MORP-03: Normalized Return Transitions, Profile Carrier Saturation, Ancient/Defect Normal Forms, and Rigidity Entry

Normalized Return Transitions, Profile Carrier Saturation, Ancient/Defect Normal Forms, and Rigidity Entry

MORP-01 proved "minimality ⟹ zero strict transition tax"; MORP-02 largely closed general local-state/active-pressure compactness, building the defect-completed packet topology. What remains is dynamical: what is the actual, correct Navier–Stokes transition acting on the minimal obstruction packet? A fixed-time-step invariance condition is too strong — a truly dangerous trajectory might temporarily exhaust itself and then re-root. The correct object is the return transition on native separated windows. Replacing the over-strong fixed-step transition invariance with this, it proves that a minimal recurrent obstruction has zero net return exhaustion and stays within the minimal level set; it defines a homogeneous native carrier/cost ratio and proves a minimal-profile splitting saturation theorem (under additive profile-carrier and cost decoupling, each nonzero component of a minimizing split must itself be a minimizer — a strictly positive splitting tax therefore excludes multi-profile minimizers); it gives a conditional state-visible Type-I route to a nontrivial bounded mild ancient solution; for a pure-defect minimizer, it computes the exact Navier–Stokes scaling of the dissipation-defect measure, proving that a return-fixed pure-scale defect is parabolically first-order homogeneous — and therefore cannot be a point atom at the singular center.