Projection Holographic Time Condensation (PHTC) Complete Research Archive: From Theoretical Conception to Methodological Case Study

This document constitutes the complete research archive of the "Projection Holographic Time Condensation" (PHTC) program. The program began with an ambitious theoreti.cal conception-whether a four-dimensional physical world could emerge from the spectral Green's function of a two-dimensional boundary screen—and concluded, after eleven rounds of rigorous peer review and author self-correction, with the author actively falsifying its core mechanism. Core conclusion: The failure of PHTC stems from a fundamental category error-spin is a representation-theoretic property of SO(3, 1) and cannot "emerge" through projection from a scalar field theory lacking such representation structure. This conclusion carries significance beyond PHTC itself. Archive structure:(1) Theoretical conception phase (Versions 5-8);(2) Rigorous examination phase (Versions 9-11); (3) Final version and program reconstruction; (4) Minimal model computation and failure; (5) Methodological reflection and conclusion.