2026/05/18 by Rowan Brad Quni-Gudzinas · 1 voice
Physics and Astronomy · Mathematics · #Quantum Mechanics and Applications #Mathematical and Theoretical Analysis #advanced mathematical theories
paper · doi:10.5281/zenodo.20266032
openalex publication_date 2026/05/18 · openalex created_date 2026/05/19 · openalex updated_date 2026/05/19
Mathematics proves logical consistency under stated assumptions; it does not prove physical reality. This essay develops a four-type taxonomy of mathematical proofs in physics (consistency, impossibility, existence, guarantee) and shows what each can and cannot deliver. Using an ultrametric error confinement architecture based on Bruhat–Tits trees as a case study, and the detailed technical review it received, I demonstrate how the “assumptions gap” operates in practice. Historical failures (surface code overconfidence, Hawking’s premature conclusion, solar system “proofs”) are balanced against successes (Noether’s theorem, Bell’s theorem, Dirac’s positron) to show that mathematics succeeds in physics precisely when its assumptions are well-matched to physical constraints and its predictions are testable. The essay proposes a “proof-physics contract” as a practical tool for making the assumptions gap visible, and concludes that while mathematics cannot prove physics, it can tell us exactly what would follow if certain conditions held — leaving experiment to determine whether those conditions obtain.