Theorem: IX-C-ST stage release

Relative to the shared inputs, Part I constructs both admitted first stages, their fixed-support continuity, the one-edge outputs, and exact descent, scalar, and coherence criteria. With Section sec:operational, it forms a local Grade S criteria package.

At this stage neither sharp second multiplication is constructed. Its factorization release is Unresolved, not a universal obstruction.

Proof. The claims are Theorem thm:first, Propositions prop:firstcontinuity, prop:oneedges, prop:placementcount, and the criteria of this section. The common operational layer does not use an unconstructed product. The graph products and relation-kernel discharges needed for a second multiplication have not been used in Part I.