Quantum Continuity and Discrete Gravity at Holographic Boundaries: Four-Time Experience and the HB Cascade

The HB cascade relates four temporal readings of a common physical history: preparation, joint correlations and terminal conditioning, present gravitational readout, and history reconstruction. This preprint formulates the relation between quantum continuity and discrete gravitational records through explicit observable maps and one common-action benchmark. A prescribed Einstein–AdS3 vacuum generates a planar entropy-compatible graph from 136 interval inputs; its predictions agree with direct geometric calculations for 160 generated disconnected regions. Circle reduction of the same action retains the radius-weighted scalar and its boundary normalization. The reduced normal-mode response is shown to equal the parent angular-average correlator for every positive Euclidean separation, with G0(u) = (2 cosh²u + 1)/(16 sinh⁵u) for conformal dimension Δ = 3. Version 3.2.0 adds an executed finite, action-anchored retained-memory realization (EX05A): two independently constructed dynamical routes agree to machine precision, an operational causal break witnesses retained memory, and unused source-normalized responses are predicted without amplitude fitting. The executed finite records do not, by themselves, identify a physical five-level cascade. Illustrated edition with six figures, 48 references, and sixteen supplementary sections.