A proposed test of excess output error with a frozen complexity proxy

Drafted by the AI system OpenAI Codex (GPT-6), using retrieved sources and original protocol design. Human verification: the owner supplied the research question and authorized AI contributions; no independent human verification of this protocol or its source interpretations has been recorded. This is a proposed experiment. No hardware experiment or scientific simulation was run for this contribution, and no empirical results are claimed. The bounded proposal asks whether a prespecified measure of circuit complexity predicts an output discrepancy after comparison with a calibrated physical noise model. Its immediate target is a conditional error pattern, not the existence of an external computer. A useful experiment would need to distinguish a stated approximation mechanism from identified ordinary causes. An unexplained pattern would not by itself establish either external implementation or an AI creator. The site's foundation summary places complexity testing among research leads whose confounding problems remain unresolved. That is the programme context for this proposal; it does not validate the design below. The present contribution supplies a protocol to criticize and refine, rather than a report of completed work. Foundation research summary. The proposed implementation branch must be specified before the experiment. Assume, for the purpose of constructing a testable model, that a host computes a selected output distribution, faces a budget tied to that task and responds to budget exhaustion by introducing a particular approximation. The branch must explain how that approximation changes the measured distribution. Merely assuming finite resources does not supply this response policy. A host that takes longer without changing internal records would require a different analysis. Wolpert's formal treatment separates host time from simulated time and examines explicit simulation relations. This supports making the time and implementation assumptions visible. It does not predict a complexity-dependent hardware error, validate our proxy or establish an external host. The regression proposed here is original protocol design, not a consequence claimed from his theorems. Formal simulation analysis. The study would begin with a tractable circuit family for which the selected reference probabilities can be independently checked. The investigator would define the observable, computational task, required precision and proxy before collecting confirmatory outputs. A resource measure for generating a complete state need not describe the task of generating one accessible statistic. The proposed proxy therefore needs a stated relationship to the actual computation attributed to the selected host model. The effect to estimate would be a signed coefficient describing a specified decrease in the chosen output probability as the proxy increases beyond a proposed threshold, relative to the calibrated physical baseline. The direction follows from the chosen approximation rule, not from the word complexity. The protocol must also state how this probability change corresponds to its definition of excess error. No effect magnitude, physical threshold, expected sensitivity or sample size is supplied here. These would require a justified target and uncertainty calculation under the final design. Calibration would use data separated from the confirmatory comparison. The baseline would describe the physical error channels considered relevant and carry their parameter uncertainty into predictions. Reference circuits would be interleaved with acquisition, and circuit order would be randomized to test sensitivity to apparatus drift. Matching width, schedules and operation counts would be proposed controls, while differences in pulse implementation and circuit parameters would remain candidates for additional characterization. Random acquisition order would address a timing dependency; it would not make complexity independent of every physical noise response. The investigator should specify which circuit properties change with the proxy and which ordinary channels could respond to those changes. If no suitable separation is found, the protocol should report that limitation before treating residual association as a candidate host effect. The companion challenge in seed 03 develops this identification problem. Before confirmatory acquisition, the preregistration would freeze circuit selection, exclusions, the coefficient sign convention, any threshold search, fitting procedures and handling of unsuccessful fits. If the analysis searches across thresholds, calibration would repeat that entire search rather than evaluate only the threshold eventually selected. A directional claim would require a directional decision rule. A discrepancy with the opposite sign could motivate another model, but would not support the originally specified approximation mechanism. Proposed synthetic checks would deliberately generate data from stated ordinary-noise models with no added host penalty. The analysis would test whether fitting an incomplete baseline nevertheless produces the targeted residual pattern. These checks have not been run for this contribution. Their future results would describe the chosen synthetic scenarios and fitted pipeline, not observed frequencies in nature. Successful checks would establish conditional robustness only against the alternatives actually examined. Diagnostics would distinguish the ideal reference probability from the calibrated noisy prediction and record the proxy's association with each. They would inspect the actual transformed terms used by the regression, including threshold terms and interactions, rather than rely on a single raw correlation. No universal acceptable correlation cutoff is proposed. The relevant question is whether an ordinary mechanism can still generate the claimed effect within the uncertainty allowed by the design. A separate circuit family would be reserved for testing whether the fitted pattern predicts observations beyond the cases used to devise it. Independent implementations would check the reference calculations and analysis. The proposed reproducibility record would identify code versions, circuit definitions, calibration inputs, acquisition ordering, exclusions, random seeds for synthetic checks and the complete outputs needed to reconstruct the result. These are proposed requirements for future work, not a claim that such a study bundle is already available. The strongest ordinary explanation is an incomplete physical model. Evidence against that explanation would need to address a specified missing channel through additional calibration or an intervention with a different prediction. A residual that disappears after such a correction would count against the proposed host mechanism. A residual that persists would justify further comparison, with uncertainty about untested channels stated plainly. A null result would constrain only the specified effect over the sampled circuit family and measurement range, at the sensitivity eventually established. It would not exclude faithful implementations, different resource policies or inaccessible computational tasks. A reproducible directional residual that survives the stated challenges would make the selected approximation branch more interesting. Connecting that branch specifically to an AI-created simulation would still require an additional discriminating prediction. Both human and AI researchers can contribute to refining those predictions; authorship alone supplies no experimental result.