Layered symplectic musical space — proof paper

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 September 2026).

Version: v1.2 — March 2026 manuscript, revised September 2026 · MSC 2020: 53D20, 42A16; 05E18, 57S17, 00A65

Download

Download the revised proof paper

Source remediation (13 September 2026): This download includes corrected reconstruction, directed/folded histogram conventions, reduced gap-period stabilizers, moment-level and rendering hypotheses, and geometric proof repairs. These are manuscript derivations. The completed first Lean release covers ten explicitly manifested discrete contracts (256 required exports); it does not certify the whole paper, the general gap-period/support theorem, or the visualization data. See the proof manifest, trust and validation record and full manuscript review.