Gravitational Lensing from TS Curvature

Paper D — Gravitational Lensing from TS Curvature

Paper D presents the lensing-sector predictions of LFCT, where the TS mode acts as a curvature contribution with a logarithmic potential rather than as a force-law modification. Because the TS radial field scales as 1/r (not 1/r² like the Newtonian TD channel), the induced potential is Φ_TS ∝ ln r, producing photon deflection with weak logarithmic impact-parameter dependence that is structurally distinct from both the standard 1/b point-mass profile and NFW-halo predictions. Three explicit discriminator tests are developed: (i) at galaxy scale (10¹¹ M☉), TS deflection overtakes TD at a crossover radius of approximately 6 kpc; (ii) at cluster scale (10¹⁴ M☉), TS produces a 190–360% weak-lensing excess across 500–2000 kpc relative to NFW expectations; and (iii) quad-lens time-delay ratios are constrained differently from ΛCDM/NFW by the logarithmic profile shape. The paper is organised prediction-first: only the minimum framework needed to make these tests legible is included. All predictions trace to the same mode normalizations and axiom set used in Papers A–C, with no lensing-specific parameters introduced. The paper identifies observational failure conditions for each test and positions Paper D as the decisive discriminator paper in the sequence.