Gravity as a Selector of Dependently Reconstructible Distinguishability on Compact S³ presents a mathematically closed framework that separates four fundamentally different layers of physical information: carrier distinguishability → spectral mode capacity → causal accessibility → physically admissible code capacity. Rather than identifying gravity with information, the work shows that gravity acts as a selector, reducing the set of kinematically available distinctions to those that remain physically realizable under causal, energetic, entropic and stability constraints. The resulting dimensionless invariant, Σgrav = Bphys/Bcausal, measures the contraction from raw distinguishability to admissible distinguishability and satisfies the universal bound 0 ≤ Σgrav ≤ 1. Assuming a conditional compact S³ carrier, the manuscript derives exact closed expressions for causal accessibility ΓR(T), spectral capacities of scalar, transverse-traceless tensor and Dirac sectors, finite-alphabet information capacities, and their physically admissible reductions. The selector architecture is intentionally modular: the causal and spectral construction is independent of the specific physical ceiling employed, allowing established entropy or energy bounds—or future independently justified constraints—to be incorporated without altering the mathematical core. In the fine-resolution Weyl regime the framework reproduces the expected cubic scaling N(ε) ∝ (R/ε)³, while revealing a universal transition between unrestricted and ceiling-limited information regimes. The paper is deliberately restricted to definitions, proved theorems, reproducible calculations, and explicit non-claims. It does not claim to establish the global topology of the Universe, solve quantum gravity, derive the Standard Model, or resolve any external open mathematical problem. Instead, it provides a rigorous theorem-level foundation together with falsifiable observational templates, offering a reproducible mathematical framework in which gravity is interpreted as a selector of physically admissible distinguishability rather than as information itself.
Batenin et al. (Mon,) studied this question.