Learned Bow Control on a Measured Bowed-String Model: a Revised Minimum-Bow-Force Law, a Recurrent Controller, and the Domain of a Supervision Ceiling

תקציר מקורי באנגליתarXiv:2609.14990v1 Announce Type: cross Abstract: A finite-difference bowed-string model with implicitly resolved Stribeck friction is presented, with a regime diagnostic, the Schelleng bow-force limits on four strings, and a comparison of learned bow controllers. Implicit resolution is necessary, and quantitatively so: a lagged contact force cannot capture the string on a discrete grid, so no stick phase forms at any bow force. With friction, impedance and quality factor taken from published measurement rather than fitted, all four strings return a stick fraction of 89.1% against an ideal 90%. Schelleng's maximum bow force is recovered on every string. The minimum is not: it follows $Z v_b \beta^{-1}$ rather than the predicted $Z^2 v_b \beta^{-2}$, reducing both squared dependences to fir