The Horizon Constant and Resolution Paradox (Ω₂₈₈₀): Recursive Discrete Geometry, Perceptual Continuity, and the Emergence of Curved Manifolds from Finite Structures | SEXA Mathematical Sciences Pacific LLC | ANY KNOWN OBJECT Advanced Aerospace & Terraforming LLC

This preprint introduces the Resolution Paradox and the Horizon Constant (Ω₂₈₈₀), proposing a recursive geometric framework for investigating how sufficiently dense discrete structures become observationally indistinguishable from continuous manifolds. Beginning with the Rubik's Cube as a remedial geometric model, the paper develops the concepts of recursive organization, admissibility, perceptual continuity, and the Skeleton Hypothesis before introducing the Horizon Principle as a benchmark for examining the emergence of curved manifolds from finite recursive assemblies. This manuscript has been submitted for journal peer review. The Zenodo record preserves the submitted preprint version while the work undergoes peer review. Upon publication, the peer-reviewed journal article and DOI will become the version of record. :contentReference[oaicite:0]{index=0}