Geometric Projection Constraints on Short-Range, Mass-Coupled Modifications of Gravity: A Design Guide from Low-q Elastic Neutron Scattering

Version 6. 0. 0 Update (The Epistemic Design-Closure Synthesis): This publication establishes the kinematic boundary on static, linear, mass-coupled short-range modifications of gravity. Version 6. 0. 0 replaces all heuristic estimates with mathematical proofs, generating an airtight, audit-ready phenomenological design guide: Strict Kinematic Audit (ql 1): Formally separates the l=0. 1 nm geometric projection theorem (ql 0. 02, 0. 20 1) from the template-specific l=1. 0 nm full form-factor integration, ensuring absolute mathematical rigor across the Kamiya SANS acceptance band. Inelastic Born Transition Rate (Temporal Evasion Lock): Eradicates the temporal evasion loophole by formally integrating a time-varying potential into the first Born approximation. Proves that coupling to the dynamic structure factor S (q, ) fundamentally shifts the transition rate by 4. 1 meV, which is strictly excluded by known Ultra-Cold Neutron (UCN) interferometry bounds (10^-14 eV). Calibrated Fourier Leakage Inequality: Replaces abstract spatial leakage warnings with a strict algebraic inequality. The spectral leakage observable (L ₁₀₍₃) is explicitly normalized and bounded against the empirically excluded Yukawa cross-section limit, providing a definitive pass/fail numerical cutoff for zero-mean kernel evasions. Targeted Claim Discipline: Delineates the theoretical jurisdiction specifically to models generating verifiable additive pseudo-potentials at the 1 nm scale (e. g. , screened chameleons, dilatons), avoiding categorical overextension into thermodynamic/emergent frameworks. Future Research Compliance Guide: Includes a newly formulated Epistemic Compliance Flowchart and logical schematic, allowing theorists and phenomenologists to instantly audit their modified gravity models against the strictures established in this paper. Files Included: main. pdf / main. tex: The definitive UNIFIED PRD manuscript. Unverified citations strictly purged and hyperbolic language neutralized for peer review. neutrongeometricₚrojectionᵥ6. py: Open-source Python toolkit (v6. 0. 0) simulating the Fourier projection, calibrated spectral leakage, inelastic S (q, ) constraints, CSV raw data exports, and the automated Epistemic Compliance Flowchart generator.