# H034: numerical correction and physical scope

1 November 2026. Publisher arithmetic check, not a real-data validation.

Predefined check: recompute the stated formula 0.18 P²/(κ Rc³), with P in eV, κ in eV/ų, Rc in Å, converting eV to meV; compare all supplied P1 CSV rows to 1e-9 meV tolerance. Compare the six rounded prose-table values to their identical inputs.

All12 CSV rows pass. The source code also implements the stated coefficient0.18. The six prose table values, rather than the CSV or formula, need correction:

| P (eV) | Rc (Å) | Published prose (meV) | Corrected (meV) |
|---|---|---|---|
|1|4|11.25|2.8125|
|2|4|45.00|11.25|
|3|4|101.25|25.3125|
|6|4|405.00|101.25|
|3|6|30.00|7.5|
|3|8|12.66|3.1640625|

Relative ratios and the formula's quadratic/inverse-cube scaling remain unchanged. Original files remain at ../nov1-results-20261101/. The supplied synthetic protocol was not independently rerun in this check.

Physical scope: integrating an assumed far-field elastic-energy density can give a tail proportional to P²/(κ Rc³). This alone does not establish a universal MLIP prediction-error law. A local atomic energy model can generate a long-range relaxed elastic field through local interactions; its cutoff is not automatically a cutoff on the total elastic energy present in a relaxed configuration. Architecture, training, boundary conditions and target definition matter. The coefficient0.18 is supplied, not independently derived. The claimed architecture-independent exponents and predictive advantage remain untested.

No compatible real-data pilot was assembled in this bounded correction. The suggested SrTiO3/germanium datasets require separate checks of exact records, references, configurations, stresses/dipoles and reuse terms before analysis.

Reproduce the arithmetic using h034_check.py with the original release sources at the relative workspace path specified in that script. Machine-readable values: h034-arithmetic.json.