05-ilang-free-fall / 10-field-own-contract
10field own contractverified
Determines the factor a body sees when the field starts in a nondegenerate eigenvector of its own contract, the second-order corrections, and their effect on fall and clock.
# Review: 10-field-own-contract v5
- **Subproject:** 05-ilang-free-fall
- **Package:** 10-field-own-contract
- **Reviewed version:** v5
- **Date:** 2026-10-11
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VERDICT: minor issues
## Issues
### I1. The equivalence for one speed is stated for any number
- **Location:** Step 3(d), "Answer at this order", second item ("With one speed $w\,d_0$ for all levels (the second or the third of (10.38), or any one number) ... it holds for all levels if and only if $g\,\rho_0=0$"); the same statement in the relation row of the table of Step 5, in the Result (item 3) and in the key result (10.40) of the JSON twin
- **Severity:** minor
- **Problem:** By (10.40), in the members with $\mathcal R^{\rm lev}_k=0$ for all $k$ the defect with one speed is $\mathcal R^{(w)}_k=(w^2-\tau_k^2)\,g$. For $\rho_0=0$ and $g\neq0$ all $\tau_k$ equal $\tau$, and the defect is $(w^2-\tau^2)\,g$: it vanishes for the second and the third reading of (10.38), which are then both $\tau d_0$, and it does not vanish for another number $w\neq\tau$. So "if and only if $g\,\rho_0=0$" holds for the two readings of (10.38) and is false for "any one number".
- **Fix:** State the equivalence for the second and the third reading of (10.38), and give separately the condition for an arbitrary number $w$ (from $\mathcal R^{(w)}_k=(w^2-\tau_k^2)\,g$). Bring the table row, the Result and the twin into agreement.
### I2. "Only" for a range that is sufficient
- **Location:** Step 3(c), paragraph after (10.37), the sentence "The statistics is then that of the standing ring clock ($r=0$) to the accuracy $\eta$ only for $\lambda\le2\eta\,\Sigma/(N(x_0)\,d_{N-1}^2)$, the range of (10.16)"
- **Severity:** minor
- **Problem:** (10.16) is an upper bound on the total variation, so the range that follows from it is sufficient for the accuracy $\eta$. The sentence states it as necessary ("only for"); that is not derived.
- **Fix:** State the range as the sufficient range of (10.16). If a statement on what happens beyond it is wanted, derive it from the phases $\delta E_k\lambda$ of (10.37); otherwise say that nothing is derived beyond it.