The Spartan Dawn Test: Breathing Hypersphere versus the Static Cosmos against CMB, BAO, and Supernovae,

"The Spartan Dawn Test: Breathing Hypersphere versus the Static Cosmos against CMB, BAO, and Supernovae," is Paper XII in Daniel Alexander Trawin's TZPID Gold Spine Series II. The paper evaluates the "breathing-enclosure" cosmological hypothesis—which describes the universe as a closed 3-sphere ($S^{3}$) with a dynamically changing radius —by fitting it against real observational data via $\chi^2$ minimization. The dataset includes the Planck 2018 cosmic microwave background (CMB) acoustic scale, twelve baryon acoustic oscillation (BAO) distances from DESI DR2, and a Pantheon supernova constraint, with a fixed sound horizon. The analysis compares four nested models: flat $\Lambda$CDM, closed $\Lambda$CDM, flat $w_0w_a$CDM, and closed breathing $w_0w_a$CDM. The results firmly reject a static closed universe, as adding curvature alone fails the Akaike information criterion. However, the dynamic "breathing" models are strongly favored over flat $\Lambda$CDM, successfully matching the evolving dark energy signature reported by the DESI collaboration. Ultimately, the author argues through a "temporal/atemporal duality" that geometric breathing can mathematically account for cosmological distances without dismantling the hot Big Bang paradigm, leaving the formal derivation of the breathing pressure term as an objective for future papers in the series.