different target population or donor
effective sample size without disclosure.

## Diagnostics and metrics

- error for the finite-bandwidth target \(\theta_{h,\mathcal Q}\);
- focal CATE error only in regimes where T3 conditions hold;
- treatment overlap and propensity extremes;
- belief-support coverage and distance concentration;
- effective neighborhood size and maximum donor weight;
- abductor calibration / proper-scoring diagnostics when oracle truth exists;
- effect ranking or policy value as secondary metrics;
- interval coverage only after a valid inference theorem exists.

## Failure criteria

The paper's added value is not supported if any of the following persists under
matched tuning and repeated seeds:

- full-\(Q\) weighting does not improve over posterior point / mean embedding;
- gains disappear after matching effective neighborhood size or nuisance folds;
- gains occur only when outcome, treatment, or query leakage is allowed;
- the method is unstable under benign latent reparameterization;
- belief misspecification overwhelms any localization benefit without a usable
  diagnostic;
- results require calling a coarsened \(Q\)-effect a focal CATE when T3 fails.

One IHDP run, factual outcome fit, or a visually appealing latent plot cannot by
itself pass this contract.

## Gate before implementation grow

Freeze one oracle DGP with explicit observed target, one misspecified-\(Q\)
variant, the exact donor-fold protocol, and the estimand shared by all baselines.
Only then create the implementation directory and an experiment ledger.