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 companion paper on admissible non-injective transitions.
Jérôme Beau (Sat,) studied this question.