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

Abstract

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.