Retained Records and Recoverable Interference in Discrete Phase Histories

This preprint, ISTP Paper II, examines which records must be retained to predict recoverable interference in a two-path quantum system. Identical path statistics can accompany different outcomes of a later joint or conditioned measurement. The analysis distinguishes coherent recombination, summation over unobserved quantum registers, and classical coarse graining after readout. An exact representation assigns nonnegative integer histories to eight phase addresses and implements a specified Clifford+T gate family. For a fixed later outcome, the reduced path state is sufficient over all joint preparations precisely when the measurement effect acts as the identity on the discarded register. Explicit equal-marginal examples demonstrate the consequences when this condition fails. With preparation, transport, record coupling and overall normalization held fixed, four discrete phase settings determine the complex interference coefficient, showing why cancellation at a single setting does not establish an absence of coherence. Three-register circuits compare an accessible path marker with a further environmental record: interference recovered by conditioning on the accessible marker remains limited by the residual environmental overlap. The gates and quadratic Born readout are adopted inputs. The results organize standard quantum structures into a conditional, exactly reproducible account of retained information and measurement access. They do not derive spatial propagation or individual detector events from discrete updates, and they introduce no new erasure principle or departure from quantum mechanics. The spatial screen map and displayed record ordering are explicitly illustrative. This v2.5.1 deposit includes the manuscript, Supplementary Information, editable manuscript sources, and reproducibility package v4.1.1, with exact rational and quadratic-surd data, executable verification commands, and an independent exact-coordinate verifier. CHSH is retained only as a supplementary implementation reference; photoemission is treated separately. Rights: CC BY 4.0 applies to the manuscript, Supplementary Information, and the author's original explanatory figures and tables. Software and build scripts retain their existing rights and are not covered by the manuscript license. See RIGHTS_SCOPE.md and the license notices within the accompanying archives.