Abstract

We formulate a delayed random-access experiment in which two fresh uniform bits are encoded before an independent query specifies which bit must be returned. The complete input-dependent classical state accessible at decoding is restricted to two values. We independently prove the established sharp classical success bound of three quarters, allowing stochastic encoding, delay dynamics, decoding, and input-independent shared randomness. The standard one-qubit code attains $1/2+1/(2\sqrt{2})$. An explicit sequential encoding uses only the current input bit and the qubit. We prove the optimal qubit bound for arbitrary binary measurements and derive exact depolarizing-delay formulas. Failure and erasure records receive neutral scores and remain in the attempted-run law. Complete-law and reference-stable implementation allowances give a robust separation from an enlarged classical null. A one-sided finite-sample rejection certificate is proved, including a history-conditional extension permitting across-run memory under a fresh current-run bottleneck. The general finite-state classical optimum is expressed as a Hamming quantization problem, with an explicit covering upper certificate and exhaustive-verification specifications. A separate classical-environment null is defined for an already quantum carrier. A Markovian qubit can violate the wholly classical bound, while a persistent classical register can create causal-break history dependence. Accordingly, the present witness does not certify quantum environmental memory. The contribution is the sequential specification, complete resource accounting, robustness ledger, and statistical assembly, not discovery of the random-access-code benchmark. No experiment, biological correspondence, asymptotic computational advantage, spacetime emergence, or inherited field-theoretic admission is asserted.