Well-posedness and Degenerate Limits of a Positive-Flux Boundary-Formation Prototype: A Source-Scoped Mathematical Analysis within Boundary Information Geometry

This source-scoped mathematical preprint examines an isotropic positive-flux nonlinear diffusion prototype associated with corrected BIG-B4.1/B4.3 numerical studies. For specified bounded nonnegative data and Neumann weak conditions, it documents a theorem-dependent weak-existence construction, same-operator L1 contraction and uniqueness, a fixed-coefficient zero-regularizer limit, and a simultaneous double-degeneracy limit to a porous-medium Neumann equation. It preserves an energy-estimate counterexample and the distinction between finite-grid near-quadratic layer fits and strict compact support. These results concern one positive-flux model, not historically printed negative-flux equations, a universal BIG law, independent physical validation, or a new general PDE method. External mathematical peer review has not been performed. The English manuscript is authoritative; the Japanese PDF is a reference translation. A short prepublication clarification separates forward uniqueness from coefficient identifiability: spatially uniform data produce a coefficient-independent solution for any gamma>0 and epsilon>=0. The paper also distinguishes strict support, level sets, response-sign boundaries, and finite-precision observational boundaries, and refers to a separately deposited but unreviewed C19-P92 history-and-steel benchmark (Zenodo 10.5281/zenodo.23965486) without equating its models or claiming physical validation.