Effective Perturbation Spectrum of the Theta Hopf Vacuum: A Constrained Multigrid Study

This work presents a reproducible numerical-mathematical analysis of effective linear perturbations around the frozen constrained Theta Hopf vacuum root.The twelve-coordinate variational system reduces to an eleven-dimensional active tangent space. An M-orthogonal decomposition identifies a three-dimensional quasi-zero sector and an eight-dimensional positive gapped quotient. The spectrum is tested on three grids and two independent radial compactifications.The study establishes multigrid stability, continuum estimates with declared numerical uncertainties, and positivity over a wide scan of the kinetic coefficient ratio \(c_4/c_2\). It also identifies a reproducible avoided crossing with character exchange between two modes near \(c_4/c_2=0.12991\), and derives a controlled quartic-dominated asymptotic spectrum from the generalized \(H/(2G_4)\) pencil.The package includes the manuscript in PDF and DOCX formats, machine-readable audit reports, calculation scripts, Zenodo metadata, requirements, and SHA-256 integrity checks.Scope limitation: the effective Lagrangian coefficients, their ratio, dimensional scales, physical time normalization, and particle interpretation are not derived from the frozen Theta Mother operator. The reported eigenvalues are dimensionless effective quantities and are not identified as physical masses, frequencies, photons, Maxwell modes, or gravitational degrees of freedom.