Weak Lensing Shear Correlation with the O'Reilly Effect: Testing Informational Contributions to Strong Gravitational Lens Morphology in SDSS J1206+4332

A synthetic modeling test of the Relativity of Information and Geometric Principles (RIGP) framework applied to strong gravitational lensing is presented. Using the quad lens system SDSS J1206+4332, an informational perturbation term Sμν—the geometric footprint of an observer's collapsed probability field—is superimposed onto a standard singular isothermal ellipsoid plus external shear lens model. The perturbation, modeled as a dipole-modulated anisotropic Gaussian at 4% amplitude, produces characteristic structured residuals after standard model subtraction. The predicted informational footprint is spatially coherent, anisotropic, and distinguishable from instrumental noise at HST sensitivity levels. A direct observational test using archival HST ACS/WFC F814W imaging is proposed. The work connects to Verlinde's entropic gravity, the ER=EPR conjecture, Penrose-Hameroff Orchestrated Objective Reduction, and Nottale's Scale Relativity.

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Abstract

This paper presents the first synthetic modeling test of the Relativity of Information and Geometric Principles (RIGP) framework applied to strong gravitational lensing. Using the well-characterized quad lens system SDSS J1206+4332, we superimpose an informational perturbation term Sμν onto a standard singular isothermal ellipsoid (SIE) plus external shear lens model and generate The Sμν term — the informational stress tensor central to RIGP theory — models the geometric footprint produced when an observer’s collapsed probability field introduces anisotropic curvature into a physical system. This is directly analogous to how mass curves spacetime in general relativity, but operating at the level of information geometry rather than mass-energy. The perturbation is modeled as a dipole-modulated anisotropic Gaussian at 4% amplitude, producing characteristic structured residuals after standard model subtraction. The four-panel figure (standard model / Sμν perturbation field / total image / residuals) demonstrates that the predicted informational footprint is spatially coherent, anisotropic, and distinguishable from instrumental noise at HST sensitivity levels. We propose a direct observational test using archival HST ACS/WFC F814W imaging of SDSS J1206+4332. This work connects to and extends several foundational theoretical frameworks including Verlinde’s entropic gravity, the ER=EPR conjecture (Maldacena & Susskind), Penrose-Hameroff Orchestrated Objective Reduction, and Nottale’s Scale Relativity — all of which point toward a deeper geometric unity between quantum information, consciousness, and spacetime structure. Modeling performed with lenstronomy 1.14.0 on Python 3.14. Code architecture by Claude (Anthropic). Theoretical development in collaboration with Google Gemini. Prior related work: O’Reilly (2026), Empirical Sensitivity Analysis of Observer-Constrained Coherence in Qubit Manifolds, Zenodo. Keywords: gravitational lensing, strong lensing, SDSS J1206+4332, information geometry, entropic gravity, RIGP, Sμν, consciousness, quantum gravity, Einstein ring, lenstronomy