05-ilang-free-fall / 04-branch-fall
04branch fallverified
Determines the drift acceleration of a branch start of a level-conserving body with position-dependent parameters, at rest and in motion, and when it is the same for all clock levels.
# External verification: 04-branch-fall - **Subproject:** 05-ilang-free-fall - **Package:** 04-branch-fall - **Verified version:** v2 - **External round:** 1 of 2 - **Date:** 2026-10-10T22:37:05+02:00 - **Focus points:** none --- VERDICT: minor issues ## Summary The first-order branch dynamics, drift acceleration, and level-independence conditions are consistently derived. The revised sharp-label analysis correctly exposes the dependence on the phase structure of the start and distinguishes it from the family-independent drift limit. The clock-rate relation and variant table follow from the stated inputs and approximations. One estimate concerning corrections beyond first order omits a term and needs a clearer range of validity; this does not affect the principal first-order results. ## Issues ### I1. Second-order window correction omits a constant term - **Location:** Step 3, paragraph immediately following Eq. (4.9) - **Severity:** minor - **Problem:** The claimed window-acceleration correction \(O(\tau L^2\mathsf b'^2\lambda)\) does not follow from (4.9) over the stated range. For a window \([0,\lambda]\), dividing that bound by \(\lambda\) retains both terms: \[ 2\tau L^2\mathsf b'\bigl(\lambda\mathsf b'+|g_\zeta|\bigr). \] The omitted contribution can genuinely remain nonzero as the window shrinks. For example, with \(G=\mathcal F=0\), away from boundary terms the quadratic acceleration operator is \[ i[C_1,\hat v_1]=\tau^2g_\zeta^2\hat x. \] Thus a translated branch start with nonzero mean position has a nonzero second-order acceleration already at \(\lambda=0\). The quoted \(O(\lambda)\) estimate therefore requires additional large-window restrictions and is not an all-window correction estimate. - **Suggested fix:** Retain the \(O(\tau L^2\mathsf b'|g_\zeta|)\) term for windows starting at zero. For general windows, give the endpoint bound obtained from (4.9), or derive a separate acceleration-remainder bound. If the existing estimate is intended only asymptotically for long windows, state that restriction explicitly. ## Focus points None given.