The Q5 Structural Spine

This document is not a new theorem, but a structural map of the Q₅ theorem series, isolating the minimal dependency chain and the forced architecture that emerges from it. We present a structural compression showing that the combinatorial geometry of the 5-dimensional hypercube Q₅, equipped with parity grading, admissible transport, and Gray-constrained traversal, forces a uniquely determined operator algebra and state-space structure on CQ5. Within this forced architecture, a minimal defect-supported carrier emerges canonically, yielding a three-dimensional Lie algebra CX isomorphic to su (2) under its natural commutator relations. Order-sensitive transport along Gray-constrained paths generates a nonfactorizable phase defect that survives projection through a sequence of reduction operators and is extracted via a canonical linear functional L. This phase is not imposed, but forced by the underlying combinatorial constraints. We further show that the embedded defect coefficient governing this phase is generically nontrivial and cannot vanish identically. This nontriviality arises from an inversion asymmetry inherent in the transport architecture. Under a compatibility condition between defect extraction and the retained transport sector, the phase reduces to a universal constant value. The resulting structure exhibits a clear correspondence with key features of quantum mechanical formalism, including graded state spaces, noncommutative operator algebras, and phase-carrying transport mechanisms. While no claim of full equivalence to quantum mechanics is made, this synthesis isolates a minimal set of combinatorial conditions under which such structures are forced, suggesting a potential geometric origin for phase coherence and its persistence under constrained transport.