Rechecking Chapter 6: Equations of Motion and Dimensionless Groups (The Kuriyama Protocol, Chapter 6)

Part 11 of a series; the sixth of fifteen chapter-by-chapter articles. Part 1: 10.5281/zenodo.23587879 · Part 2: 10.5281/zenodo.23587670 · Part 3: 10.5281/zenodo.23526074 · Part 4: 10.5281/zenodo.23609857 · Part 5: 10.5281/zenodo.23610607 · Part 6: 10.5281/zenodo.23682055 · Part 7: 10.5281/zenodo.23684537 · Part 8: 10.5281/zenodo.23684996 · Part 9: 10.5281/zenodo.23685960 · Part 10: 10.5281/zenodo.23686289 Chapter 6 of The Kuriyama Protocol (dimensionless reformulation with seven groups, body-derived reference scales, and the infeasibility of uniform form instruction) was published earlier as Part 3. This article re-audits it with the procedure used in Parts 6–10 and reports three gaps. (1) Π₆ was used in two inconsistent senses. The book takes the rigid-rod leg pendulum as the denominator (about 77 steps/min for a 0.9 m leg) and reads the 1.4–1.6× excess of natural cadence as muscle effort, yet places the efficiency peak at Π₆ = 1. A segmental calculation shows knee flexion shortens the pendulum period by only about 5%, so the gap is not geometric. Following the force-driven harmonic oscillator view (Holt et al., 1991), Π₆'s denominator is redefined to include the musculotendinous spring; effort is then the deviation from one's own spring-inclusive frequency. (2) The claim that 4.8 km/h matches the optimal Froude number 0.25 is loose. Human minimum-cost walking speed is about 1.23 m/s (Ralston, 1958), i.e. Fr ≈ 0.17–0.21, below the 0.25 often cited across animals. The walk–run transition agreement (Fr ≈ 0.5) stands. (3) The chapter's verification log still carried superseded values (σ = 22.5 N/cm², Π₂ ≈ 8.8) after the text had been corrected (26.8 N/cm², 10.5). Three falsifiable predictions are registered (numbered 49–51, continuing the series): - P49. At matched Froude number, cadence in body-time units is independent of leg length; the rigid-pendulum Π₆ at preferred speed falls in 1.4–1.6 for everyone. - P50. Individual minimum-cost walking speeds, expressed as Fr, cluster around 0.15–0.22 and do not correlate with leg length. - P51. Deviation from the spring-inclusive natural frequency predicts lower-limb EMG at matched Fr better than deviation from the rigid-pendulum frequency. Part 3 will be corrected as a new Zenodo version, with its predictions and registration date unchanged. Refutations are welcome. The author has no formal research training. The article body is in Japanese. An English summary, the registered predictions and the reference list are included in the document. Contact: [email protected]