Useful Demo — Part 3

Design:In validated regimes, SPSP–SSC overlays coincide with textbook GR; any verified departure is a falsifier.

Solar Light Deflection

Textbook (GR) null-geodesic deflection by mass \(M\) vs. impact parameter \(b\). Near the Sun’s limb, \(\alpha \approx 1.75''\). SPSP–SSC uses the same exterior propagation; projection fixes \(M_{\rm enc}\), so the curves coincide.

Mass \(M\) (in \(M_\odot\)) Min impact parameter \(b_{\min}\) (in \(R_\odot\))

Max impact parameter \(b_{\max}\) (in \(R_\odot\)) Samples (points)

SIS Weak Lensing (Tangential Shear)

Singular Isothermal Sphere with velocity dispersion \(\sigma_v\): Einstein angle \(\theta_E^{\rm SIS}\) and \(\gamma_t(\theta)=\theta_E^{\rm SIS}/(2\theta)\). SPSP–SSC uses the same mapping; projection determines \(\sigma_v\).

Velocity dispersion \(\sigma_v\) (km/s) Distance ratio \(D_{ds}/D_s\)

θ_min (arcsec) θ_max (arcsec) Samples (points)

Why this Works as a Falsifier

Projection → parameter → observable. SPSP–SSC fixes the source parameter (e.g., \(M\) or \(\sigma_v\)); all exterior propagation is standard GR/QM. Therefore the overlays coincide in validated regimes. If future data points do not (with systematics controlled), SPSP–SSC is falsified there.