Tone Theory in D Module Algebraic Geometric Foundations
Anthony SANTANA
Published Sep 2, 2026• 0 citations
Abstract
AbstractStandard quantum field theory isolates physical observables by projecting state vectors acrossan un-falsifiable, non-physical Hilbert space, introducing profound ontological paradoxes concerningnon-local signaling and wave-function collapse. This paper establishes a strict algebraic and geomet-ric foundation for the Tension-Optimized Newtonian Entropy (TONE) framework by mapping itscontinuous, deterministic real-fluid equations onto the rigorous mechanics of algebraic D-modulesand the geometry of abelian varieties. Following the foundational frameworks of Sato, Kashiwara,and Bernstein, we replace the caricature of subatomic entities as zero-dimensional point-singularitieswith regular holonomic sheaves of differential operators acting over a flexible 10D tripartite manifoldsubstrate. By embedding the fluidic continuity constraints of half-submerged fermionic vortices intothe non-commutative Weyl algebra An, we demonstrate that quantum commutator relations areexact manifestations of local boundary-layer friction. Furthermore, we deploy the homological ma-chinery of derived categories, utilizing the Fourier–Mukai transform on complex tori and Deligne’stheorem on absolute Hodge classes to track how continuous waves navigate the uniform, poroussurface lattice. We show that the Riemann–Hilbert correspondence acts as an exact geometric filterthat smooths out microscopic Planck pore variations. This topological low-pass filtration causes thechaotic sub-structural tracking of pore circumnavigation to analytically cancel to zero, forcing thephysical metric to smoothly collapse into a uniform, covariant Minkowski spacetime continuum forall macroscopic internal observers. Keywords: TONE Theory, D-Modules, Abelian Varieties, Riemann–Hilbert Correspondence, WeylAlgebra, Fourier–Mukai Transform, Geometric Rigidity.PACS: 02.40.Ma, 02.30.Jr, 03.65.Ud, 11.10.KkCopyright: Copyright Pending © 2026DOI: 10.5281/zenodo.22260153
- DOI
- 10.5281/zenodo.22260152
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