Canonical Trace Selection and No-Go Theorems for Unique Quantum Dynamics in Typed 3+2 Gauge Geometry: Exact Audit and Reproducibility Archive

This record contains the exact audit and reproducibility archive supporting the manuscript “Canonical Trace Selection and No-Go Theorems for Unique Quantum Dynamics in Typed 3+2 Gauge Geometry.” It consolidates three preregistered stages of the QDL Predictive-Dynamics Completion Program: QDL-PD-I, which classifies invariant gauge metrics and local, spectral, and determinant action candidates; QDL-PD-I-B, which derives the canonical closure-neutral tracial state and audits the dynamical limitations of central closure data; and QDL-PD-I-C, which classifies Hodge-Dirac, spin, complex-structure, line-bundle, finite-operator, superconnection, and flavor alternatives. The positive results establish that closure neutrality uniquely selects the normalized Hilbert trace tau_* = Tr_5/5 on M_3(C) direct sum M_2(C). Equal atomic weight, maximum entropy, and restriction of the ambient normalized trace independently select the same state. The inherited closure-lattice metric also determines the de Rham Hodge-Dirac differential calculus d + d* on the closure four-torus up to one overall length scale. The no-go results establish that the frozen typed 3+2 data do not uniquely determine a complete positive quantum action, a physical noncentral finite operator, a regulator and finite-counterterm prescription, a Higgs potential, a nonzero type-(1,3) horizontal vacuum, or numerical flavor coefficients and phases. Fully gauge-invariant finite operators are central; noncentral block-mixing alternatives either break the typed gauge symmetry or retain continuous singular-value moduli; the untwisted Hodge index is zero; and spin structures, compatible complex structures, line-bundle twists, Yukawa matrices, and physical phases remain nonunique. The archive includes formal reports, LaTeX sources, exact symbolic Python audits, regression tests, machine-readable classifications and verdicts, consolidated execution records, reproduction instructions, and SHA-256 checksums. The bundled execution wrapper reruns all three audits and 23 regression tests using open-source software. This record is derived from the earlier QDL Structural-to-Dynamical Completion Program evidence archive, DOI 10.5281/zenodo.21311773.