Non-Factorisability and the Emergence of Heisenberg Structure from Admissibility Constraints

We prove that the admissibility axioms of the Cosmochrony framework, together with Born--Infeld parity, uniquely determine the algebraic structure of the admissible fibre Fₙ. The central result is that any structure of observable directions that is finite, minimal, and genuinely non-pre-resolved is necessarily of Heisenberg type: the symmetry group of Fₙ is isomorphic to Heis₃ (Z/qZ) for a prime q, and Fₙ is isomorphic to the Weil representation V_ on L² (Z/qZ). The proof proceeds through a single structural lemma — admissible non-factorisability — which is a direct formalisation of Axiom A3, and requires no input beyond A1--A3, Born--Infeld parity, and classical classification results. As a corollary, the Heisenberg uncertainty principle is derived as a structural property of the non-resolved proto-state, not as an independent postulate about observables. This paper provides the detailed proof of the result stated in sketch form in the Foundation companion paper on admissible non-injective transitions.