GAMUT Paper
Layered symplectic musical space — proof paper
The academic flagship and current formal authority: theorem-driven, AMS-format, and intended for submission as a mathematics preprint. Contains the full proof trail from discrete seed to cardinality-graded symplectic quotient.
This is the academic flagship paper and the current formal authority for the project, intended for submission as a mathematics preprint (arXiv/journal). The revised AMS draft proves the layered Fourier embedding, the standard exact symplectic thickening in chosen Fourier coordinates, Hamiltonian circle extensions for transposition and cyclic reindexing, anti-symplectic inversion, and the finite cyclic quotient/orbifold-stratum picture.
Relationship to other documents: The technical survey predates this revision and should be read as an earlier interdisciplinary exposition. The camera-ready volume is the public-facing essay collection. This proof paper is the most formal of the three and is the authoritative reference where any language diverges.
Citation
Jason St George, “Cyclic Autocorrelation, Permutation Fibers, and a Layered Symplectic Model for Pitch-Class Space,” GAMUT Research Program, March 2026 (revised May 2026).
Version: v1.1 — March 2026 manuscript, revised May 2026 · MSC 2020: 53D20, 42A16; 05E18, 57S17, 00A65