Three-Dimensional Integral Balance and Diffusive-Advective Transport: An Executable Code-to-Mathematics Equivalence Audit

Abstract

Version 2.0.0 of the independent 3D-FIELD technical note. This release translates the sparse-polynomial Python implementation into conventional mathematics over Q[x,y,z,t] and explains the original six rational-arithmetic fixture checks step by step. Four further exact checks cover the Leibniz rule, the fundamental theorem of calculus, commutation of a fixed-domain volume integral with time differentiation, and zero net flux for a constant field. All ten declared checks pass in exact arithmetic. The deposited PDF and editable source provide the English manuscript. The accompanying ZIP preserves the executable checker, machine-readable results, code-to-mathematics ledger, licenses, and SHA-256 manifest. The manuscript and documentation are CC BY 4.0; original code is MIT as identified in the package. Scope and limits: these are correlated checks on finite polynomial fixtures, not ten independent proofs, a PDE solver, a general PDE existence or convergence theorem, or physical validation. The work was assembled and checked with computational/AI assistance under the responsibility of Riccardo Giudici as an independent author. It does not imply supervision, validation, or endorsement by the University of Insubria.