Abstract

We develop a conditional operational certification framework for a finite quantum circuit with a supplied coherent Boolean oracle. The universal constant-error synthesis assertion recorded as OpenAI 283-01 is documentary only: it is neither verified nor used as a premise. For any independently specified circuit instance, we prove reference-preserving error budgets, clean-subspace composition lemmas, finite channel-certification procedures, and a transport composition theorem with explicit endpoint, arrival, and resource obligations. The full-diamond tolerance $1/2$ corresponds to half-diamond tolerance $1/4$, not $1/2$.

A uniform phase-oracle family supplies a nonempty exact pilot without establishing universal unitary synthesis. A tripartite qubit process realizes its one-qubit instance; higher-dimensional insertions are explicit carrier changes. Informationally complete destructive tests give a finite-confidence certificate, whereas a source-weight estimate, computational-basis records, or a dimension-unadjusted Bell test does not certify a general channel. We account separately for oracle calls, truth-table storage, reversible oracle realization, physical routing, test shots, and residual outputs.

We prove that sparse truth-table errors can be maximally large in diamond distance, that vanishing local errors can accumulate, and that constant-error synthesis does not by itself provide an arbitrary-precision or null-boundary limit. Serial teleportation and finite first-passage comparisons are constructed only with their additional resources declared. Cone-generation, finite-future, symmetry, regularity, and one-time-dynamics counterexamples delimit all geometric interpretations. No Lorentz-cone extraction, Einstein dynamics, physical emergence, or inherited characteristic quantum-coefficient admission is established.