Structural Projection and Invariant Ratios From Activated Trajectories to Relational Signatures

This work presents a fully structural projection framework that maps activatedrelational histories into dimensionless relational signatures without invokingspacetime, physical dynamics, quantum fields, or phenomenological parameters.The formulation is governed by a minimal set of structural axioms (layeredslicing, additivity, reversibility, and coherence preservation), which uniquelydetermine the discrete support sequence P_n = 3 * 2^n and the canonicalinvariant ratio 5:27:68. Activated trajectories inherit their initial relational structure from atruncated 4-simplex, leading to discrete angular growth, suppression oflow-l modes, weak large-scale alignments, and a structural expansion-collapseduality. These signatures arise purely from structural admissibility and do notrely on cosmological assumptions or physical mechanisms. The appendices explore structural origins of anisotropy, non-ideal supportconfigurations, structural memory, toy models for robustness testing, and arelational interpretation of observed CMB anomalies. The framework is entirelypre-physical; any connection to empirical observables requires additionalassumptions beyond the scope of this work.