GATE D18
Final connected order, fixed degree-5 refuted, adaptive route
What changed
D18 first tests whether a degree-4 dual alone can close the generic branch. An exact degree-4 minorant is found, positive on the independent benchmark, but an exact map of the realizable region refutes the route. At the worst prime p=197 a real proper vector is exhibited for which every degree-4 certificate fails, the best possible degree-4 bound is exactly 0, while degree 5 recovers the exact loneliness probability 5/98. So degree 5 is the minimal information level, and the support-5 machinery is built and verified, the exact fifth connected cumulant with all ten two-plus-three partitions, its tensor Fourier identity, the exact adverse direction, and a mandatory witness control. The current subphase D18-G then tries to freeze the support-5 structured versus residual split before the analytic bound. Three natural cuts are each proved degenerate at p=197, the bounded-height modular rank saturates to full for every vector, bounded-height support-5 relations are unavoidable, and the adverse fifth-order mass is diffuse. The invariant that does separate is coherence, the tight family adds mass without cancellation while the generic residual is small only through heavy sign cancellation. The cut cleanly removes the already-handled tight family but does not reduce the residual, whose control is the full signed fifth-order Fourier sum. That signed bound was then attempted directly in D18-H and REFUTED, an exact real proper vector at p=197 drives the fixed fifth-order margin negative, and the signed inverse theorem also fails as posed. The correct object is instead the adaptive fifth-order dual, choosing the best certificate for each vector, which holds on every case tested. Proving it uniformly over every vector, including hypothetical empty-loneliness profiles, is the open frontier D18-I. LRC(13) remains open.
Evidence
Verification: double · I2 · 90 artifacts (reports, verifiers, corruption suites, manifest with SHA-256)