Unified Coherence–Projection Framework: Public-Safe Structural Formulation

This paper presents a public-safe coherence-based framework in which observable structure emerges through admissible projection from a higher-order relational manifold. Building on earlier work relating entropy to coherence deficit under projection, the framework introduces a constrained geometric representation layer based on triadic sphere systems, admissible tetrahedral decompositions, Gaussian occupancy fields, nonlinear projection coupling, and observer-relative coherence propagation. The framework treats entropy not as intrinsic disorder but as coherence deficit induced by admissible projection. Structural time emerges from irreversible coherence reduction rather than existing as a primitive parameter. Finite observers are modeled as embedded coherence substructures capable of sensing more relational structure than can be fully metabolized through bounded projection. The work explicitly separates: formal coherence-theoretic claims, admissible projection structure, geometric representation hypotheses, and speculative physical analogy. The publication intentionally omits implementation-specific invariants, optimization operators, convergence conditions, scaling bounds, recursive search procedures, and high-capability reconstruction mechanisms. This work is published through the Carlonoscopen Journal of Coherence Intelligence (CJCI) as a public-safe structural formulation intended for academic discussion of admissible projection, coherence entropy, observer-limited reconstruction, and relational structure under finite bandwidth constraints. Official CJCI publication:https://www.carlonoscopen.com/journal/v1i11