Abstract
Let a collection of independent canonical oscillator fibers depend smoothly on shared base coordinates through positive frequency profiles. Applying a Cayley update to each fiber while holding the base momentum fixed preserves the fiber areas and quadratic forms, but generally does not preserve the canonical structure of the full base–fiber space. The paper gives an explicit base-momentum correction that restores exact canonicality without changing any prescribed fiber output.
Scope
The result covers an arbitrary finite-dimensional vector base and finitely many independent scalar fibers with state-independent real Cayley parameters. It does not establish integration order, global accuracy, stability, asymptotic preservation, runtime advantage, or an application-specific performance claim. Coupled matrix-valued fibers and noncanonical target brackets remain outside its scope.
Reproducibility
The release includes the canonical LaTeX source, an exact SymPy checker, expected output, environment information, and a SHA-256 supplement manifest. The checker verifies a generic two-dimensional base with two independent fibers and unequal symbolic parameters. The arbitrary finite-dimensional statement rests on the analytic proof.
Citation
Avila, Connor. “Cotangent compensation for parameter-dependent Cayley maps with independent oscillator fibers.” Version 1.0.1. Zenodo, 2026. https://doi.org/10.5281/zenodo.22049535.