FA-87309 / Physics integrator stability / Member archive

Crossing that lands exactly on a zero sample is missed · case 04

Sampled trajectories with exact zeros report missing periods.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

solve(xs, dt, omega): integrator frequency diagnostic. Upward crossings are samples with x[i-1]<0<=x[i], timed by linear interpolation. Period is the mean interval (last-first)/(count-1); relative error vs 2*pi/omega. Fewer than two crossings gives [None, count, None]. Return [period, count, error] rounded to 6.

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
case 0	`[5.529726, 2, 0.971387]`	`[2.764863, 3, -0.014307]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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