P1  derived error law  error ~ c * P^2 / (kappa * Rc^3)
     P (eV)   kappa (eV/A^3)  Rc (A)  E_out (meV)  E_out/E_out(4A)
        1.0             1.00     4.0        2.812            0.111
        1.0             1.00     6.0        0.833            0.033
        1.0             1.00     8.0        0.352            0.014
        2.0             1.00     4.0       11.250            0.444
        2.0             1.00     6.0        3.333            0.132
        2.0             1.00     8.0        1.406            0.056
        3.0             1.00     4.0       25.312            1.000
        3.0             1.00     6.0        7.500            0.296
        3.0             1.00     8.0        3.164            0.125
        6.0             1.00     4.0      101.250            4.000
        6.0             1.00     6.0       30.000            1.185
        6.0             1.00     8.0       12.656            0.500

    scalings implied by the law: quadratic in |P|, inverse-cube in Rc,
    inverse-linear in stiffness.  A model with the SAME Rc but a different
    architecture may differ in c only; the exponents are architecture-blind.

P2  PROTOCOL DEMONSTRATION (synthetic data -- NOT evidence about real MLIPs)
      regime      split     simple    +dipole  improvement
      signal     random      0.858      0.803        0.055
      signal    grouped      0.979      0.931        0.048
        null     random      0.871      0.870        0.001
        null    grouped      0.856      0.924       -0.068

    reading the table:
      signal/grouped improvement >> 0  -> the dipole adds information
      null/grouped   improvement ~ 0   -> it does not
      any regime/random improvement > 0 -> material leakage, not signal

wrote /home/toby/Desktop/nov1/Incoprea_E4_H034_2026-11-01/results/h034_results.csv (16 rows)