Boundary-Access Holonomy and the Quantum Reversible Quotient: A Finite-Distinction Framework for the Zero-Record-Holonomy Sector

Boundary-Access Holonomy and the Quantum Reversible Quotient: A Finite-Distinction Framework for the Zero-Record-Holonomy Sector introduces FDS-Q0, an upstream quantum-foundations paper in the Finite Distinction Systems (FDS) program. The central question is why reversible quantum mechanics has a symmetric distinguishability structure at all. Standard finite-dimensional quantum mechanics is usually formulated after this symmetry has already been assumed: states live in complex projective Hilbert space, reversible dynamics is unitary, and distinguishability is symmetric inside the closed-system formalism. Q0 asks what finite boundary-access conditions make such a reversible symmetric sector available. The proposal is that standard Hilbert-space quantum mechanics is located as the zero-holonomy reversible quotient of a more primitive asymmetric finite-boundary access dynamics. A physical distinction is first directed, boundary-relative, capacity-limited, and record-sensitive: a system may export, preserve, erase, or recover a distinction differently across different boundaries. The central object is the boundary-access holonomy H∂, an operational obstruction to closing a directed access loop through system, apparatus, environment, record, and recovery channels. Q0 defines finite boundary-access systems, operational directed access, access asymmetry, boundary-access holonomy, and three holonomy sectors: coherent holonomy, record holonomy, and leakage holonomy. It gives a restricted access-category theorem showing that zero record holonomy makes the reversible quotient well-defined; in the restricted quantum-access category, the recovered-state kernel is symmetric. The paper explicitly does not claim to derive the full Hilbert reconstruction, the Born rule, objective collapse, hidden variables, quantum field theory, or all of quantum mechanics. The paper also supplies two minimal operational normal forms. First, a Mach-Zehnder stable-record model separates ordinary coherence overlap from stable accessible record holonomy, predicting that recoverable visibility can split at fixed overlap when stable record accessibility differs. Second, a QEC directed-leakage model treats leakage from the computational subspace as directed leakage into uncorrectable boundary sectors, predicting that logical failure can split at matched physical error when uncorrectable leakage differs. The compressed thesis is: H∂ = 0 ⇒ reversible Hilbert sector,H∂ ≠ 0 ⇒ record, decoherence, measurement, and maintenance sectors. Q0 supplies an upstream quantum-access layer for the FDS quantum sequence. Its immediate scientific task is to make boundary-access holonomy a calculable and testable quantity. Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory