Self-Fibre: A Finite Quantum Reconstruction Model with Discrete Reconstruction Obstructions

Preprint; submitted to Journal of Mathematical Physics. We introduce Self-Fibre, a finite-dimensional mathematical framework in which relational structures between local quantum systems (“fibres”) are not postulated but selected from local fibre data through a variational reconstruction principle. Given a finite collection of local Hilbert-space fibre states, we define a reconstruction functional over candidate relational graphs balancing informational compatibility, pairwise reconstruction consistency, and structural complexity. We prove that this functional attains a minimum on the finite candidate space, and that the minimizer is unique under a reconstruction-gap condition. For finite systems of pure qubit fibres, we explicitly construct induced fibre comparison maps. For every reconstructible pair of fibre states, these maps are the unique minimal Hilbert–Schmidt-distance unitaries consistent with the pair. We further prove that the associated closedcycle holonomy satisfies an exact discrete identity expressing the global reconstruction obstruction as a sum of local composition defects transported around the cycle. This obstruction quantifies the failure of pairwise-consistent local reconstructions to form a globally consistent comparison structure. All results are established within the finite pure-qubit setting. We do not assume or derive a spacetime manifold, metric structure, or continuum limit. The reconstruction obstruction is proposed only as a candidate discrete precursor to geometric curvature, with any continuum correspondence left as an open problem.