Two Companion Papers on a Speculative Geometric Framework: (1) A Geometric Candidate for Two Open Questions in Physics; (2) Tracing Motion as Geometry

This record contains two related papers exploring a speculative geometric framework built on the 24-cell (icositetrachoron), a self-dual four-dimensional polytope. The first paper, "A Geometric Candidate for Two Open Questions in Physics," presents the framework's verified geometric core, tests a vantage-point principle against historical and astronomical data, and identifies two genuinely unresolved physics questions — the number of fermion generations and the nature of time — where this geometric structure makes contact with existing, contested research. The second paper, "Tracing Motion as Geometry," tests a specific closure rule (that combined periodic motions trace a repeating shape only under an exact frequency ratio) in molecular vibration, confirming it with real spectroscopic data and reporting two related findings honestly as closed rather than disqualifying. Both papers distinguish clearly between verified mathematics, open hypotheses, and claims that were tested and did not hold, with real citations throughout.