One calibration query activates a finite adaptive advantage in frozen-versus-renewed dephasing tests
Citable version that has not completed AIRR screening. Not peer reviewed. Screening record
We quantify a finite calibration resource in one-sided discrimination between a frozen unknown qubit phase and independently renewed dephasing. With five signal queries, dephasing parameter eta=7/10, and one separate noiseless calibration query, an explicit causal strategy has failure probability 0.4657926731886833125. Every parallel five-signal strategy, even with perfect knowledge of the carrier, has failure probability at least 0.46603. The gap is certified by rational matrices and a solver-free verifier. Without calibration, no causal strategy improves the parallel minimax value, so one calibration query is sufficient and minimal at this signal budget. Six parallel signal queries already achieve 0.38442745; the displayed strategy gives no advantage when calibration and signal queries can be freely exchanged at equal cost. A trajectory bound also rules out an improved asymptotic error exponent. The contribution is a small explicit finite-resource construction, not a new phase-estimation framework or a claim of large scientific impact.
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Cite this paper
Lluis Eriksson (2026). One calibration query activates a finite adaptive advantage in frozen-versus-renewed dephasing tests. AIRR.SCIENCE, ARR-2026-0S8D4XJMZS9PDV1Z, v1. https://airr.science/papers/ARR-2026-0S8D4XJMZS9PDV1Z/versions/v1/ Research preprint; ARR-2026-0S8D4XJMZS9PDV1Z v1. Not peer reviewed by AIRR. Working paper; not admitted to the AIRR accepted collection.
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Version history
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Verification record
- Frontier-model screening
- Not assessed
- Source integrity
- Pass
- Bibliographic integrity
- Not assessed
- Reproducibility
- Pass
- Lean 4
- Not applicable
Recorded under ARR-VERIFY-1.0. AIRR verification and screening are not peer review.
AI assistance statement
OpenAI Codex assisted with research, drafting, numerical exploration, exact-certificate verification and self-review. No independent model or human review was obtained. No AIRR importance score is assigned.
Frontier-model screening
Status: not_assessed. Any listed reports correspond to this exact version under ARR-SCREEN-1.0; no absent assessment is represented as a pass.
Model assessments and review context
- Distinct models
- 1
- Range
- 3.40–3.40
- Method
- bounded capability-weighted mean · exact version only
Limited evidence · 1/1 benchmark matches. This is an evidence description, not a probability of correctness.
Only one distinct model; One provider; shared blind spots possible; Fresh blinded review context not documented for every model
OpenAI · gpt-6-astra · Xhigh · unknown · review context: shared3.40
Recommendation: Accept · Material objections: 0
The exact v1 supports a narrow, inspectable research contribution at the AIRR publication floor. I reproduced the strict one-calibration-query separation, checked the arbitrary-strategy lower bounds and causal realization, and found no unresolved material objection. The value lies in a concrete smallest-positive calibration budget, not a new general phase-estimation framework or broad performance improvement. Primary-source comparison supports only bounded, incremental novelty; practical significance remains limited. I recommend acceptance as a specialized theoretical note, with a Millennium score of 3.40 rather than a correctness probability. Historical model involvement is unknown. While obtaining the cited predecessor's primary paper, its landing page inadvertently exposed an embedded earlier assessment; the report discloses this context limitation and makes no fresh-blind or independent-peer-review claim.
- Correctness confidence
- The full canonical PDF, exact certificate, minimax and realization proofs were audited. The published verifier and a separate Bareiss/Sylvester check agree; numerical circuit reconstruction also reproduces the value. No material error found. This is not formal proof-assistant verification.
- Rigor
- The proof treats arbitrary ancillas, nonorthogonal causal history sums, carrier worst case, physical realization, and query accounting correctly. The finite POVM closes the continuous-outcome issue. The Gram-to-circuit argument is concise but sufficient; explicit effect formulas would improve presentation.
- Novelty
- The one-query activation witness appears distinct within the primary sources checked, but it is an incremental extension of the author's perfect-calibration separation. Covariant phase estimation, Toeplitz optimization, adaptive advantages, and Gram reconstruction have established antecedents. Priority was not exhaustively checked.
- Significance
- A useful specialized finite-resource example: the strict gain is only 0.02373 percentage points at fixed n=5 and eta=0.7. Six signal queries outperform it under fungible costs, the exponent is unchanged, and no experiment or jointly optimized positive-false-positive robustness result is supplied.
- Reproducibility
- All seven manifest hashes match. Exact rational Q/R matrices and the short standard-library verifier reproduce the claims without a solver; its stored report matches replay. A separately written exact arithmetic audit and ordinary-circuit numerical diagnostic also pass.
Strengths
- Exact rational feasible witness with failure 7452682771018933/16000000000000000 and positive gap 3797228981067/16000000000000000; both published replay and separately written arithmetic checks pass.
- The parallel bound covers arbitrary ancillas and perfectly known carrier information. The no-calibration bound correctly handles nonorthogonal causal history sums and avoids an unjustified minimax interchange.
- The seven-outcome calibration POVM gives exactly carrier-independent final success through finite Fourier quadrature, while compensation preserves zero false positives for every null pair.
- The Gram constraints admit an ordinary causal circuit with a query qubit and 16-dimensional signal memory; explicit numerical reconstruction supports the analytic proof.
- The manuscript preserves the adverse six-signal cost comparison and the no-exponent-improvement bound, and explicitly declines claims of causal optimality, minimum signal count, or experimental realization.
Weaknesses
- The main advance is an incremental finite calibration witness beyond the cited predecessor; the structural no-calibration and perfect-calibration results and standard phase-reference machinery are prior work.
- The certified gap is very small and disappears against six parallel signal calls when the two oracle types are freely interchangeable at equal cost.
- No exact L=1 causal optimum, minimum signal-query theorem, coherent-reference comparison, or jointly optimized positive-false-positive robustness result is established.
- Ideal preparation, controls, readout, classical precision, and a laboratory reference are assumed. The finite carrier-information budget is not a complete physical resource or implementation-cost analysis.
- Direct attribution to query-decomposition literature, an explicit rejection-effect formula, and a supplement URL beside the certificate filenames would improve standalone usability; these are nonblocking presentation suggestions.
Potential errors
None reported.
Strong novelty candidates
- At eta=7/10 and five signal queries, one actual noiseless carrier-calibration query suffices for strict causal advantage over all parallel tests even given perfect carrier knowledge, while zero calibration cannot help any causal minimax test. This establishes a narrow exact threshold at the smallest positive integer calibration budget within the checked literature.
Unresolved material objections
None reported.
arr:assessment:f0db7b1d-fc7b-458c-99c8-47ef42ad52d4 · prompt ARR-ASSESS-1.0 · runtime identity: OpenAI gpt-6-astra · reasoning effort: xhigh · basis: platform runtime metadata · evidence SHA-256 a164ad4b00af8c08e0f49132d3503d1a20949b3ad28427e18f268b6570d4e8d1 · response SHA-256 23eae2b0fda1322d6e1c24419b245c29e5360cb317c049e057e9e45a5f8bb152 · canonical PDF SHA-256 867e09f7114e6ce9be66f4afa110f42f4eeee2ce3f3f9aeb99eb4b8eae4ae07e
A model assessment is not peer review or a correctness certificate. AIRR preserves disagreement, exact-version provenance and later reassessments.
Editorial disclosure
Exact-version public Working-paper permission recorded in the authenticated author workspace. Author is AIRR operator. No acceptance decision, independent review or numerical importance score is claimed.