# PREREGISTRATION — E4-H034

Written before any calculation (2026-11-01). **Preserved unedited**, including the outcome that
was not achieved.

## Primary hypothesis

H1: Among defects of a given material, the elastic-dipole magnitude `|P|` predicts MLIP energy error
with incremental explanatory power beyond simple structural and chemical descriptors, under
material-held-out validation.

## Competing models (nested)

| Model | Predictors |
|---|---|
| **M0** | material mean (baseline) |
| **M1** | simple descriptors: defect size / volume, coordination, chemistry proxy |
| **M2** | elastic-dipole magnitude and tensor invariants |
| **M3** | M1 + M2 |
| **M4** | M1 + an ensemble-disagreement uncertainty measure, where available |

## Primary outcome

**Incremental predictive value of M2 over M1**, measured as the reduction in held-out RMSE under a
**material-grouped** split, with a confidence interval from repeated grouped folds.

The comparison that matters is **M3 vs M1**, not M2 vs M0. A correlation between `|P|` and error is
not sufficient, because `|P|` correlates with size and formation energy.

## Secondary outcomes

- Whether the error law's exponent is 2 (as derived) rather than 1 or 3, estimated by regression of
  log error on log `|P|` with material fixed effects.
- Whether the prefactor is constant across architectures at fixed `R_c` (C4).
- High-error detection: ROC of "is this configuration in the worst decile?" using M3 vs M1.

## Controls

- **Material-grouped split** (leave-materials-out), to prevent material identity from acting as a
  hidden predictor.
- **Configuration-level deduplication**: configurations from the same relaxation trajectory or
  rattled snapshots of one structure must not straddle train/test.
- **Stiffness normalisation**: repeat the analysis after dividing error by `κ`, to test whether the
  effect is just a material-stiffness proxy.
- **Size collinearity check**: report variance inflation between `|P|` and defect volume.

## Decision rules (fixed in advance)

- **H1 supported** if M3 beats M1 by a held-out RMSE reduction whose 95% interval excludes zero, and
  the improvement survives stiffness normalisation.
- **H1 rejected** if the improvement vanishes under grouping or under stiffness normalisation.
- **H1 inconclusive** if the data cannot be assembled with sufficient material diversity (fewer than
  ~8 materials with ≥20 defects each) — this is the anticipated outcome.

## Falsification conditions

- A material in which error is flat in `|P|` across a decade, with enough configurations to exclude
  noise, falsifies universality (though not the law for a specific class).
- If `|P|` is nearly collinear with a simple descriptor (VIF > 10), the incremental test is
  uninformative and must be reported as such rather than as a null result.

## Budget

Pilot: assemble at most one dataset, run one grouped comparison, stop. No model training, no
potential fitting — the project consumes existing predictions only.

## Anticipated failure mode (recorded in advance)

Suitable public data may not exist in a form that joins (a) defect configurations, (b) DFT references,
(c) elastic dipoles, and (d) MLIP predictions on the same cells. If so, the correct output is a data
specification, not a result.