Deformation Channels and the Consistency Window of Finite Accessibility

This paper introduces the deformation-channel formalism that constrains admissible gravitational modifications under the principle of finite accessibility. Building on Papers I–III of the Finite Accessibility Series, we formalize how temporal and radial certification channels deform under matter load while preserving intersubjective consistency. The central result is the identification of a consistency window: only deformations that preserve bounded distinguishability, additive Fisher structure, and channel factorization survive as physically admissible geometries. Gravity is therefore not postulated but constrained by certification coherence. Core Framework Finite accessibility imposes bounded distinguishability. For a spherically symmetric source of mass M at radius r, temporal certification depletes as: Omega_t(r) = 1 - GM / (c^2 r) Radial certification deforms according to channel consistency: Omega_r(r) = 1 / Omega_t(r) The effective certification capacity factorizes: Phi_cap(r) proportional to Omega_t(r) * Omega_r(r) Channel deformations must preserve: Finite Fisher distinguishability Additive composition Local certification closure Intersubjective invariance Any deformation violating these conditions exits the admissible window. The Consistency Window Admissible deformations must satisfy: 0 < Omega_t(r) ≤ 1Omega_t(r) * Omega_r(r) = 1lim(r→∞) Omega_t(r) = 1 Within this window: Newtonian limit is recovered Schwarzschild geometry emerges Post-Newtonian consistency holds No additional tuning parameters are required Outside this window: Fisher additivity fails Reference frames dissolve Intersubjective geometry becomes unstable The Schwarzschild form is therefore not chosen — it is structurally forced. Structural Results This paper demonstrates: • Channel factorization is the unique deformation preserving certification closure• The 1/r profile arises from flux conservation under bounded accessibility• Spatial curvature follows from temporal depletion consistency• The PPN parameter gamma = 1 is structurally enforced No free deformation functions remain once accessibility axioms are imposed. Keywords Finite accessibilityCertification bandwidthDeformation channelsConsistency windowFisher information geometryGravitational depletionSchwarzschild metric derivationOperational gravityPost-Newtonian constraintsStructural forcing Finite Accessibility Series — Complete DOI Index I. Gravitational Geometry and Schrödinger DynamicsDOI: 10.5281/zenodo.18601600 II. Inertia, Motion, and Wave PropagationDOI: 10.5281/zenodo.18625174 III. Quantum Records, Definite Outcomes, and Born RuleDOI: 10.5281/zenodo.18625192 IV. Deformation Channels and Consistency WindowDOI: 10.5281/zenodo.18654364 V. Certification Manifold (Dark Matter)DOI: 10.5281/zenodo.18654433 VI. Frame Dissolution and Planck CeilingDOI: 10.5281/zenodo.18654458 VII. Exclusion Theorems (Seven No-Go Results)DOI: 10.5281/zenodo.18654493 VIII. Dark Energy as Mandatory Certification OverheadDOI: 10.5281/zenodo.18654523