The Temporal Dynamics Framework: A Unified Geometric Theory of Nuclear Structure, Prime Distribution, and Particle Stability

This paper presents the complete Temporal Dynamics Framework (TDF), a geometric and number-theoretic construction built on six Universal Primes {2, 3, 5, 7, 11, 13} and the golden ratio . From these inputs it builds a standing-wave product and a derived cavity-depth coordinate , and maps known structure in nuclear mass numbers, prime distribution, and the Riemann zeros onto that geometry. This synthesis reports, with equal weight, what the construction does and where it stops. Every claim below carries a tag — identity, derived, fit, flag, or null-fail — and the key to those tags is Section 0. The reproducible observation: the depth coordinate , computed from the mass number and the six primes with no measured mass input, places the doubly-magic mass numbers in its central (modal) bin more often than the background rate (6 of 9; nominal ). Two caveats are essential and are stated plainly throughout. First, this is a clustering of mass NUMBERS: is a function of the mass number alone and cannot distinguish isobars, so it assigns the same value to a stable SNP-core (TDF) and to its radioactive neighbours of the same mass number ( is identical for oxygen-16, nitrogen-16, and fluorine-16). Second, the six primes were chosen in part because they cluster the magic numbers more tightly than other sets; under a look-elsewhere correction for that selection the nominal p-value does not survive — trying as few as three alternative sets pushes the corrected value above 0.05. The clustering is therefore an exploratory observation. This record holds one paper on its own and is refreshed every couple of months. The complete deposit, 10.5281/zenodo.21788037, holds every paper with its code and data and is updated first; for the newest version of this paper, go there.