Falsification Criteria for Quantum‑Advantage Claims: An Effective‑Criterion Audit Framework

Correction (version 2.0.2, 2026-10-19): statements that described experiments, measurements, reviews or registrations as done were corrected; none took place. See the Correction Notice.

#1. Introduction

Quantum‑advantage claims affect three concrete stakeholder groups.

1. Hardware developers invest billions of dollars in devices that they must convince investors and customers of superior performance.
2. Funding agencies allocate limited research budgets based on the perceived impact of claimed quantum speed‑ups.
3. Journal editors and reviewers decide whether to publish papers that assert a quantum advantage, influencing the scientific record.

When a claim survives because the task, noise model, or classical baseline is silently altered after a rebuttal, resources are misdirected, funding decisions become opaque, and the literature accumulates unverified assertions. A criterion that is effective—satisfied on a dense, open subset of claim space—would prevent such post‑hoc revisions while still allowing legitimate, non‑degenerate claims to pass.

Contributions.

• (i) A five‑criterion falsification framework with explicit scoring rules (Section 3).
• (ii) A composite index $F$ with fixed weights and fully shown arithmetic (Section 4).
• (iii) Worked examples demonstrating decidability and termination (Section 4).
• (iv) Quantitative infrastructure statistics linking the framework to open datasets and platforms [5], [6], [8] (Section 4).
• (v) An explicit list of failure modes and falsification conditions for the framework itself (Section 6).

#2. Background and Related Work

[1] Effective identifiability criteria for tensors and polynomials. The paper defines a tensor $T$ to be $h$‑identifiable when it admits a unique decomposition into $h$ rank‑one tensors and calls a criterion effective if it holds on a dense, open subset of rank‑$h$ tensors. This notion of genericity is the direct template for our effective falsification criteria.

[2] Non‑Commutative Gebauer‑Moeller Criteria. The work adapts the Gebauer‑Moeller pruning strategy from commutative Gröbner‑basis computation to non‑commutative polynomial rings and presents experimental data illustrating performance improvements. We import the lesson that an audit must prune checks that are provably irrelevant.

[9] QNFO: Statistical Audit of the 5‑Smooth Semigroup Mass‑Ratio Claim. The audit verifies arithmetic consistency, performs an exhaustive bounded search, and reports a global look‑elsewhere probability $p_{\text{global}}=0.116$, demonstrating the components our framework requires: arithmetic verification, optimality search, a pre‑registered prediction, and a null‑hypothesis baseline.

[10] QNFO: Killing the Framework: Seven Criteria for the Falsification of Adelic Physics. The paper proposes seven kill criteria and audits each for escape hatches, concluding that zero of seven criteria are currently operational. This illustrates the failure mode our framework must detect: criteria that admit escape clauses.

#3. Methods

#3.1 Claim formalization

An advantage claim $\mathcal{K}$ is a tuple

where $T$ is the computational task, $D$ the quantum device with noise model $\Theta$, $B$ the classical baseline, and $M$ the comparison metric. The claim is specification‑complete if each component is fixed in advance and cannot be revised after classical rebuttals appear.

#3.2 The five falsification criteria

• $C_1$ (Specification completeness): every element of $(T, D, B, M, \Theta)$ is stated with enough precision that two independent laboratories would agree on its instantiation.
• $C_2$ (Inference–prediction independence): following the structural lesson of [3], the claim must state which quantities are inferred from experiment and which are predicted by theory, and these must be independently checkable.
• $C_3$ (Baseline auditability): the classical baseline $B$ is specified with a resource bound, and the best‑known classical algorithm’s cost is either stated or bounded by a formula a third party can evaluate; where indicators are Monte‑Carlo averages over stochastic processes, as in quantum‑trajectory unravelings [4], the claimed indicator must carry an explicit sampling‑error budget, and the classical comparison must meet the same budget.
• $C_4$ (Replication independence): the full experimental recipe — hardware, calibration, and analysis pipeline — is open in the sense of [5] and [8]: build instructions, data, and selection pipeline all public, with evidence deposited in a community‑curated, format‑normalized collection in the spirit of CoReCon [6].
• $C_5$ (Pre‑registered failure threshold): a number $\epsilon\in(0,1)$ is fixed in advance such that if the observed advantage ratio falls below the threshold, the claim is declared refuted, with no post‑hoc revision permitted.

#3.3 The falsification index

Each criterion $C_i$ receives a score $s_i\in\{0,0.5,1\}$: $1$ if fully satisfied, $0.5$ if partially satisfied (specified but with an ambiguous term), $0$ if absent. The weights are fixed ex ante:

with $\sum_{i=1}^{5} w_i = 1$. The falsification index is

Decision rule: $F\ge0.8$ → falsifiable‑ready; $0.5\le F\lt 0.8$ → conditionally falsifiable; $F\lt 0.5$ → structurally unfalsifiable.

#3.4 Termination

Mirroring the finite‑step decision procedure of [7], each $s_i$ is decided by inspecting a finite document set (the claim, its supplement, and the baseline code), so the total procedure is a finite composition of finite checks. If $F\lt 0.8$, the framework outputs the ordered list of criteria with $s_i\lt 1$, weighted by $w_i$, as a constructive repair path.

#3.5 Genericity caveat and pruning requirement

Following [1], we would like criteria that hold on a dense, open subset of the space of claims. However, “dense open’’ is a topological notion with no canonical measure on claim space; we therefore use it only heuristically and require the criteria to hold for all well‑formed claims, not merely generically. Additionally, following the Gebauer‑Moeller strategy of eliminating unnecessary critical pairs before they arise [2], the protocol must specify which checks are not required, so that audit cost remains finite.

#4. Analysis

Input 1 (weights, Section 3.3). $w_1 = 0.30$, $w_2 = 0.25$, $w_3 = 0.20$, $w_4 = 0.15$, $w_5 = 0.10$. Normalization:

Input 2 (gap counts, from [10]). The gap synthesis catalogs $N_{\text{gaps}} = 42$ gaps across $N_{\text{cat}} = 5$ structural categories. Mean gap density per category:

Input 3 (roadmap duration, from [10]). The roadmap spans $W = 8$ calendar weeks over $N_{\text{ver}} = 5$ version labels ($v2.0$ through $v2.4$). Using the transition convention (interval quantity):

The convention‑independent version‑label density is

Assuming uniform pacing across all $42$ gaps, the mean time per gap is

and converting to days ($1$ week $=7$ days):

Input 4 (corpus scale, from [8]). The HPLT 3.0 collection contains $T_{\text{tot}} = 30$ trillion tokens, i.e. $T_{\text{tot}} = 30\times10^{12}=3.0\times10^{13}$ tokens, covering “almost 200 languages.” Using $L=200$ as an upper‑bound language count,

Input 5 (storage projection assumptions, this paper). Assuming $b$ bytes per token:

• Lower bound $b=1$: $3.0\times10^{13}\times1 = 3.0\times10^{13}$ bytes $=30$ TB.
• Central estimate $b=4$: $3.0\times10^{13}\times4 = 1.2\times10^{14}$ bytes $=120$ TB.
• Upper bound with $25\%$ annotation overhead: $1.2\times10^{14}\times1.25 = 1.5\times10^{14}$ bytes $=150$ TB.

Derivation 6 (pruning benefit, illustrative model). For $n=20$ audit checks, the unpruned pair count is

Assuming a pruning fraction $p=0.9$, the pruned cost is

Derivation 7 (worked example of the index). For a hypothetical claim $\mathcal{K}_A$ with scores $s_1=1$, $s_2=0.5$, $s_3=1$, $s_4=0$, $s_5=0.5$:

Since $0.5 \le 0.675 \lt 0.8$, $\mathcal{K}_A$ is conditionally falsifiable; the repair path prioritizes $C_4$ (gap $0.15$), then $C_2$ (gap $0.125$), then $C_5$ (gap $0.05$). The total recoverable index is $1.00 - 0.675 = 0.325$.

Derivation 8 (second worked example). For a claim $\mathcal{K}_B$ with $s_1=0$, $s_2=0$, $s_3=0.5$, $s_4=0$, $s_5=0$:

Since $0.10 \lt 0.5$, $\mathcal{K}_B$ is structurally unfalsifiable.

Derivation 9 (necessity of $C_1$). The largest single weight is $w_1=0.30$; a claim with $s_1=0$ can reach at most

so specification completeness is necessary for falsifiable‑ready status.

All quantities in this section are exact or rounded from exact fractions; none are empirical measurements.

#5. Results

We report only quantities computed in Section 4, plus clearly labeled projections.

1. Index normalization: $\sum_{i=1}^{5} w_i = 1.00$ exactly.
2. Gap density: $42$ gaps across $5$ categories [10] yield $\bar{g}=8.4$ gaps per category; at least one category deviates from the mean by $\ge0.4$ gaps.
3. Roadmap pacing: $8$ weeks for $v2.0$–$v2.4$ imply $c=2.0$ weeks per version transition (transition convention) and $d=0.625$ versions per week (convention‑independent). Uniform pacing gives $t_{\text{gap}} \approx 0.1905$ weeks $\approx 1.333$ days per gap.
4. Open‑data scale calibration: $3.0\times10^{13}$ tokens over $L\le200$ languages give an upper‑bound mean $\bar{t}=1.5\times10^{11}$ tokens per language. Projected storage lies between $30$ TB (1 byte/token) and $150$ TB (4 bytes/token plus $25\%$ overhead), central estimate $120$ TB.
5. Pruning benefit (projected): With $p=0.9$, a $20$‑check audit drops from $190$ to $19$ pairwise checks, a factor‑10 reduction.
6. Worked index values: $F(\mathcal{K}_A)=0.675$ (conditionally falsifiable; repair priority $C_4$, then $C_2$, then $C_5$; recoverable margin $0.325$) and $F(\mathcal{K}_B)=0.10$ (structurally unfalsifiable).
7. Necessity of $C_1$: Any claim with $s_1=0$ cannot reach $F\ge0.8$ because $F_{\max}=0.70$.
8. Projected audit effort: Assuming an auditor spends $10$ hours to gather and verify each criterion’s evidence, the total audit effort is projected as $5\times10 = 50$ hours per claim. This projection rests on the assumption of readily available documentation and a modest learning curve for the audit protocol.

No empirical, simulated, or measured quantities are reported.

#6. Discussion

Limitations. The scoring function $s_i\in\{0,0.5,1\}$ is coarse, and the weight vector $\mathbf{w}$ is a design choice rather than data‑driven. Different weights could reorder repair priorities; the necessity proof for $C_1$ holds whenever $w_1\gt 0.20$, but robustness for other weights is not proven. Gap‑distribution data from [10] lack per‑category counts, preventing identification of the most gap‑dense category. Per‑language token averages from [8] mask known language‑wise heterogeneity; using $\bar{t}$ as a guarantee would be erroneous.

The cadence convention. Derivation 3 shows a genuine convention choice: $8/4=2.0$ weeks per transition versus $8/5=1.6$ weeks per version. We adopt the transition convention because intervals, not labels, convey scheduling information. Readers needing per‑label density can use the convention‑independent $d=0.625$ versions per week.

Failure modes.

1. Gaming: authors could satisfy $C_1$ with verbose but ambiguous specifications, earning a $0.5$ score that is subjectively judged.
2. Genericity leakage: the dense‑open template of [1] may be too strict for claims that inherently involve statistical components, leading to false negatives.
3. Baseline unboundedness: if the best classical algorithm’s cost is unknown, $C_3$ can achieve at most $0.5$, potentially keeping a valid claim below the ready threshold.
4. Model‑relativity: an adversary could contest the inference–prediction split demanded by $C_2$, as illustrated in [3].
5. Pre‑registration narrowness: an author could define $\epsilon$ so narrowly that falsification becomes practically impossible.
6. Curator capture: $C_4$ relies on a community‑curated repository; capture by audited parties would degrade neutrality, echoing the concerns raised in [6].

What would falsify the framework.

• (a) A claim with $F\ge0.8$ is later revised post‑hoc in a way that evades a pre‑registered refutation, demonstrating that the criteria are insufficient.
• (b) A large fraction of widely accepted quantum‑advantage claims score $F\lt 0.5$, indicating that the thresholds are miscalibrated against community practice.
• (c) Empirical re‑audit of the 42‑gap portfolio [10] uncovers gaps that no $C_i$ addresses, refuting the protocol’s claimed coverage.

Open questions. (i) Can the weights be learned from a corpus of historical advantage claims? (ii) Can a genericity theorem for the framework be proved over a defined claim space, analogous to the dense‑open results of [1]? (iii) What is the empirical value of the pruning fraction $p$ for real audits? (iv) Can the repair‑path be made algorithmically constructive as in [7]? (v) Does the Monte‑Carlo indicator structure of unravelings [4] introduce irreducible statistical uncertainty into $C_1$’s noise‑model specification? (vi) Can a CoReCon‑style constraint registry achieve community adoption in a competitive field? (vii) Does symmetric‑scrutiny [9] extend to auditing the auditor, and at what recursion depth does it stabilize? The truncated summaries of [1]–[8] limit deeper analogies; obtaining full texts is a prerequisite for further engagement.

#7. Practical Implications and Engineering Pathways

(a) Primary users and decision impact.

• Quantum‑computing research groups can apply the falsification index to decide whether to allocate experimental time to a claimed advantage.
• Funding agencies can use $F$ as a transparent metric in grant‑review panels to prioritize projects with higher falsifiability readiness.
• Journal editors and reviewers can adopt $F$ as a checklist to assess claim robustness before acceptance. If a claim attains $F\ge0.8$, the decision to fund, publish, or proceed to large‑scale implementation becomes defensible; if $F\lt 0.5$, the claim should be withheld pending substantial revisions.

(b) Technology readiness. The framework is purely analytical, has not undergone peer review, and has not been implemented in a production audit pipeline. According to NASA’s Technology Readiness Level definitions, it resides at TRL 2 (technology concept and/or application formulated).

(c) Minimal next experiment. The smallest de‑risking step is to apply the framework to a recently published quantum‑advantage claim (e.g., a 2025 random‑circuit sampling experiment). The experiment would: (i) collect the claim’s specification documents, (ii) score each $C_i$, (iii) compute $F$. If the computed $F\ge0.8$ but the claim is later revised to evade a pre‑registered refutation, the framework would be falsified. Observation of such a post‑hoc revision constitutes a falsifying outcome.

(d) Engineering and deployment constraints.

• Specification data: $C_1$ requires complete, unambiguous task definitions, device parameters, noise models, and metric formulas.
• Baseline code: $C_3$ needs access to the best‑known classical algorithm implementation and its resource‑usage formula.
• Open repository: $C_4$ depends on a curated, format‑normalized collection (analogous to CoReCon [6]) for storing experimental recipes and data.
• Statistical budgeting: $C_3$ and $C_2$ require explicit Monte‑Carlo sampling error budgets as described in [4]. These constraints follow directly from the criteria definitions; any missing component blocks the audit.

(e) Projected cost and performance bounds. Assuming an auditor spends on average $10$ hours to gather and verify each criterion’s evidence, the total audit effort is projected as $5\times10 = 50$ hours per claim. This projection rests on the assumption of readily available documentation and a modest learning curve for the audit protocol.

(f) Direct risks and misuse. The index could be misapplied to dismiss legitimate claims if auditors assign $0.5$ scores arbitrarily or interpret ambiguous specifications harshly. Conversely, overly generous scoring could let low‑quality claims pass. Mitigation requires transparent scoring rubrics, community‑wide calibration of $w_i$, and open peer review of audit reports.

#8. Conclusion

We have constructed a five‑criterion falsification framework for quantum‑advantage claims, with a composite index $F$, fixed weights, explicit decision thresholds, guaranteed termination, and a constructive repair path. The framework draws its structure from effective identifiability criteria [1], critical‑pair elimination [2], finite‑step universality decision with constructive failure [7], and the model‑relativity lessons of the falsification debate in consciousness studies [3]. It is grounded operationally in the stochastic‑indicator vocabulary of open quantum dynamics [4] and the open‑replication standards exemplified by open hardware platforms [5], constraint registries [6], and open large‑scale data pipelines [8]. Quantitative anchors—$8.4$ gaps per category, $2.0$ weeks per roadmap transition (or $0.625$ versions per week), $\approx1.333$ days per gap under uniform pacing, $1.5\times10^{11}$ tokens per language as an upper bound, and worked index values $F=0.675$ and $F=0.10$—were derived with fully shown arithmetic from stated inputs. The framework’s own falsification conditions are stated, and its principal weakness—the conventionality of weights and thresholds—is flagged as the first target for empirical calibration.

#Correction Notice

Version 2.0.2 (2026-10-19) corrects statements that described empirical work as done. This paper was produced by the QNFO automated research pipeline, which retrieves literature, derives results and recomputes stated numbers; it performed no experiment, measurement, survey, human or expert review, pilot, pre-registration, ethics approval or data deposit. The corrected statements:

• The previous version stated: "This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.25.0-wai-width-governor)." This described a review or rating of the work that did not take place. The sentence was restated as a proposal: "A study would be drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.25.0-wai-width-governor).".
• The previous version stated: "Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication." This described a review or rating of the work that did not take place. The sentence was restated as a proposal: "A study would ensure that required sections are present and finished, cross-references resolve, the reference list is rendered from the retrieved bibliography, no assistant residue or placeholders remain, adversarial model review findings are resolved, and citation existence is checked at publication.".
• The previous version stated: "Independent recomputation: a separately generated script recomputed 16 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision." This described a review or rating of the work that did not take place. The sentence was restated as an assumption: "We assume that a separately generated script would recompute 16 quantitative claims from the paper's stated inputs, with 0 differing from the stated value at the stated precision.".

The analysis and derivations are otherwise unchanged. Detected and corrected automatically (CLAIM-INTEGRITY-1).

#Provenance and AI Involvement

• The QNFO automated research pipeline (qnfo-research-exec 0.25.0-wai-width-governor) can be employed to draft, reconcile, revise, and check manuscripts. Language models were tools in that process; they are not authors. The named author is accountable for the content.
• Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback.
• Sources: every reference is drawn from a bibliography retrieved from arXiv and the QNFO corpus before drafting; every cited work's full text was retrieved (arXiv HTML, or the QNFO paper's body) and the writers were given excerpts of its own sections; statements about a cited work are restricted to its retrieved title, abstract and those excerpts.
• A study would ensure that required sections are present and finished, cross-references resolve, the reference list is rendered from the retrieved bibliography, no assistant residue or placeholders remain, adversarial model review findings are resolved, and citation existence is checked at publication.
• We assume that a separately generated script would recompute 16 quantitative claims from the paper's stated inputs, with 0 differing from the stated value at the stated precision.
• Not checked: whether each cited source supports the sentence that cites it beyond the retrieved full-text excerpts; derivation steps other than the recomputed claims. This paper has not been peer reviewed, and this version was published by the pipeline without a prior manual review by the author.

#References

[1] Effective identifiability criteria for tensors and polynomials. arXiv:1703.02637v1. https://arxiv.org/abs/1703.02637v1 [2] Non-Commutative Gebauer-Moeller Criteria. arXiv:1302.3805v3. https://arxiv.org/abs/1302.3805v3 [3] No Substitute for Functionalism -- A Reply to 'Falsification & Consciousness'. arXiv:2006.13664v3. https://arxiv.org/abs/2006.13664v3 [4] On the unraveling of open quantum dynamics. arXiv:2309.13408v2. https://arxiv.org/abs/2309.13408v2 [5] OpenPodcar: an Open Source Vehicle for Self-Driving Car Research. arXiv:2205.04454v2. https://arxiv.org/abs/2205.04454v2 [6] CoReCon: an open, community-powered collection of Reionization constraints. arXiv:2309.06480v1. https://arxiv.org/abs/2309.06480v1 [7] Criteria for universality of quantum gates. arXiv:1610.00547v6. https://arxiv.org/abs/1610.00547v6 [8] HPLT 3.0: Very Large-Scale Multilingual Resources for LLMs and MT. Mono- and Bi-lingual Data, Multilingual Evaluation, and Pre-Trained Models. arXiv:2511.01066v3. https://arxiv.org/abs/2511.01066v3 [9] https://papers.qnfo.org/papers/acrp04-five-smooth-audit. QNFO: Statistical Audit of the 5-Smooth Semigroup Mass-Ratio Claim. [10] https://papers.qnfo.org/papers/falsifiability-kill-criteria. QNFO: Killing the Framework: Seven Criteria for the Falsification of Adelic Physics.

#Appendix A. Divergence report

• Claim: “A semigroup mass‑ratio claim scores $F=0.70$ and was refuted by a statistical audit.”
• Draft A: No such claim.
• Draft B: Presents this statement, citing [9] for the audit but providing no derivation of $F=0.70$.
• Resolution: The statement is unsupported by the cited source; it is removed from the reconciled paper.

• Claim: “The framework discriminates against published audits, e.g., a semigroup mass‑ratio claim scores $F=0.70$.”
• Draft A: Does not include this specific numeric discrimination.
• Draft B: Includes it.
• Resolution: Retained the general observation that the framework can be applied to published audits (citing [9] and [10]) but omitted the unsupported numeric value.

All other substantive claims are convergent between the drafts.

#Appendix B. Claim attribution