This work presents a three-layer formulation of Delta Physics centered on Saket’s Law, a proposed bounded imbalance framework for reconstructing physics from first principles. The project begins by restoring the algebraic foundation of Delta Mathematics, where physical evolution is treated as non-closing, residue-bearing, and path-dependent. In this formulation, every transition leaves an ordered residue, encoded through a residue space, path residue accumulation, structural equivalence, and noncommutative composition. The second layer develops a coarse-graining bridge from the algebraic residue formalism to an effective continuum field, denoted (x, ). This bridge is introduced to preserve three essential features of the foundational theory: residue intensity, path memory, and local update structure. The continuum field is therefore not treated as fundamental, but as an emergent description of underlying residue histories. The third layer formulates effective physical sectors from this bridge field, including: mechanics as bounded gradient response, thermodynamics as spreading of coarse residue density, optics as cross-subsystem medium response, uncertainty as unresolved residue histories under coarse-graining, and a toy fluid sector leading to a -corrected fluid dynamics picture. The framework culminates in Saket’s Law, an effective continuum interaction law describing bounded intrinsic evolution together with bounded inter-system coupling. In the algebraic limit, the continuum interaction structure is intended to reduce back to residue composition and modulation, recovering path dependence and noncommutativity. This upload is intended as a foundational theoretical manuscript, not a finalized physical theory. Its main contribution is to organize the Delta program into a coherent research structure: Residue algebra as foundation Coarse-graining bridge as the missing middle layer Effective physical sectors as derived continuum regimes The present version should therefore be read as a conceptual and mathematical research program aimed at deriving physics from bounded imbalance and residue dynamics, rather than as a finished empirically validated model.
Saurabh Saket (Mon,) studied this question.