External review, round 2 of pair level next order v2 — Clocks and free fall in a field, from the description language Ilanguage 1.b

05-ilang-free-fall / 14-pair-level-next-order

14pair level next orderverified

Determines the bound level of a pair of two bodies one order beyond leading order: binding cost, curvature, rest-term weights and curvature inertia, and whether the inertia follows the binding cost.

External review, round 2 · reviews v2 · verdict: correct

# External verification: 14-pair-level-next-order

- **Subproject:** 05-ilang-free-fall
- **Package:** 14-pair-level-next-order
- **Verified version:** v2
- **External round:** 2 of 3
- **Date:** 2026-10-18T12:49:03+02:00
- **Focus points:** none

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VERDICT: correct

## Summary

The fourth-order effective contract is correctly derived: the mixed kinetic terms cancel, and the conserved parity explains why w₁₂ and w₂₁ affect only the odd-separation sector. The bound-level correction, Hellmann–Feynman derivatives, curvature, inertia, and leading failure of the binding-cost relation follow consistently. The wide-pair analysis accounts for cancellations of the nominal leading coefficients, and the supplied code and outputs support the stated formulas and error scaling within the reported numerical accuracy.

## Issues

None.

## Focus points

None given.