Particle Genesis from the Horizon Code: Thresholds, Spin Emergence, and the Neutrino as a Partial-Lock Case

This work develops a mathematics-first framework where elementary particles, spin, and vacuum structure emerge from informational and horizon principles. The central idea is that particle activation thresholds are governed by a universal horizon-bit energy scale. This provides a unified explanation for why photons and gluons remain massless, how W and Z acquire mass in a collective way, why fermions obey four-pi periodicity, and why neutrinos have small but nonzero masses without introducing new fields. The construction is internally consistent, preserves all local tests of general relativity, and treats the cosmological vacuum as principle-locked to the Hubble rate. Beyond technical proofs, the text includes plain-language explanations of each result. The aim is to offer a coherent and logically closed account of particle genesis and spin emergence, serving as a foundation for further theoretical and empirical exploration.