Measuring the Gravitational Response to Structure

This paper presents an empirical measurement of how gravitational lensing response depends on the internal spatial organization of matter, rather than solely on its total mass. It is a direct continuation of Gravity as a Response Field in Spacetime and is intended to accompany Scale-Selective and Geometric Coupling Between CMB Lensing Convergence and Large-Scale Structure, extending those results from localization to quantitative measurement. Using Planck PR4 CMB lensing convergence (κ) cross-correlated with SDSS/BOSS CMASS galaxy overdensity (δg), the analysis constructs a scale-selective, structure-conditioned κ×δg response surface across multiple independent structural proxies. The measured response exhibits three robust features:(i) confinement of the κ×δg coupling to a narrow multipole band,(ii) collapse of the signal under rotation-based null tests, and(iii) systematic variation of the response amplitude with structural coherence at fixed mass proxies. These behaviors persist across alternative tracers, masking schemes, and dark-matter-compatible null ensembles. The results demonstrate that gravitational response inferred from lensing cannot be treated as a purely mass-determined quantity under standard averaging assumptions. Instead, the data require that matter’s spatial organization enters as an independent empirical variable controlling when and how gravitational coupling is realized. This work is constraint-focused and model-agnostic. It does not propose new gravitational field equations or a specific microphysical mechanism. Rather, it provides a reproducible observational target that any mass-derived, modified-gravity, or emergent-gravity framework must account for. All data products and analysis outputs needed for independent replication are provided in an accompanying Zenodo dataset.