Effective Perturbation Spectrum of the Theta Hopf Vacuum: Nonlinear Modal Dynamics and Certified Operational Windows

This version extends the reproducible constrained-multigrid perturbation study of the frozen Theta Hopf vacuum with a post-publication nonlinear twelve-mode effective model. It freezes the complete cubic tensor and a trajectory-controlled symmetric quartic truncation containing 102 unique components.Finite-protocol numerical audits locate the pure-data operational boundary in the interval [0.0274375, 0.027625), the boundary robust to a 0.1% mode-11 displacement in [0.0255, 0.026), and a multidirectional safe amplitude of 0.0255 across six phase and velocity probes. The resulting nonlinear effective-dynamics checkpoint is frozen as THETA-OR14-ED-3397.The accompanying package includes the revised manuscript in PDF and DOCX formats, machine-readable audit records, the frozen numerical payload, reproducibility scripts, Zenodo metadata, SHA-256 manifests, and an automatic integrity checker.Scope limitation: these amplitudes are dimensionless modal coordinates obtained within a finite twelve-mode truncation and finite-duration numerical protocols. The 102-component quartic tensor is trajectory-controlled and is not the complete 1,365-component symmetric quartic tensor. The results do not establish an analytic convergence radius, global nonlinear stability, a physical scale, particle identity, Maxwell dynamics, Lorentzian geometry, or gravitational dynamics derived from the frozen Theta Mother operator.