DRC-07: Unified Dynamic Reservoir Cover, Type-I Ancestry Recompilation, Chain-Necessity Audit, and Cycle-III Closure

Unified Dynamic Reservoir Cover, Type-I Ancestry Recompilation, Chain-Necessity Audit, and Cycle-III Closure

Cycle II ends with four reservoir/source residual classes (R_EXP, R_DISS, R_DIL, R_SRC); Cycle III absorbs, compresses, or reclassifies them one by one. After DRC-06, at the level of Type-I reservoir-mechanism classification: 𝔯_(III,res)^(Type-I,reservoir)=∅. This round asks the essential logical question: does reservoir closure imply chain necessity? The answer is: no. Compiles DRC-01 through 06 into a Type-I state-ancestry skeleton with finite final singular-center branching, concentric backward parabolic core reuse, absolute local UV stock, and a new local-core-to-global high-pass state injection. Audits the precise quantifier gap between node-by-node reservoir/source ancestry and a single compatible, traceable infinite chain. Identifies source–core ancestry (SCPB), recursive-edge compatibility (REC), and non-Type-I entry as the main chain-necessity gaps. Shows that accumulated coercive-action coverage is not a finite-obstruction theorem, since it maps a hypothetical singular point to a necessarily divergent action rather than a dynamical impossibility. Cycle III therefore concludes with reservoir classification completed on the Type-I branch; full chain necessity, finite obstruction, and Navier–Stokes regularity remain OPEN — formally handing off to NS-ANP (Cycle IV).