This is version formalizes the Epistemological Proof of Uniqueness for Single-Field Density-Dependent Scalar Theories. This version consolidates the axiomatic formulation, strengthens the logical consistency of the proof, and extends its applicability beyond the Stratophysical model to the broader class of single-field screened-scalar frameworks. It supersedes earlier drafts developed during the exploratory Stratophysics project. The author conceived this work as an experiment in reasoning using AI assistance not as a source of content, but as a collaborator in structuring, verifying, and testing logical consistency. All scientific arguments, derivations, and theoretical insights remain the original work of the author, developed as part of an independent study on the epistemic limits of gravitational modification. This research was undertaken out of personal scientific curiosity and a desire to understand the boundaries of knowability in physics. While not yet peer-reviewed, it is released in the spirit of open theoretical exploration to encourage scrutiny, discussion, and refinement by the scientific community.

This work presents a mathematical and epistemological proof for single-field, density-dependent scalar theories of gravity. Under a minimal set of axioms derived from the Impossibility Theorem for Gravitational Amplification and the Screening Trilemma, only one effective-mass law remains mathematically consistent, energetically stable, and epistemically closed. The resulting form:m_eff²(ρ) = m₀² + A·min(ρ^α, ρ_t^α) is not postulated but derived as the sole expression satisfying the requirements of vacuum stability, local energy conservation, bounded amplification, and mathematical regularity. This uniqueness transforms the effective-mass relation from a phenomenological assumption into a logical necessity within the axiomatic structure of single-field screened-scalar theories. The Stratophysical formulation serves as a concrete realization of this general framework, unifying the consistency conditions of density-dependent gravitation into a single, mathematically complete expression.