ZModel Discrete–Continuous Closure: Conditional Structure Theorems and Reproducible Synthetic Validation

This technical report presents a conditional discrete–continuous closure construction and reproducible synthetic validation. For a nonnegative weighted ten-cycle with positive edge weights, unit cycle product, and unit retention, the characteristic polynomial is λ¹⁰ − λ⁹ − 1, and its inverse Perron scale satisfies q¹⁰ + q = 1. An exact mapping-torus suspension preserves the section return map and principal readout. Separate local geometric and frozen input/output contracts establish conditional ten-dimensional minimality. Explicit examples distinguish periodic closure, transverse recovery, residual compensation, and non-monotone storage balance. Private hybrid-runtime tests are reported as bounded, author-maintained operational evidence; their core implementation and raw traces are not publicly reproducible. A fully executable two-state temporal-prediction supplement includes 226 trajectories, causal next-step policy selection, negative controls, memory ablation, and independent replay. The work builds on established mathematical objects and cites the prior qSR report. It does not claim assumption-free universal dimensional necessity, biological consciousness, or empirical determination of physical constants. The public release provides self-contained proofs, verification scripts, frozen configurations, synthetic evidence, and file-integrity manifests.