Strong-Field Tensorial Accessibility and the Inverse Constraint: How Photon Spheres and ISCOs Select the Constitutive Law

Arc V — Gravity & Quantum Theory Paper 4 Title Strong-Field Tensorial Accessibility and the Inverse Constraint:How Photon Spheres and ISCOs Select the Constitutive Law Zenodo DOI 10.5281/zenodo.18225925965 Description This paper develops an inverse-constraint analysis of strong-field gravity within the finite-accessibility framework. Rather than assuming a constitutive law for tensorial accessibility and deriving consequences, the analysis proceeds in reverse: empirically established strong-field structures are used to constrain the admissible accessibility response. Focusing on invariant features of the Schwarzschild exterior—specifically the photon sphere and the innermost stable circular orbit (ISCO)—the paper shows that only a narrow class of tensorial accessibility profiles can reproduce these structures consistently. Exact conditions for null circular orbits and marginally stable timelike orbits are imposed directly at the level of accessibility-modulated geodesic motion. This inverse approach reveals that strong-field observables act as constitutive selectors, ruling out large families of otherwise admissible accessibility laws. In particular, it demonstrates that exponential accessibility depletion is not merely sufficient but effectively required to recover the correct photon sphere radius and ISCO location simultaneously. The analysis reframes classic strong-field landmarks as operational fixed points: locations where accessibility gradients enforce universal behavior independent of probe details. Strong-field gravity is thus shown to constrain the microscopic accessibility law itself, completing the logical loop between operational principles and observed geometry. Keywords strong-field gravity; photon sphere; ISCO; inverse problems; tensorial accessibility; constitutive constraints; operational horizons Notes Arc V — Gravity & Quantum Theory (constitutive, strong-field, inverse analysis) Strong-field observables used to constrain accessibility laws Photon sphere and ISCO treated as operational invariants Demonstrates necessity (not just sufficiency) of exponential accessibility depletion Closes the constitutive loop between operational principles and empirical structure