Abstract We introduce Remainder Dynamics: the complete theory of physical reality as the dynamics of remainder propagation across sovereign domain hierarchies. Classical mechanics, quantum mechanics, and general relativity are not unified by Remainder Dynamics — they are contained within it as limiting cases corresponding to different suppressions of the full categorical structure. The foundational object is the category CSRNUDT, whose objects are sovereign domains (triples of cell, sheaf stalk, cosheaf costalk), whose morphisms are boundary-compatible remainder-preserving causal maps, and whose central structure is the pairing ⟨R, γ⟩: H¹ (F) ⊗ H₁ (F̆) → ℝ between remainder obstruction classes and propagation path classes. The fundamental equation of Remainder Dynamics is this pairing. The SRNUDT Boundary Theorem — that remainder localizes to the fixed-point set of domain symmetry — is the master theorem of Remainder Dynamics. The Riemann Hypothesis and Navier-Stokes global regularity follow as conditional corollaries. The theory makes new predictions at every scale from quantum gravity to cosmology.
Bradley Ploof (Mon,) studied this question.