05-ilang-free-fall / 15-curved-profile-fall
15curved profile fallverified
Determines how a body at rest accelerates when its level profiles are curved, how far the local slope describes the fall, and whether the fall stays the same for all clock levels.
# Review: 15-curved-profile-fall v1
- **Subproject:** 05-ilang-free-fall
- **Package:** 15-curved-profile-fall
- **Reviewed version:** v1
- **Date:** 2026-10-18
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VERDICT: minor issues
## Issues
### I1. The window condition of item 2 is not stated in the quantities that the question names
- **Location:** Step 3 (v_osc), Step 7, (15.11), (15.12), Result (15.11)–(15.12); "Open issues", first item
- **Severity:** minor
- **Problem:** Item 2 asks for the conditions on $H_k$, $\mathcal H_k$, $W$, $\delta p$ and $\lambda$ under which the window average equals (4.16) up to a stated relative error. (15.11) contains the term $2v_{\rm osc}/\Lambda$, but $v_{\rm osc}=4\int\frac{\mathrm dp}{2\pi}\omega\lvert f\rvert$ is not bounded in these quantities, so the window length that the criterion needs is not given; the joint limit of (15.12) likewise rests on $v_{\rm osc}(g_n)/\Lambda_n\to0$ without saying how $v_{\rm osc}$ scales along the family. "Open issues" lists this, but it is part of what item 2 asks.
- **Fix:** Give an explicit upper bound on $v_{\rm osc}$ (or directly on the window average of $A_{\rm osc}$) in terms of $\tau$, $M$, the slopes, the curvatures and moments of the start ($W$, $\delta p$, or the norms of $\eta g$, $\eta^2g$, $g'$), and state the condition on $\Lambda$ in (15.11) and along the families of (15.12) with it. Remove the item from "Open issues".
### I2. "There is no term in $W^2$" is stated without its restriction to the non-oscillating part
- **Location:** Result (15.10); twin key result 15.10
- **Severity:** minor
- **Problem:** The sentence reads as a statement on the whole curvature contribution. Step 3 shows that $S_{-+}$ contains the part $\frac H4\eta\frac\nu\omega\eta$, so the oscillating amplitude $f$, and with it the curvature part of $A_{\rm osc}$, contains second moments of the position of the start. Only for the non-oscillating part is the absence of a $W^2$ term derived.
- **Fix:** State the absence of a $W^2$ term for the non-oscillating part only, and say how the curvature part of the oscillating terms depends on the start, with the bound of I1. Same in the twin.