Priority Registration Document — Model Version 1.0 (Calibrated)Digital Record Protection Date: June 3, 2026 This preprint introduces a self-consistent field-theoretic mechanism within the Photon Paradox / Photon-String-Higgs (PSH) model framework to address the anomalous high-redshift galaxy mass function observed by the James Webb Space Telescope (JWST). By analyzing the cosmic dawn epoch at z ≈ 29 (scale factor a ≈ 0.0333, governed by model parameter K4 = 0.0333), we formalize the primordial phase transition of the homogeneous Genesis Field via synchronized gravitational instabilities and false vacuum decay. This localized fragmentation ("glacial crevasses") implants highly dense, non-Gaussian dark matter halo seeds in the critical mass range of 10^7 to 10^8 M_sun. Applying a modified Press-Schechter formalism incorporating asymmetric heavy tails, we derive an accelerated baryonic collapse and an enhanced star formation efficiency (f_star ≈ 0.15 - 0.35). This framework successfully reproduces the observed stellar masses of anomalous early structures without violating global baryonic budgets, Cosmic Microwave Background (CMB) anisotropies, or Big Bang Nucleosynthesis (BBN) spectral constraints (|μ| < 4.7 x 10^-5, |y| < 8.3 x 10^-6). This work operates as a companion publication to the core PSH foundational framework (DOI: 10.5281/zenodo.20515313). All structural data tracks and cosmological scaling equations are fully cross-calibrated against late-time dark matter density flattening and upcoming CMB-S4 spatial distortion maps.