Shock Breakout in Core-Collapse Supernovae Within the Cosmological Thermosynthesis Theory v3.2: Entropic Crystallization, Etherion-Mediated Nucleosynthesis, and Falsifiable Predictions for Multi-Messenger Observations

This work presents a rigorous mathematical reformulation of shock breakout phenomena in core-collapse supernovae within the Cosmological Thermosynthesis Theory v3.2 (TTC v3.2). Rather than treating shock breakout as a purely hydrodynamic process in standard stellar evolution, TTC v3.2 proposes that the initial radiation flash and subsequent nucleosynthetic yields emerge from entropic crystallization events in the primordial etherion superfluid an ultralight scalar field with mass me = (1.00 ± 0.05) × 10−22 eV—confined within the collapsing stellar core. We derive: (i) the modified shock propagation equation incorporatingetherion-mediated pressure corrections; (ii) the entropic amplification factor for early-time luminosity; (iii) the asymmetric emission signature predicted by topological vortex dynamics in the superfluid condensate; and (iv) the connection between shock breakout observables and the cyclic cosmological parameters of TTC v3.2. Integrating recent observational constraintsfrom JWST (early massive galaxies at z > 10), DESI DR2 (dynamic dark energy with w0 = −0.717, wa = −1.72), and LIGO-Virgo-KAGRA (core-collapse gravitational wave limits), we demonstrate quantitative consistency with TTC v3.2 predictions. All definitions specify domains, codomains, hypotheses, and mathematical spaces; lemmas, propositions, and theorems include explicit proofs. The framework yields falsifiable predictions for JWST, Euclid, LISA, CMB-S4, and next-generation supernova surveys, positioning shock breakout observations as a critical empirical test of TTC v3.2’s unified superfluid dynamics at stellarscales.