Math Mapgenerated 2026-10-25 · a354234
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run 017Held

Is the walk-run transition Froude number the kinematic ceiling, or a biological constant?

slug
gait-froude
state
draft
created
2026-09-13
settles
CASE-17
script
R17_gait_froude_check.py
source
../lab/runs/017-gait-froude.md

Blocked onliterature assembly — per species at the transition, speed, leg length under one consistent definition, and stride length

PredictionA flat scatter near 0.5 with no dependence on relative stride length — biological, not kinematic

Falsifierobserved transition Froude tracking 3cos(alpha) - 2 in average-speed units across species

Confidence0.7

The compute is trivial; the work is literature assembly, which is why this is still a draft. Per species at the transition: speed, leg length under one consistent definition, and stride length. Froude is linear in leg length, so a 20% definitional difference moves it by 20% and would swamp the effect.

The contact-loss ceiling in average-speed units is about 0.62 at observed gait geometry, not the textbook 1.0. Animals transition near 0.45, so roughly three-quarters of the ceiling.

Branch 1 predicts the points lie on the ceiling curve — species with longer relative strides transitioning at lower Froude. Branch 2 predicts a flat scatter. Branch 3 predicts a line parallel to the ceiling at a constant fraction.

Prior: relative stride length at the transition clusters near 2.0 across species, and a quantity that does not vary cannot explain one that does.

generated 2026-10-25the lab index