Operational Accessibility and the Emergence of Modular Time: A Conditional Reconstruction from Atemporal Quantum Information

This paper investigates whether quantum accessibility data specified without a preferred physical time can support the reconstruction of affine modular dynamics. Complete coherent CCR data identify symplectic blind directions and closed real subspaces; standardness is imposed where needed. Inclusion order alone does not determine a common affine motion. We therefore distinguish additional real-geometric hypotheses—strongly continuous reflection coherence (R) and outgoing completeness (O)—from the operational data. Reflection-geodesic integration and the outgoing real Lax–Phillips representation then provide an affine translation structure. Schober’s classification shows that this real structure admits non-Borchers quantum realizations. Under the stated outgoing-standard hypotheses, quantum reversal compatibility (Q′), requiring the canonical real reversal to be anti-symplectic, selects the Borchers-type symbol h(x)=i sgn(x)1. A nonzero orientation-aligned positive-energy sector then forms a positive standard pair and obeys the Borchers modular dilation law with its universal 2π normalization. We establish conditional rigidity and quantitative estimates and analyze conjugation-sensitive operational information. Neither R, O, nor Q′ is derived in general from the primitive accessibility data, and the physical identification of a preferred global orientation remains a separate question. The result is a conditional reconstruction relevant to time emergence, not an unconditional derivation of physical time. This manuscript was developed through an extended, author-directed research process with substantial assistance from OpenAI’s ChatGPT. AI assistance included mathematical formulation, derivation development, literature investigation, critical examination of assumptions, manuscript drafting, and editorial preparation. The author directed the conceptual investigation, evaluated its conclusions, and accepts responsibility for the submitted work. The manuscript has not undergone independent expert peer review, and its mathematical claims remain open to external verification.