The Z-Model was originally formulated as a minimal structural framework in which observable regularities may emerge from the dynamics of an abstract structural operator \(Ω\), with twelve measurable implications spanning spectral asymmetries, polarization, residual noise, effective-constant drift, clock desynchronization, energy-level shifts, and numerical phase geometry. The original formulation intentionally left the nonlinear closure operator \( U(Ω)\) under-specified in order to preserve falsifiability and avoid premature over-parameterization. Here we develop a source-aligned deep-prediction version of those twelve implications. The current reconstruction introduces a candidate \(9+1\) closure geometry consisting of nine internal structural degrees of freedom and one global closure/readout degree. A controlled-swing realization, \[ J=qQ, QTQ=I, \] permits substantial internal directional change while preserving a uniform structural contraction magnitude \(q\). In a ten-dimensional closed representation this gives \[ | J|=q¹⁰. \] Under the additional, explicitly open complement-closure hypothesis \[ | J|=1-q, \] the system yields \[ q¹⁰+q-1=0, \] with the unique root \[ q_*=0.8350790427…. \] This relation is treated as a reconstruction candidate rather than a historically established component of the original Z-Model. The twelve original prediction classes are upgraded into auditable protocols by assigning each prediction a frozen observable, primary statistic, null hypothesis, explicit falsification criterion, and independent replication rule. The framework further requires dimensionless cross-domain mapping, strict separation between discovery and replication, matched null pipelines, provenance tracking, and prohibition of post-failure remapping without version change. Additional high-risk tests target the \(9+1\) dimensional structure, controlled-swing isotropy, determinant-complement closure, and the insufficiency of scalar return alone as an identity criterion. The resulting framework, designated ZDP-12 v2.0, does not claim empirical validation of the Z-Model. Its contribution is instead a sharpened transition from qualitative structural implications to a reproducible and rejectable prediction architecture in which both positive and negative results can constrain the theory.
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Bingchao Zhang (2026) studied this question.
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