Structural Projection and Invariant Ratios From Activated Trajectories to Relational Signatures

This work introduces a fully structural, pre-physical framework for analyzing activated relational systems and their admissible projections. The framework does not assume spacetime, physical dynamics, quantum fields, or phenomenological parameters. Instead, it operates entirely at a structural level, governed by a minimal set of axioms: layered slicing, additivity, reversibility, and coherence preservation.Within this setting, activated trajectories inherit their initial relational organization from a truncated 4-simplex. This inheritance constrains the class of admissible projections and leads to a canonical triple structural partition, represented by the ratio 5 : 27 : 68, understood as a structural attractor class rather than a rigid numerical identity.The framework yields discrete structural hierarchies and robust relational signatures, including suppression of low-order angular modes, weak large-scale alignments, and an expansion–collapse duality. These features arise purely from structural admissibility and do not rely on cosmological assumptions or physical mechanisms.The appendices explore structural memory, non-ideal support configurations, and toy models used to test robustness under admissible deformations. The entire construction is pre-physical; any connection to empirical observables requires additional assumptions and is explicitly left outside the scope of this work.