MORP-04: Ancient-State Liouville Cuts, Local-Energy-Slack Rigidity, Zero-Tax Splitting, and Equality-Manifold Exclusion Audit

Ancient-State Liouville Cuts, Local-Energy-Slack Rigidity, Zero-Tax Splitting, and Equality-Manifold Exclusion Audit

Under the explicit compactness/transition assumptions, MORP-03 reduced the recurrent minimal obstruction to three normal forms: state-visible recurrent/ancient profiles, minimal equality splitting, and pure parabolically-first-order-homogeneous defect measures. This round audits: which of these equality-manifold objects are already incompatible with suitable weak Navier–Stokes structure or known Liouville theorems? The main new result: once MORP-02's strong state compactness is used correctly, the simplest "pure dissipation defect" branch is excluded by the local energy inequality — it proves the dissipation-defect measure is quantitatively dominated by the slack in the suitable weak solution's local energy inequality, so zero local energy slack forces zero dissipation defect, and a state-trivial interior limit cannot carry a nonzero pure dissipation defect. It also proves a model-cone equality theorem, imports Albritton–Barker's Type-I ancient-solution equivalence and backward-sequence L³ Liouville theorem as an external state-visible exclusion cut, and proves a zero-tax profile-support reduction theorem. The surviving equality manifold is thereby reduced to: ancient states falling outside known Liouville classes, trace/scale/spatial escape carriers, transition/recurrence residuals, or zero-tax equality splittings built only from these surviving carriers.