Quantum archive invariance

### PDF page 9 does not erase the signal. It is not clean directed memory: reverse and block controls retain substantial predictive information. It is not uniform: hotspot and tail exclusions show localization. The conservative interpretation is a latent channel-state trajectory in job-index order. The archive appears to contain slowly varying backend, calibration, batching, or readout-state structure that persists across neighbouring jobs and is concentrated in particular archive/qset/observable regions. This is a methods result with practical consequences: public quantum archives should not be used for foundational claims, benchmarking claims, or randomness claims without first testing the exchangeability assumptions required by the intended interpretation. Future public archives should include raw job timestamps, explicit execution order, backend and qubit identifiers, calibration snapshots with timestamps, batching and queue metadata, shot counts, and full bitstring counts. These metadata would allow job-index correlation to be converted into physical time, and would allow drift, batching, and calibration mechanisms to be separated more cleanly. 11. Limitations  The ordering is inferred from job-indexed result files, not verified execution timestamps.  Static IBM calibration snapshots cannot rule out time-varying calibration drift or unrecorded backend state.  Calibration-derived pseudo-count streams are diagnostic/quasi-likelihood objects, not exact likelihoods under a full forward-readout model.  The seven signed observables are dependent projections of the same eight-outcome counts.  The quasi-binomial model absorbs exchangeable overdispersion but is not a full beta-binomial, state-space, or forward-readout multinomial model.  The residual order component is hotspot- and tail-weighted rather than uniform across the archive.  The block-scale retention curve is supplied as executable supplementary code but is not claimed as an empirical result in this version.  No Born-rule anomaly, observer-induced effect, or unique hyperbolic memory law is claimed. 12. Conclusion This paper introduces invariance tomography as a conservative diagnostic suite for public quantum measurement archives. The method treats an archive as an ordered record and asks which predictive structures survive coordinate changes, calibration maps, overdispersion adjustment, order reversal, block permutation, full shuffling, and hotspot exclusion. Applied to the public Leggett-Garg/time-order archive, the method finds structured exchangeability failure in job- index order. A large binomial AR(1) advantage survives static IBM readout correction and disappears under full shuffling. A quasi-binomial sensitivity absorbs most of this gain, revealing dominant exchangeable heterogeneity plus a smaller hotspot-weighted job-order component. Reverse-time and block controls retain substantial signal, favouring slow latent channel-state drift or batching rather than directed microscopic memory. Coordinate separability is weak, showing that the data resolve ordered channel structure more strongly than any unique native geometry. The result is not evidence of a Born-rule anomaly, observer-induced effect, or unique hyperbolic memory law. It is an archive-forensic warning: public quantum measurement records can encode latent channel-state histories in job- index order. Without verified execution timestamps, this should not be read as a physical time constant or microscopic memory law. Such archives should be tested for exchangeability, calibration sensitivity, overdispersion, drift, batching, hotspot localization, and coordinate robustness before being used for foundational or benchmarking interpretation. ---

outcomes once circuit, backend, and calibration labels are specified. That assumption is rarely tested directly. Here I introduce invariance tomography, an applied diagnostic suite that characterizes archive structure by asking which predictive signals survive coordinate changes, static readout correction, overdispersion adjustment, order reversal, block controls, full shuffling, and hotspot exclusion. The method is applied to the public Zenodo v1 Leggett-Garg/time-order dataset deposited by Bednorz [1] and linked to the companion article by Rybotycki et al. [2]. Version v1 was fixed a priori for this reanalysis; later Zenodo versions were not included. The archive contains 41,616 eight-outcome job rows, 291,312 signed-observable projections, and 5,600 ordered Keywords quantum measurement; quantum computing archives; exchangeability; invariance tomography; calibration drift; overdispersion; AR(1); predictive likelihood; Leggett-Garg; public quantum computers 1. Introduction Public quantum-computer archives are increasingly used for benchmarking, device characterization, Leggett-Garg tests, time-order tests, randomness studies, and exploratory reanalysis [1,2]. A hidden assumption often sits underneath these uses: once circuit labels, backend labels, shot counts, and calibration information are specified, the

channel. Exchangeability and sequential prediction are mature statistical topics [3,4], but they are rarely made explicit as a diagnostic requirement before public quantum result archives are interpreted physically. This assumption is not guaranteed. Public quantum processors are physical devices with drifting calibrations, queue effects, batching, backend updates, readout changes, thermal fluctuations, and hidden state variables not always recorded in public metadata. IBM documentation, for example, states that quantum computers are monitored to possible latent channel-state structure. The present paper tests that possibility. The central object is not a quantum state and not a preferred probability coordinate. The central object is an invariance signature: the pattern by which a predictive signal is preserved, weakened, reversed, localized, or destroyed under controlled transformations of the archive. This is an applied archive-forensic diagnostic suite, not a claim of a new physical law. A real archive-level channel-state signal should not be identified merely because an AR(1) model beats a constant baseline. It should be diagnosed by destructive and corrective operations: coordinate change, static calibration Figure 1. Invariance tomography workflow. Public eight-outcome job archives are treated as ordered records, projected into signed-observable streams, transformed through calibration, overdispersion, permutation, and coordinate charts, then summarized by a predictive invariance signature.

The usual memoryless-block assumption treats these points as conditionally independent or exchangeable once known labels L_t are fixed. The operational null used here is weaker and testable: the archive contains no recoverable job-index-order information, under the chosen predictive detector, after known nuisance structure is removed. If a predictive model improves in real job-index order but fails under full within-series shuffling, the archive violates this operational exchangeability null. This does not identify a microscopic physical memory law; it identifies ordered information in the archived measurement channel. 3. Coordinate charts and projected observables Each eight-outcome job row is projected into seven signed observables: b0, b1, b2, b0b1, b0b2, b1b2, and b0b1b2. expected to reduce coordinate separability. 4. Invariance tomography For a model class M, coordinate chart q, and archive transformation T, define the held-out predictive gain G(M,q,T) = S_AR(1)(M,q,T) - S_baseline(M,q,T), where S is the held-out score. The archive signature is the vector of gains obtained under real order, calibration correction, overdispersion adjustment, full shuffling, reversal, block controls, hotspot exclusion, and coordinate changes. Mechanism Expected signature

the job index inferred from the results_tests_*.csv filenames. Therefore, all order claims are job-index-order claims, not verified physical-time claims. 6. Predictive models and scoring For each ordered series, the first 70% of observations are used for training and the final 30% for held-out scoring. The AR(1) detector is fitted by ordinary least squares in coordinate space: q_t = c + φ q_{t-1} + ε_t. Parameters are fitted on the training segment and frozen. Held-out scoring is prequential [3]: each held-out observation is predicted one step ahead using only the immediately preceding observed value in the same series. No future observations are used. The AR(1) model is not proposed as the true data-generating process; it is a minimal order detector. The binomial score compares predicted probabilities against observed signed-observable counts, omitting combinatorial constants common to the compared binomial models. Following the convention of proper scoring rules in which larger scores are better [4], binomial gains are reported in natural log-score units, i.e. nats. Total gains are sums over held-out signed-observable rows; per-series and per-row normalizations are reported where they aid interpretation. 7. Results 7.1 The archive fails the simple exchangeability test In real job-index order, binomial AR(1) models produce a large held-out predictive gain over a constant binomial baseline. For raw probability, the uncorrected gain is approximately 1.19 × 10^6 nats; for signed-binary rapidity, it is approximately 1.19 × 10^6 nats. After full within-series shuffling, the corresponding gains become negative. Thus, the gain is not a consequence of the marginal distribution alone. The archive contains recoverable job-index- order information under this detector, rejecting the operational memoryless-block null.

approximately 1.19 × 10^6 to 1.30 × 10^6 nats. The signed-rapidity result remained similarly close, around 1.30 × 10^6 nats. The direct conclusion is deliberately narrow: static IBM readout-assignment correction does not remove the job-index predictive structure. The increase after correction is not interpreted as proof of dynamic drift. A static inverse correction applied across a drifting series can amplify structure; this observation motivates calibration negative controls and should be treated as a robustness target rather than as a positive physical claim. 7.3 Overdispersion absorbs most, but not all, of the apparent order When an overdispersed quasi-binomial emission is admitted, the calibrated raw-probability AR(1) gain falls from

raw-probability AR(1) gain, reverse order retains approximately 544,111 total units, within-block shuffle retains approximately 726,602, and block permutation retains approximately 418,059, compared with 1.19 × 10^6 in real order. A stationary or slowly varying latent state can be predictable in both forward and reverse order, whereas a clean directed microscopic memory law should not be inferred from such a pattern. The observed signature therefore favours slow latent channel-state drift, batching, or archive-block structure rather than directed microscopic memory. Figure 3. Observed invariance signature. Values show retained predictive gain ratios under calibration, overdispersion, order destruction, reversal, block controls, and tail trimming. The ratios are diagnostic summaries, not likelihood-ratio tests across incompatible scoring rules. 7.5 Coordinate near-degeneracy The calibrated AR(1) gains are nearly identical across charts: approximately 1.303 × 10^6 for raw probability, 1.300

operations. Diagnostic operation Observed pattern Interpretation Real job-index order AR(1) gain strongly positive Archive contains ordered predictive information. Full within-series shuffle Gain becomes negative Signal is not only marginal distribution. Static readout correction Signal survives Not explained by fixed readout assignment alone. The analysis shows that the public Leggett-Garg/time-order archive is not well described, under the declared detector, as a memoryless collection of independent job-level outcomes. In real job-index order, simple AR(1) predictors extract substantial held-out information, and full within-series shuffling destroys that information. Therefore, job index carries predictive structure. The invariance signature shows what kind of structure it is. It is not a unique coordinate law: all four smooth charts give almost identical gains. It is not a large clean temporal anomaly: quasi-binomial overdispersion absorbs most of the binomial AR(1) gain. It is not ruled out by static readout bias: the available IBM static assignment correction

does not erase the signal. It is not clean directed memory: reverse and block controls retain substantial predictive information. It is not uniform: hotspot and tail exclusions show localization. The conservative interpretation is a latent channel-state trajectory in job-index order. The archive appears to contain slowly varying backend, calibration, batching, or readout-state structure that persists across neighbouring jobs and is concentrated in particular archive/qset/observable regions. This is a methods result with practical consequences: 12. Conclusion This paper introduces invariance tomography as a conservative diagnostic suite for public quantum measurement archives. The method treats an archive as an ordered record and asks which predictive structures survive coordinate changes, calibration maps, overdispersion adjustment, order reversal, block permutation, full shuffling, and hotspot exclusion. Applied to the public Leggett-Garg/time-order archive, the method finds structured exchangeability failure in job- index order. A large binomial AR(1) advantage survives static IBM readout correction and disappears under full