A refuted-and-vindicated pre-registration test of a spectral error model on a superconducting processor

We pre-register and test a spectral-error-mitigation prediction for the two-qubit gate fidelity of Quantum Inspire's Tuna-9 9-qubit transmon processor and execute it in four cryptographically timestamped stages. Stage 1 locks a SHA-256 hash of a three-model prediction family — spectral, \(T_1\)-only, and gate-error-only — at depths \(m \in \{0, 2, 4, 8, 16, 32, 64\}\) of H-sandwiched CZ chains on four disjoint pairs. Stage 2 measures \(m=64\) and observes a \(0.273 \to 0.682\) fidelity revival on the cleanest pair (Q0-Q1), falsifying every monotone stochastic decay at \(8\)-\(10\sigma\) in the log-domain. Stage 3 refines the model by adding a single coherent parameter, \(\delta\) (per-CZ Z-rotation phase), derives an exact even-\(m\) degeneracy \(\chi^2(\delta) = \chi^2(\pi-\delta)\) on the training set, and pre-registers three hypotheses (naive, slow-coherent \(\delta \in (0, \pi/2)\), fast-coherent \(\delta \in (\pi/2, \pi)\)) with forward predictions at the parity-sandwich \(m \in \{63, 65\}\); the cryptographic stamp is completed before the submission of jobs 743595 and 743596. Stage 4 executes the forward test: the observed fidelities at \(m = 63\) and \(m = 65\) select the fast branch on both discriminative pairs (Q0-Q1 and Q4-Q7) and refute the slow branch at \(17.6\sigma\) on a single point (Q4-Q7 at \(m=65\): predicted \(0.939\) vs observed \(0.326\)). The refined coherent-error model is vindicated with a pre-registered maximum \(\sigma\)-gap of \(1.24\) across all eight forward-test data points. The physical interpretation is that the CZ gate on Tuna-9 implements an operation close to \(\text{CZ}\cdot Z\) — a systematic \(\pi\)-over-rotation with residual \(\pi - \delta \approx 0.12\)-\(0.33\) rad per application. A follow-up second prospective test across a fresh calibration boundary (Stage 5–6, 2026-04-19; v2\_fwd, SHA-256 983503bc…, OTS 4-of-4) falsifies the single-\(\delta\) refined model at aggregate \(\chi^2/\text{ndof} = 59.6\) and promotes it to an L5 in which per-CZ coherent \(R_X(\eta)\) drive is free on every pair; under an epoch-split drift budget the generalised model (L5\('\)) passes three of four pairs on the forward set (\(\chi^2/5 \le 1.74\)), with Q3-Q6 revealed as structurally irreducible under any \(R_X \otimes R_X\) ansatz (global post-hoc best \(\chi^2/5 = 9.35\) from a multi-start Nelder-Mead search, still above the \(\le 4\) cutoff) — a pre-registered, cryptographically stamped negative result that sharpens both the refined model and the next pre-registration target. The experiment demonstrates that a single pre-registered-and-then-refined benchmark on a fully-public superconducting processor can produce a decisive test of a structured-noise error model at a cost of \(\sim 36{,}000\) shots total, a turnaround of under a day, and zero gatekeepers.