Abstract

We study destructive computational-basis readout under a finite live-qubit budget and a separately specified grammar of consumable geometric resources. The operational assumptions and their capacity restrictions are stated explicitly; results about the specified Born semantics are not imported into an unknown measurement strategy. Identified latent links and active edges give cut-indexed monotones, a bound on cross-cut activations, and decreasing potential reachability. A geometric diamond is proved for read–write independent, guard-stable updates, rather than inferred from quantum-name disjointness alone. For a precisely delimited decohered fine-graining certificate, reduced integer multiplicities give the exact register cost

This cost is not the unrestricted forcing threshold: the registered three-qubit permutation-symmetric witness already anchors $(1/3,2/3)$ at capacity three. Fine-graining and symmetry certificates yield finite rational nets and continuity-controlled approximation bounds wherever the requisite records fit. The principal new conditional result is exact Born readout on every sub-capacity input, at every capacity $N\ge 3$, when positive-branch residuals have the projective computational diagonal on those inputs. Its proof derives a cocycle on an explicit open domain and solves the resulting functional equation. Global diagonal faithfulness additionally removes the full-capacity boundary freedom in outcome laws. Unrestricted finite-capacity uniqueness remains open; finite partial slack models are not admissible counterexamples. A compactness theorem is proved under an additional uniform regularity assumption on selective outputs, without claiming an LP formulation or a computable convergence rate. A separate one-shot instrument ledger distinguishes coherent environment size from adaptive peak occupancy. A standalone computational appendix supplies exact arithmetic regressions and sampled diagnostics, not certificates of universally quantified statements.