Revision and proof-obligation ledger

The changes from the preceding draft are substantive.

• Stable inheritance. Registered I labels replace drifting internal numbers as the primary source locators. The characterization remains restricted to its declared strategy class.

• Three-qubit symmetry retained. The four-qubit fine-graining optimum is no longer identified with unrestricted forcing of $(1/3,2/3)$. The registered three-qubit certificate is included and proved.

• Primitive rational representation. The register formula and code reduce multiplicities by their greatest common divisor. Zero outcomes are handled separately.

• Correct reduced-state calculation. The cocycle witness has specified reduced-state diagonals, not generally diagonal reduced states.

• Correct capacity bookkeeping. General one-qubit record comparisons use $n+1\le N$. Only the scalar witnesses have the fixed three-qubit bound.

• Faithfulness scope separated. Sub-capacity faithfulness gives the headroom theorem. Global faithfulness additionally gives full-capacity outcome rigidity. Neither condition is silently equated with the full record requirement.

• Geometric identity counts. Active edges retain identifiers, including parallel edges. Activation then really preserves the scalar and crossing-link counts.

• Ownership and read dependencies. Quantum-name disjointness no longer implies disjoint geometric frames. Read footprints and guard stability are explicit.

• Acyclicity enforced. An activation that creates a directed cycle is refused before constructing the new geometry.

• Occupied slots protected. Permanent capacity retirement requires a free unit. Measurement removes names, not their regions.

• No-signaling observations delimited. Incident link status is not declared literally invisible. Private observations, shared status, enablement, and communication are distinguished.

• Fixed-library restriction. Downward closure is proved for a fixed experimental library. No unproved closure under newly enabled graph-dependent operations is claimed.

• Boundary approximation withdrawn. The mesh bound is not used to identify an unknown residual with the original state's Lüders conditional. Unsupported support-graph classification and state-uniform boundary constants are removed.

• Compactness repaired. Selective-output regularity is added explicitly to the compactness theorem. Finite constraints are not called a finite LP, and compactness is not called effective computability.

• Partial slack honestly labelled. An exact partial compensation replaces the asserted all-state level-one witness. Its extension to all required experiments remains an open obligation.

• One-shot and adaptive instruments separated. The one-shot environment lower bound is proved in its own model. An adaptive counterexample excludes the former prefix Choi-rank claim about instantaneous quantum memory.