# LIMITATIONS — E4-H034

## 1. The central question was not tested

No dataset was available, so the primary outcome — whether `|P|` adds information beyond simple
descriptors for real MLIPs — is **unanswered**. Everything in `RESULTS.md` is either a derivation or a
synthetic demonstration.

## 2. The prefactor is stipulated, not derived

`E_out ≈ 0.18 P²/(κR_c³)`: the `1/3` comes from integrating `r⁻⁴` from `R_c`, and the remaining factor
is an order-unity angular average that I asserted rather than computed. The *exponents* are robust;
the absolute magnitude could be off by a factor of a few. Anyone using the tabulated meV values should
treat them as order-of-magnitude.

## 3. `P` is not an inference-time feature

Computing the elastic dipole requires a DFT relaxation. So the hypothesis is either:

- **a diagnostic** ("after you have done DFT, predict the MLIP error cheaply"), which is useful but
  does not avoid the expensive step; or
- **a transferable coefficient** ("compute `P` once per defect class, apply forever"), which is the
  original's actual claim and is **untested**.

The original does not distinguish these, and the distinction decides whether the idea is practical.

## 4. Collinearity may make the test uninformative

`|P|` scales with defect size and formation energy, which are cheap descriptors. If the variance
inflation factor exceeds ~10, the incremental test cannot separate the models and the honest output is
"uninformative", not "null". This was pre-registered and was not reached.

## 5. The derivation assumes a lot

Point dipole, isotropic infinite medium, elastic energy as the only missing contribution, and a single
scalar `κ`. Real defects are anisotropic, surfaces and interfaces break the `1/r³` form, and
**electronic** contributions (charge transfer, magnetism, band-gap error) may dominate the error
entirely — in which case the elastic argument concerns a small correction.

## 6. The synthetic demonstration is easy by construction

I chose a generator where the dipole term was 40× the derived `E_out` and uncorrelated with the
nuisance beyond the size descriptor. Real data will be messier, and the protocol's power on realistic
collinearity is unknown. **The demonstration shows the protocol is not broken; it does not show it will
work.**

## 7. Prior art unverified

The *npj Computational Materials* paper on UQ for misspecified MLIPs may already answer the question.
It was identified by title only.

## 8. No independent implementation

The grouped-CV and OLS are standard and short enough to audit by eye, but they were not re-implemented
by a second route. A bug in the fold assignment would bias the result; the demonstration's *correct*
behaviour in both regimes is weak evidence against that, not proof.

## 9. What would overturn everything

A demonstration that MLIP defect error is dominated by electronic/chemical factors uncorrelated with
elastic dipole magnitude. That is plausible, and would make the hypothesis a second-order effect.