# PRIOR ART — E4-H034

**Search performed:** 2026-11-01, two web queries on elastic-dipole descriptors, MLIP error
prediction, and uncertainty quantification for interatomic potentials. **Not a systematic review.**
Full texts were not retrieved; the entries below record what a search surfaced.

## Claims under investigation

| # | Claim | Prior-art status |
|---|---|---|
| C1 | The elastic dipole tensor is the leading moment of a defect strain field | **Well established** (Kanzaki force / dipole tensor literature). Not novel. |
| C2 | A finite-cutoff MLIP cannot represent the long-range part of that field | **Plausible and largely established** in spirit; the `R_c`-dependence of elastic-energy error is elementary. Not novel by itself. |
| C3 | Error scales as `P²/(κR_c³)` | **Derived here from elementary elasticity.** Likely known in some form; I did not find it stated as an MLIP error law. |
| C4 | Only the prefactor is architecture-dependent, exponents are not | **Candidate original element.** Unverified. |
| C5 | `|P|` adds predictive information beyond simple descriptors | **Untested here; unknown in the literature I could see.** This is the load-bearing claim. |
| C6 | The coefficient is transferable across materials | **Untested.** |

## Closest identified prior work

1. **"Uncertainty quantification for misspecified machine learned interatomic potentials"**
   (*npj Computational Materials*, 2025; also OSTI 2588080). **Identified by search; full text not
   retrieved.** The title indicates that UQ under *misspecification* — the regime where the model is
   structurally wrong, not merely noisy — is an active area. This is the closest conceptual neighbour:
   if that work already supplies an error predictor that beats simple descriptors, the marginal value
   of the elastic dipole falls sharply.

2. **"Atomistic Machine Learning with Cartesian Natural Tensors"** (arXiv 2510.04015, surfaced in
   search). Suggests that tensorial (including dipole-like) descriptors are being developed for MLIPs.
   If such tensors are already standard inputs, `P` may be subsumed rather than novel.

3. **Radiation-damage MLIP papers for tungsten** (surfaced in search, e.g. a deep-learning potential
   for bulk tungsten) — the natural data source for defect-error studies. **Not retrieved**, so
   whether any of them report per-defect errors against DFT is unknown.

## What this means for novelty

- **C1, C2 are not novel** and should not be presented as such.
- **C3 is a derivation** that is probably reproducible by any competent elastician; its value is as a
  *falsifiable quantitative prediction*, not as a discovery.
- **C4 and C5 are the only candidate original contributions**, and both are unverified.
- **The strongest honest statement** is: *the original hypothesis contains a testable claim (C5) that
  appears not to have been tested, and this project builds the test rather than performing it.*

## Honest novelty rating

| Question | Assessment |
|---|---|
| Is the dipole tensor as a defect descriptor new? | **No** |
| Is an elasticity-based error law new? | **Unlikely** |
| Is "only the prefactor is architecture dependent" new? | **Unknown** |
| Is the incremental-information test new? | **Unknown**, but it is the right test |

**Overall: a testable hypothesis with an unverified novelty position and no empirical test performed.**