OBSOLETE Finite Closure Geometry (FGC): Information, Gravity, and the Meaning of the Infinite

This companion paper explores the conceptual consequences of Finite Closure Geometry (FCG) for the interpretation of information, gravity, and the role of the infinite in physical theories. Rather than introducing new dynamical laws or speculative mechanisms, the work develops an interpretive framework in which several persistent problems—black hole entropy, cosmological constants, horizons, and singularities—are understood as manifestations of structural non-closure.

Within the FCG perspective, finite closure schemes are unavoidable in any operational description of systems with infinitely many degrees of freedom. Residual terms arising from the failure of global closure are interpreted as carriers of structurally inaccessible information: information that is neither hidden nor lost, but cannot be localized within any finite descriptive regime.

Gravity is reinterpreted as a constraint enforcing compatibility between local closures across spacetime, while horizons and singularities mark boundaries where closure coherence fails. The cosmological constant is discussed as a possible global residue required to sustain consistent local descriptions in an expanding universe.

A central epistemological consequence is emphasized: the appearance of infinities in physical theories is not an ontological statement about nature, but a diagnostic signal of descriptive breakdown. Infinities function as indicators of non-closure rather than as physical substances.

This paper is conceptual and non-dynamical in scope. It does not propose new models or parameters, but provides an interpretive synthesis connecting geometry, information, and gravity within the Finite Closure Geometry program.

A global conceptual map, epistemological positioning, and guided reading of the foundational FCG papers is provided in the foundational Paper 0:
https://zenodo.org/records/18001440