Nonlinear Vacuum Medium Model: Research Proposal / Collaboration Brief 2.0

Research Proposal / Collaboration Brief 2.0 presents the current research and collaboration program for the Nonlinear Vacuum Medium (NVM) framework. It is intended to provide mathematical physicists, computational researchers, foundational physicists, and experimental specialists with clearly defined technical problems that can be independently investigated, criticized, reproduced, constrained, or falsified without requiring prior acceptance of the broader NVM ontology. The document summarizes the current canonical NVM realization and distinguishes what has been mathematically specified or derived from what remains unestablished. It organizes the research program around localized nonlinear solutions, Legendre regularity and strong hyperbolicity, dynamical stability and persistence, accessibility and typicality, spectral structure and emergent propagation, electromagnetic correspondence, gravitational correspondence, quantum correspondence, and ultimately differential empirical prediction. The immediate research priority is Test A: determining whether the canonical NVM action admits at least one converged, finite-energy, localized nonlinear solution that remains within the required Legendre-regular and strongly hyperbolic domain. The collaboration program explicitly welcomes positive results, null results, exclusion results, nonexistence theorems, failed reproductions, correspondence failures, and identification of internal inconsistencies. NVM is presented here not as a completed alternative to established physics, but as a specified candidate research program whose mathematical and physical claims are intended to be progressively exposed to independent testing and potential falsification.