Gravitational Lensing as Resonance-Gradient Refraction in USP Field Theory: GR Baseline Recovery, Achromatic Path Geometry, and Bounded Residual Tests

This document is a foundation-level reconstruction of msf: 49800. The earlier edition used gravitational refraction as a broad physical analogy and proposed uncalibrated Delta-f relations, visible color-dependent arc displacement, and a direct replacement-style lensing law. Version 3. 0 removes those claims and rebuilds the framework around a strict hierarchy: General Relativity first. USP interpretation second. Bounded residual tests last. General Relativity, null-geodesic propagation, and the standard thin-lens formalism remain the quantitative baseline for: deflection angles, image positions, Einstein rings, multiple images, magnification, convergence, shear, critical curves, caustics, and arrival-time delays. For a point mass M and impact parameter b, the required weak-field baseline is: alphaGR = 4GM / (c squared b). The standard lens equation remains: beta = theta - (DLS / DS) alpha. For perfect point-mass alignment, the Einstein angle is: thetaE = square root of 4GM / c squared multiplied by DLS / (DL DS). The USP interpretation introduces an operational resonance potential: PsiUSP = alphag (Delta fₚroxy - Delta fᵢnfinity). This potential must carry the same units as the standard gravitational potential. It is decomposed as: PsiUSP = Phiₛtandard + delta PsiUSP. The standard term is mandatory. The residual term is optional and bounded. The photon path equation is: d squared xₚerpendicular / ds squared = -Kgamma gradₚerpendicular PsiUSP / c squared. The corresponding deflection is: alphaUSP = (Kgamma / c squared) integral along the path of gradₚerpendicular PsiUSP ds. For the point-mass potential: PsiUSP = -GM / r, the transverse-gradient integral gives: 2GM / b. Therefore: alphaUSP = Kgamma 2GM / (c squared b). Recovering the GR result requires: Kgamma = 2. This factor is fixed by baseline recovery. It is not a free fitting parameter. The calibrated foundation equation is therefore: alphaUSP = 2 / c squared times the path integral of gradₚerpendicular PsiUSP ds. When PsiUSP equals the standard potential, this is a resonance-gradient translation of the standard weak-field GR result. The document retains the refraction analogy only as a guarded mathematical bridge. A graded-index material and a gravitational lens can both be represented as stationary-path or phase-gradient problems. However: shared path mathematics does not imply identical microscopic physics. Material refraction normally depends on frequency because matter has dispersive internal modes. Vacuum gravitational lensing in the geometric-optics baseline is achromatic. The document therefore does not predict visibly separated red and blue gravitational arcs. Different bands can produce different apparent arc shapes or centroids because of: source color gradients, differential magnification, dust extinction, microlensing, plasma dispersion, point-spread-function differences, detector response, astrometric registration, source variability, and lensing time delays. These standard explanations must be modeled before a USP residual is considered. The complete observational chain is: mass distribution to gravitational or resonance potential to deflection field to lens mapping to source reconstruction to lensed surface brightness to PSF, pixels, noise, and detector data. A bending equation alone is not a complete lensing model. Any proposed USP term must survive this entire mass-to-detector chain. A measured multi-band angular difference is decomposed as: delta alphaₒbserved equals delta alphaₛource plus delta alphadust plus delta alphaₚlasma plus delta alphaₘicrolensing plus delta alphaPSF plus delta alphaₐstrometry plus delta alphaᵥariability plus delta alphaUSP plus statistical noise. The USP term is therefore the final unexplained residual, not the first interpretation. A minimal residual family is written as: delta alphaUSP equals alphaGR multiplied by etaₗambda gₗambda plus etaₚolarization gₚolarization plus etacoherence gcoherence. The null state is: etaₗambda = 0 etaₚolarization = 0 etacoherence = 0. These coefficients define tests. They do not predict that blue light bends more than red light. Version 3. 0 introduces the conservative project-level screening condition: absolute delta alphaUSP divided by absolute alphaGR less than or approximately equal to 10 to the power minus 3. This is a project guardrail. It is not claimed as one universal empirical limit for every lensing dataset. The purpose is to prevent the framework from producing visibly separated multi-band arcs before a proper constraint analysis exists. A valid USP residual must also satisfy cross-observable consistency. The same residual potential must predict compatible changes in: image positions, magnification, shear, critical curves, caustics, and arrival-time delays. A correction that improves one observable while degrading the others is rejected. The document defines experimental and observational tracks for: solar and stellar weak-field recovery, multi-band strong-lens astrometry, time-delay consistency, polarization and coherence tests, weak-lensing population studies, plasma-separation tests, strong-field compact-object guardrails, and held-out statistical validation. A null result is treated as a successful constraint. If all apparent multi-band differences are explained by source structure, dust, microlensing, plasma, instrument response, and timing, then the chromatic USP term is unnecessary. The resonance-gradient language may still remain as a non-distinct interpretation of the standard gravitational potential. Non-replacement statement This work does not replace: General Relativity, metric gravity, null-geodesic propagation, weak or strong gravitational-lensing theory, thin-lens formalism, standard mass reconstruction, source reconstruction, time-delay cosmography, plasma optics, interstellar scattering, dust extinction, microlensing, instrument point-spread-function models, detector calibration, or astrometric calibration. These remain the quantitative and observational baseline. USP Field Theory is presented only as a calibrated interpretation and bounded residual-testing layer. A USP term is not accepted merely because it can be written. It must recover the standard result, use declared units, survive predeclared null models, and improve prediction across more than one observable.