What stopping distance can a twin with independent terrain cells certify?

research/terrain-twin

Stopping distance certified by a twin with independent per-cell friction: exact incomplete-gamma law (matches braking simulation), 100 twin cells certify 1.17× the mean distance but real terrain with 1–10 patches exceeds it 44%–18% (claimed 0.1%), finer cells are worse, the mean is nearly right, and the measured patch count repairs it.

5 tests

What it found

Braking on Gamma-distributed patch friction has an exact incomplete-gamma law. A twin drawing 100 independent cells across the stopping distance certifies 1.17× the mean-friction distance at level 10⁻³; on real terrain with 1, 3 or 10 patches across it the exceedance is 0.44, 0.33 and 0.18, and finer twin cells make it worse. The mean stopping distance is nearly right (1.00–1.32×) while the tail is not. Matching the measured patch count restores the level; overstating it 2× gives 16× the claimed risk. Stylised.

A figure from its own output

Figure produced by research/terrain-twin: required_vs_patches — terrain-twin/experiments/required_vs_patches.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.