T72 develops a relational geometry framework emerging from an admissible transport structure within the reduced Q5 architecture. Building on the quotient-stable cyclic sectors and transport-preserving transformations established in T69-T71, the theorem constructs effective geometric relations from admissibility, transport compatibility, and preserved reduction structure rather than from an externally imposed background geometry. The resulting framework organizes reduced transport sectors into a relational admissibility geometry generated intrinsically by cyclic transport compatibility and quotient-preserving evolution. T72 is structurally important because it shifts the framework from transport classification toward emergent relational organization. The theorem treats geometric structure not as a primitive background container, but as a consequence of admissible transport relations and preserved reduced-sector connectivity. Cyclic closure, admissibility preservation, and quotient-compatible transport transformations therefore induce an effective relational geometry on the reduced transport sectors. T72 does not derive physical spacetime, Lorentzian geometry, metric tensors, or gravitational field dynamics. The theorem establishes only the emergence of a reduced relational transport geometry generated by admissibility structure and transport compatibility within the Q5 reduction framework. The resulting geometry is therefore best interpreted as an internal relational organization of admissible transport sectors rather than a completed physical spacetime theory. Status: solid for the admissibility-induced relational transport geometry under the stated quotient and reduction assumptions; conditional on the inherited cyclic transport and admissibility-preserving structures from T64-T71; speculative for any direct identification with physical spacetime or gravitational geometry.
Craig Edwin Holdway (Sat,) studied this question.