This work presents the Gravitational Potential Response Framework (GPRF), a structural approach to galactic dynamics that recovers the empirical successes of both dark matter and Modified Newtonian Dynamics — flat rotation curves, the tight mass-velocity correlation observed across all spiral galaxies, and the finite boundary of the galactic halo — from a single linear constitutive relation and one coupling constant, without new particles, modified gravity, or ad hoc assumptions. The MOND formula emerges as a mathematical consequence rather than a starting assumption. The constitutive relation ρ_nb = α δφ — that non-baryonic density responds proportionally to the local gravitational potential — combined with the standard Newtonian operator yields an augmented Poisson equation whose induced-density Yukawa profile recovers deep-MOND scaling and the baryonic Tully-Fisher relation as exact consequences of a single coupling constant α. The Yukawa exterior solution introduces a structural outer halo cutoff at k⁻¹ ≈ 14 kpc, derived from the BTFR normalization alone. This coincides with the Keplerian decline recently revealed by Gaia DR3 without rotation-curve fitting. Because k⁻¹ ∝ v²_flat/a₀, the cutoff radius is galaxy-specific: lower-mass galaxies are predicted to show their decline at proportionally larger radii, potentially beyond current observational limits. The Square Kilometre Array and the Nancy Grace Roman Space Telescope are well positioned to test this prediction systematically across the galaxy population.

The Gravitational Potential Response Framework (GPRF) Dark Matter Induced by Gravitational Potential: MOND-like Phenomenology at Galactic Scales Rotation Curves, the Baryonic Tully-Fisher Relation, and the Outer Halo Cutoff This work presents the GPRF, in which a single linear constitutive relation ρ_nb = α δφ combined with the standard Newtonian operator yields an augmented Poisson equation whose induced-density Yukawa profile recovers deep-MOND scaling, the baryonic Tully-Fisher relation, and a structural outer halo cutoff — all as exact consequences of a single coupling constant, without modifying gravity. Key results: MOND phenomenology emerges as a consequence, not an assumption Outer halo cutoff at k⁻¹ ≈ 14 kpc, consistent with Gaia DR3 without rotation-curve fitting Three-regime mass structure: dwarfs (interior-dominated), MW-mass (cutoff visible), massive spirals (cutoff beyond survey reach) — explains why the cutoff is not seen in SPARC Implied RAR derived analytically; LMC/SMC sit on the observed RAR; NGC1052-DF2/DF4 fall below it — both naturally explained by the non-local character of δφ Tidal dwarf galaxies follow MOND predictions naturally through environmental potential embedding While the current work focuses on outer galactic scale dynamics, the framework shows promise of extending to Solar System, intra-galactic, cluster, and cosmic scales — to be explored in future work.

v1.0.2 Substantially revised from v1.0.1 Augmented Poisson naming throughout; non-locality framing; Zwicky-Rubin historical opening; RAR figure with LMC/SMC/DF2/DF4; cutoff scale figure; a₀ ~ cH₀/2π coincidence; Kroupa 2012 and van Dokkum 2018 citations; updated conclusion with six result bullets; concept DOI in watermark. Version note: v1.0.2 supersedes v1.0.1 (May 29, 2026). Please cite using the concept DOI 10.5281/zenodo.20450130, which always resolves to the current version. v1.0.3 changes from v1.0.2: New abstract leading with plain-language significance; k² physical interpretation sentence in Framework; trontological phase interpretation of induced mass in Discussion; FAQ appendix (Appendix A) addressing common questions and scope; Appendix D gauge claim corrected — framework acknowledged as zero-point dependent by construction, with sign closure deferred to GPRF II; likelihood comparison left to independent investigators; Roadmap scope language refined; LaTeX header with copyright and version history added. Version note: v1.0.3 supersedes v1.0.2 (June 2, 2026). Please cite using the concept DOI 10.5281/zenodo.20450130, which always resolves to the current version.

Contents: Introduction — motivation, scope, prior work Framework — constitutive relation, augmented Poisson equation, feedback structure Spherical example — Yukawa solution, acceleration field, MOND-like scaling Rotation curve phenomenology — BTFR derivation, Gaia DR3 consistency check Discussion — cluster regime, Bullet Cluster, UDGs, lensing outlook Conclusion — six result bullets Roadmap and Outlook — cluster scales, lensing, Solar System Appendices: A. Common Questions, Scope, and Deferrals (FAQ) B. GPRF and MOND comparison C. Cluster-scale δφ integration D. Gauge Freedom and Sign Convention E. The Machian Reference Frame F. On the Necessity of Linear Constitutive Relations