ANP-01: Source–Core Provenance, Adjoint Causal Tubes, Scale-Resolved Vorticity Renewal, and the C2→C3 Gap

Source–Core Provenance, Adjoint Causal Tubes, Scale-Resolved Vorticity Renewal, and the C2→C3 Gap

ANP-00 defines a proven recursive causal-ancestry edge as a C3 edge: forward PDE contribution plus same-branch ancestry plus recursive parent-node legality. The Type-I DRC architecture already provides a late-time singular-core state, an absolute local UV lower bound, a global high-pass state, and node-by-node global source ancestry. The open question: can source ancestry connect to the late-time singular core itself? This round instead uses the pressure-free vorticity equation with a terminal core-anchored adjoint cutoff, rather than directly localizing the pressure-bearing strain equation, and proves the first rigorous ancestry bridge — an exact weighted forward causal-ancestry identity. Under the Type-I weak-L³ bound, the adjoint footprint carries conserved mass, core-scale high-influence volume, and its center of mass stays within O_M(R) of the singular center over one parabolic time — so output-local source–core ancestry is proven in the weighted adjoint sense. Geometric parent-source localization, suppression of diffuse low-influence source contributions, and recursive reuse of the selected parent node remain open problems.