Kuramoto-lean: Lean 4 Library for Finite-N Kuramoto Synchronisation Dynamics

kuramoto-lean is a Lean 4 / Mathlib library for finite-N Kuramoto oscillator
dynamics, taking a finite-dimensional geometric approach distinct from
Ott-Antonsen / continuum-limit formalisms. It contains 39 public theorem
declarations, all machine-checked sorry-free, admit-free, and with no
project-defined axioms; committed #print axioms transcript guards for the
headline frontier and discrete results record the footprint
{propext, Classical.choice, Quot.sound}. Nine theorems form the algebraic core
(order-parameter boundedness, gradient and Lyapunov-descent identities,
contraction sign facts, Hebbian phase-plus-weight descent); fourteen frontier
theorems add ODE existence and uniqueness via Picard-Lindelof, Lyapunov
stability along trajectories, and convergence to synchrony from any
open-semicircle initial condition, first for all-to-all coupling and then for
any symmetric coupling with a uniform positive off-diagonal floor; and sixteen
discrete theorems establish fixed-step skew confinement, a stochastic-matrix
reformulation, geometric contraction, and convergence of the skew to zero. The
continuous convergence theorems are precisely scoped by their hypotheses, and
the discrete convergence theorem additionally requires at least three
oscillators and a positive step size; none is a general Kuramoto
synchronisation result. The repository is the formal proof spine for the
companion flywheel-universe project on budgeted Hebbian Kuramoto dynamics for
Max-Cut.