xPeerd (AI review)

October 4, 2026

AI Review (xPeerd — DAReview)

Summary

This manuscript proposes two finite-sample conformal constructions for adaptive within-document AI-text screening under document-level exchangeability. Its central claim is that one can preserve a document-level false-alert target while adaptively choosing prefixes and detectors, provided the selection mechanism is constrained in one of two ways: either by a pre-registered finite family with fixed error allocations (Construction A), or by a development-fixed adaptive route whose complete-path maximum is calibrated once (Construction B). The abstract is appropriately cautious in stating that the paper addresses false-alert control rather than detection power, and explicitly notes that “Detection power and computational savings remain questions for empirical evaluation.”

The main strengths are conceptual clarity about scope, careful separation of marginal validity from stronger conditional notions, and repeated emphasis that alerts concern departure from a human reference distribution rather than proof of AI authorship. The main weaknesses are the absence of empirical validation, limited treatment of practical detector implementation, unresolved issues around deployment-wide multiplicity and subgroup validity, and some overstated framing around contribution relative to closely related conformal and sequential-testing literature. The manuscript appears coherent and mathematically self-aware, with no immediate signs of fabricated results; however, several claims of usefulness remain hypothetical because “No detector experiments or computational savings are reported.”

Potential Major Revisions

1. The manuscript’s practical contribution remains under-demonstrated because it explicitly provides no empirical evidence of utility.

The paper states in Section 1.2 that “No detector experiments or computational savings are reported” and reiterates in the conclusion that “A companion empirical study must determine whether either rule offers useful power and computation savings on text.” This is a legitimate limitation for a theory paper, but it materially weakens the manuscript’s applied relevance because the work is framed around adaptive AI-text screening. At present, the reader learns that the procedures can be valid yet possibly powerless: “The proofs also allow valid but powerless scores.” That admission is honest, but it also means the manuscript stops short of showing whether the proposed rules improve anything that a practitioner would care about, such as sensitivity under realistic paraphrase attacks, computational savings, or robustness across document lengths.

A major revision should either add a focused empirical section or substantially sharpen the framing so that the paper is presented strictly as a theoretical note. If empirical evaluation is deferred, the introduction and contribution statements should be downgraded to avoid any implication of demonstrated screening effectiveness.

2. The novelty positioning should be tightened to avoid ambiguity about what is genuinely new.

The authors write in Section 1.1: “Thus, deriving stopping-valid decisions from fixed-decision guarantees is not a new general principle. Our contribution is a specification of two such constructions for within-document detector selection, including the restrictions on routing and calibration reuse.” This is a careful sentence, but the manuscript still risks appearing incremental because it explicitly “do[es] not claim to originate conformal AI-use detection or foundational sequential-testing theory” and later states in the declarations: “We do not claim new foundational theory or an exhaustive novelty review.”

That combination leaves the novelty claim somewhat under-specified. Is the contribution theorematically nontrivial, methodologically novel, or mainly expository and synthetic? The manuscript should make this explicit. For example, it should distinguish more sharply between:

• what follows directly from standard conformal rank validity plus a union bound,
• what is specific to within-document adaptive routing,
• what is merely a deployment protocol recommendation,
• and what theorem would fail if one tried a more naive adaptive scheme.

Without this sharpening, some readers may conclude that the paper repackages known ideas with domain-specific notation.

3. The deployment claims are narrower than the applied framing may suggest, and this should be foregrounded earlier and more prominently.

The framework targets “marginal document-level control” and explicitly states that it “does not condition on a realized calibration set, document length, subgroup, or selected route, and it does not control multiplicity across a collection of screened documents.” Later, the discussion adds: “A pooled marginal bound does not ensure protection within a subgroup” and notes bias concerns against “non-native English writing.” The paper also states: “Screening many documents, or rerunning one document under several policies, requires additional multiplicity accounting if the target is deployment-wide family-wise error or false-discovery control.”

These are not minor caveats. They substantially limit the policy relevance of the proposed guarantees. In real screening systems, users typically care about batched review pipelines, fairness across writer populations, and drifted deployment environments. Because these limitations are central rather than peripheral, they should appear already in the abstract or at least in a dedicated paragraph near the end of the introduction. As written, the caveats are mathematically present but strategically deferred.

4. The manuscript would benefit from a stronger reproducibility bridge between abstract theory and implementable detectors.

Section 2 defines the framework abstractly: “Fix score maps, model checkpoints, preprocessing, action families, transformations, and error weights using development information Ddev.” Construction A then requires a fixed action family and score map, while Construction B requires a fixed route generator and complete-path calibration maxima . Yet the declarations state: “Code availability. No study-specific detector implementation accompanies this article.”

For a theory manuscript that is acceptable in principle, but here the bridge from symbols to deployment is thin. The paper should include at least one full worked protocol instantiation, using a named detector family and a concrete token-budget schedule, showing exactly what is fixed in development, what is calibrated, what is stored, what is computed at test time, and what can or cannot be changed without invalidating guarantees. Otherwise, reproducibility is only formal, not operational.

5. The manuscript leaves unresolved the scientific meaning of the target hypothesis, especially under mixed authorship and domain shift.

The paper commendably states: “Rejecting P0 does not identify a member of Q, because other human populations can also differ from P0.” It also clarifies that “An alert concerns departure from the human reference, not a posterior probability of AI authorship” and that “Mixed human/AI authorship requires a specified target population and label definition.”

These are epistemically important admissions. However, they imply that the practical interpretation of alerts may be much less intuitive than the paper’s application domain suggests. A major revision should add a dedicated subsection clarifying what scientific question each construction actually answers. For example: is the test about provenance, stylistic conformity to a calibration corpus, or deviation from a protected reference distribution? Without this clarification, readers may misread false-alert control as meaningful authorship evidence when the manuscript itself says it is not.

6. Some supporting results may distract from the main contribution unless better integrated.

The manuscript includes an oracle total-variation identity, an illustrative Hoeffding budget, a distribution-shift bound, and a Clopper–Pearson audit bound . These are mathematically standard and useful, but their role in the argument is uneven. The declarations acknowledge that the “supporting propositions use the additional assumptions stated in each result.”

Because these propositions are not on the same footing as the main theorems, the manuscript should better separate core results from contextual appendices or supporting remarks. Otherwise, the paper risks appearing broader than it is, especially when some propositions rely on assumptions not implied by the main exchangeability setup.

7. Anti-fraud / paper-mill assessment

I do not see strong evidence of fabrication or paper-mill characteristics. The manuscript is internally coherent, cites limitations against its own claims, and repeatedly narrows scope rather than inflating it. Particularly credible are the cautionary statements such as “Our rank proofs construct no such process and establish no conditional supermartingale property for products of transformed ranks” and “Marginal rank validity alone cannot justify those products.” Such self-limiting technical statements are usually inconsistent with formulaic fraudulent writing.

However, there is one integrity-related concern requiring revision: the declarations admit “AI tools assisted with literature synthesis, drafting, editing, and mathematical review,” while also stating that the authors “must verify the claims, proofs, references, and final text before submission.” Given the mathematical nature of the paper, the authors should explicitly describe their proof-verification workflow, especially because AI assistance in “mathematical review” can introduce subtle formal errors.

Potential Minor Revisions

1. Page/section numbering and formatting problems reduce professionalism.

The manuscript shows formatting artifacts such as “11 Introduction” where the section heading appears merged with a page number or numbering stream . Similar artifacts appear later as “12Deployment-wide multiplicity” and “13Author contributions” . These should be corrected throughout. They make the PDF feel insufficiently typeset for submission.

2. The manuscript contains several statements indicating incompleteness before submission.

The front matter includes “Classification to be confirmed before submission.” This should not remain in a submission-ready manuscript. Likewise, “Competing interests. The authors must confirm their relevant financial and non-financial interests before submission.” and “Ethics approval and consent... The authors must confirm any institutional requirements before submission.” are placeholders rather than finalized declarations. These need completion before any serious review venue.

3. Some prose is dense and could be simplified for accessibility.

For example, the sentence “Thus B implements an observable conservative lower bound on that induced test, not its conditional expectation” in the section “Relationship to induced sequential tests” is mathematically meaningful but compressed . Similar density appears in “The product-law condition in Proposition 6.3 is an additional assumption: document-level exchangeability alone does not imply independence of a new document and its calibration set.” These passages could be followed by one-sentence intuitive glosses.

4. Terminology should be standardized more consistently.

The manuscript alternates among “false-alert,” “alert,” “flag for review,” “rejecting P0,” and “non-rejection” across the framework and discussion . While all are understandable, a terminology table or explicit conventions paragraph would help readers distinguish operational actions from statistical events.

5. The manuscript should add a compact notation table.

The paper introduces many symbols in quick succession: X, P0, Q, π, τ, Nτ, Cτ, Ddev, A, wa, Mπ, ppath, pfull, and others . A notation table would improve readability, especially for interdisciplinary readers from machine learning rather than mathematical statistics.

6. Citation and URL formatting should be cleaned.

Several URLs appear line-broken awkwardly in the references, for example the ACL DOI and some proceedings links . These should be normalized. Also, if the target venue uses a standard bibliography style, direct “Accessed” web-reference formatting should be made consistent.

7. The distinction between calibration feasibility and practical adequacy should be emphasized visually.

The paper correctly states that calibration counts “permit rejection on the rank grid; they do not ensure that a score attains the minimum rank or has useful power” and similarly that “The calibration counts describe rank feasibility, not sufficient data for useful power.” This is an important message. It deserves boxed remarks or explicit examples because it is easy for readers to over-interpret sample-count formulas.

8. AI content analysis for this post-2021 manuscript

Estimated AI-generated content: moderate to high, roughly 35%–55%.

Basis for estimate:

• The declaration explicitly states: “AI tools assisted with literature synthesis, drafting, editing, and mathematical review.”
• The prose is unusually uniform in cadence, highly hedged, and repeatedly uses symmetrical contrastive constructions such as “We distinguish...,” “We also separate...,” and “We do not claim...” across sections .
• The manuscript contains polished but formulaic disclaimer language, especially in the conclusion and declarations: “The authors are responsible for the manuscript and must verify the claims, proofs, references, and final text before submission.”

Highlighted likely AI-assisted sections:

• Abstract, especially the compressed global summary of both constructions and limitations
• Introduction/Positioning, where literature is summarized in a highly balanced, template-like register
• Statements and Declarations, explicitly acknowledged as AI-assisted

Assessed epistemic impact:

• Moderate. Here, AI use does not by itself invalidate the paper because the core contribution is mathematical and the text openly discloses assistance.
• The main risk is not rhetorical assistance but possible unverified mathematical exposition, misplaced novelty framing, or subtle proof-description errors introduced during drafting.
• Because the manuscript is theory-heavy and lacks code or experiments, human verification of proofs and references is essential before publication.

Recommendations

1. Reframe the manuscript unambiguously as a theoretical contribution unless empirical evidence is added. The current text is strongest when it speaks narrowly about validity, not when it implies practical detector gains.

2. Add one concrete end-to-end instantiation of Construction A and one of Construction B using named detectors, specific prefix budgets, a calibration protocol, and a deployment workflow. This would materially improve reproducibility and applied interpretability.

3. Move the strongest limitations earlier. In particular, foreground in the abstract or introduction that the guarantees are marginal, single-document, reference-population-specific, and not deployment-wide.

4. Clarify novelty with a sharper theorem-to-literature map. State explicitly which steps are standard, which are adapted, and what exact gap in the literature is being closed.

5. Add a short subsection on interpretational scope: what an alert means, what it does not mean, and why this is not equivalent to proving AI authorship or misconduct.

6. Finalize all submission placeholders, especially MSC classification, competing interests, and ethics wording, and correct visible PDF formatting defects.

7. Add a notation table and a practical assumptions checklist so readers can verify when theorems apply in real screening systems.

8. If AI assistance was used in mathematical review, provide a brief statement of human verification procedures for proofs, references, and theorem claims.

Overall, I judge the manuscript intellectually careful and potentially useful as a theory paper, but not yet strong enough in its present form for submission without substantial revision to novelty framing, practical reproducibility, and submission readiness.

XSci (AI review)

October 4, 2026

Referee Report

Manuscript: "Two Conformal Constructions for Adaptive Within-Document AI-Text Screening"

Recommendation: Major revision required.

Summary and Recommendation

This manuscript addresses false-alert control for an analyst who inspects one document adaptively for evidence of AI authorship, choosing how far to read, which detector to apply, and when to stop. Under Assumption 2.1, which pairs development separation with document-level exchangeability between $m$ human calibration documents and a new null document while imposing no restriction on within-document token dependence, two rules are proposed. Construction A pre-registers a finite family of prefix–detector actions, fixes error allocations $w_a$ with $\sum_a w_a \leq 1$, and alerts when an executed action's conformal rank falls below $\alpha w_a$; Theorem 4.1 shows by a union bound over the registered family that validity survives any score-dependent choice of executed subset. Construction B freezes a route generator, calibrates the complete-path maximum $M_\pi$, and alerts at the first executed action whose partial-path maximum attains a rank below $\alpha$; Theorem 5.1 derives stopping validity from $M_{\pi,t}(X) \leq M_\pi(X)$ and the resulting event containment. Corollaries 4.3 and 5.3 give the calibration counts under which rejection is attainable, and Section 6 adds oracle, shift, and audit results.

The technical core is correct and in places elegant. Complete-path calibration is a clean way to purchase early stopping without splitting an error budget, and treating the document rather than the token as the exchangeable unit is the right structural choice for text. The authors' epistemic discipline is unusual: they decline to claim an e-process, exhibit rather than conceal the gap between marginal and calibration-conditional validity, and insist that an alert is a departure from a reference law rather than a finding about authorship. The manuscript nonetheless cannot be published as it stands. Its claims about adaptive screening rest on no empirical or numerical evidence, and the cost of its own validity is unquantified; the distance between the quantity it controls and the quantity a deployer operates is identified repeatedly and never closed; and several design features require analysis the paper does not supply. The revisions below extend the framework rather than replacing it.

Major Concern Category 1: Evidentiary Basis and the Unquantified Cost of Validity

1.1 No empirical or numerical evaluation

The paper is framed from its title onward as a contribution to screening practice, yet reports, in its own words, no detector experiments and no computational savings. The difficulty is not that a theory paper must contain experiments; it is that the manuscript's own assertions cannot be assessed without a numerical illustration. Whether any realistic curvature-based or contrasting-model score on a truncated prefix attains a conformal rank below the threshold $1/1200$ implied by twelve equally weighted actions at $\alpha = 0.01$ is answerable by simulation from a parametric score model, with no text data required. So is the tradeoff the authors state and leave unresolved: Construction B spends no error budget but inflates its reference through max-aggregation, while Construction A splits the budget but compares against a per-action reference. A simulation reporting realized size and power across a grid of $m$, family size, and weight allocations is the minimum the stated tradeoffs require.

1.2 The calibration requirements are the most consequential output but are framed as a technical aside

Corollary 4.3 yields $m \geq 1{,}199$ at $\alpha = 0.01$ and $m \geq 11{,}999$ at $\alpha = 0.001$ for twelve equally weighted actions; Corollary 5.3 gives 99 and 999 for Construction B; Proposition 6.5 adds $N_0 \geq 2{,}995$ further documents to certify a rate below 0.001 with zero observed alerts. These appear to be the most actionable findings, yet they are presented as statements about rank feasibility and are never aggregated. The requirement is also conjoined with an exchangeability condition whose cost grows with $m$: assembling twelve thousand documents exchangeable with an arbitrary submission is qualitatively harder than assembling one hundred, and the paper's own subgroup discussion multiplies the burden by the number of strata. The comparison between constructions is not on equal footing either, since B's calibration documents must each be run through a complete route. A table of required calibration count, offline evaluation count, threshold, and audit size for matched designs would make it legible.

1.3 Conservativeness is unquantified, and the two constructions are never formally related

Every result in Sections 4 and 5 is an upper bound, and nothing establishes that either construction approaches the nominal level. The slack compounds: Lemma 3.1 yields $\lfloor (m+1)u\rfloor/(m+1)$, the conservative tie-counting rank adds more whenever scores tie, and Construction A then charges the analyst for actions never executed. Construction B's slack differs in kind, since $p_t^{\mathrm{path}} \geq p^{\mathrm{full}}$ can be near-vacuous at early $t$, where one transformed score is compared against calibration maxima over entire routes. The manuscript also offers two rules without relating them; a containment result for matched families and routes, an expected-cost comparison under the null, or a hybrid allocating weights across the complete-path maxima of several frozen routes would all be informative, and the last follows directly from combining the two theorems. The proof of Theorem 4.1 notes that it assumes no dependence structure, yet the registered scores come from related detectors on nested prefixes of one document and are strongly positively dependent — precisely where Bonferroni is most wasteful and Simes-type refinements recover the most. Since the required count scales as $1/(\alpha \min_a w_a)$, any such refinement directly relaxes the paper's heaviest requirement.

Major Concern Category 2: Distance Between the Formal Guarantee and the Deployment Object

2.1 The human reference law and the calibration corpus are never operationalized

Because the document includes its length and acquisition metadata, Assumption 2.1 requires the calibration corpus to be exchangeable with the submission in length, topic, genre, register, prompt, author population, and collection circumstances. The manuscript never discusses how such a corpus would be assembled, how an analyst would judge the assumption tenable, or what evidence could bear on it. This matters because the assumption does nearly all the inferential work — both proofs are short precisely because exchangeability plus Lemma 3.1 supplies the rank bound immediately — and because it fails in the settings described, where calibration documents come from past cohorts on different prompts or from archives unlike any particular submission. A corpus-construction protocol matching on length band, discipline, and collection period, with exchangeability claimed at the stratum level, together with diagnostics exploiting the approximate uniformity of leave-one-out calibration ranks, would be achievable without new theory.

2.2 The marginal guarantee is mismatched to a deployment in which one fitted pipeline is reused

Equation (1) averages over the calibration draw, and Example 6.4 shows that the conditional error given a realized calibration value can substantially exceed the nominal level even when the marginal error is exactly nominal. This clashes with the paper's own deployment narrative: Section 5 computes complete routes once per calibration document and then follows prescribed routes at deployment, Proposition 6.5 conditions on a fitted pipeline and treats its false-alert probability as fixed, and the discussion after Proposition 6.3 states that the theorems supply an average bound rather than one for each realized mechanism. An institution that calibrates once and screens for a year draws a single calibration set and lives with its conditional rate. What makes this major rather than an acknowledged limitation is that the supporting results themselves depend on closing the gap, and the only remedy offered is an audit costing nearly three thousand further documents. Calibration-conditional statements of PAC form are available for split-conformal objects at a computable price; since both constructions produce such objects, even stating the conversion and its cost in $m$ would be more useful than exhibiting the gap and stopping.

2.3 Per-document control is not what institutional screening needs, and operating characteristics go undiscussed

The target concerns one null document, and the manuscript states clearly that it does not control multiplicity across a collection. The candour is appreciated, but the gap is wider than a disclaimer can absorb in a paper about screening, which is by definition applied to a population: at $\alpha = 0.01$, a cohort of one thousand human submissions produces roughly ten alerts in expectation. The tension sharpens in Section 6.4, where the audit targets 0.001 and thereby concedes that the stricter figure is operationally relevant, making the eleven-thousand-document requirement the binding one. An unexploited connection sits within the paper: the per-document ranks are exactly what deployment-wide procedures consume, so stating what a Bonferroni or Benjamini–Hochberg step across terminal ranks would deliver would convert a limitation into an extension. Relatedly, the manuscript never says how $\alpha$ should be chosen or what an alert triggers, the asymmetry between a concrete individual cost and a diffuse institutional one is not analyzed, and the cited bias against non-native English writing indicates that false alerts would not fall uniformly across authors.

Major Concern Category 3: Design-Level Gaps in the Two Constructions

3.1 Document length interacts with both constructions in unanalyzed ways

Scoring at $\min(b_k, L)$ tokens is necessary but consequential. For a document shorter than several registered budgets, all actions with $b_k \geq L$ score identical text and produce identical ranks, so the family collapses while the error budget has already been divided among all its members; a short document is then tested at threshold $\alpha/12$ using perhaps four distinct tests. The loss falls systematically on short submissions, which are common in the settings targeted and are where the cited detectors are least reliable. Across documents, a large-budget action compares a test score on $\min(b_k, L)$ tokens against calibration scores on $\min(b_k, L_i)$ tokens for varying $L_i$, so for detectors whose statistics drift with the number of tokens scored the comparison conflates signal with a length effect and the procedure becomes partly a length test. Construction B inherits a related issue through route length, since longer documents traverse longer routes and a maximum over more actions is stochastically larger. Length stratification of the family and weights, fixed during development, would address all three cases.

3.2 The transformations in Construction B carry the procedure's behaviour but receive one sentence

Because $M_\pi$ maximizes across actions using different detectors on different prefix lengths, the transformations $g_a$ must place heterogeneous scores on a common scale, or the maximum is determined by whichever action produces numerically large values rather than by whichever carries the most evidence. The manuscript's treatment is the single suggestion that $g_a$ may be the negative logarithm of a tail rank computed against a separate development reference set. That set is never characterized, although its size bounds the resolution of the tail rank, so the maximum saturates and ties proliferate at exactly the extreme values where alerts occur; and it is a third data requirement, beyond the calibration and audit corpora, absent from the paper's accounting. More fundamentally, if one detector is better calibrated on short prefixes than another, the maximum is dominated by the miscalibrated action for calibration and test documents alike, so validity survives and power does not. Since B's advantage rests entirely on max-aggregation, the quality of that aggregation deserves formal requirements on $g_a$ and guidance on the reference-set size.

3.3 The failure sentinel protects validity but creates an exploitable channel

The mathematics of failure handling is careful, and the worked arithmetic for empty calibration routes is a useful implementation note. What is not considered is that, from the perspective of an author wishing to avoid an alert, the sentinel is a deterministic acquittal device. Detector failures arise from tokenization errors, unsupported character sets, malformed markup, and timeouts, all of which an author controls, so a submission containing homoglyph substitutions or formatting that breaks the inspection tokenizer may induce failure across the registered family. The adversarial discussion addresses document selection and paraphrasing but not this threat, which attacks validity rather than power. Failure is also part of the score profile under the fixed map, so if the realized failure rate differs between calibration and deployment the reference distribution contains a different mixture of sentinels and exchangeability fails. Routing documents that fail a fixed validity check out of the procedure, rather than silently acquitting them, would address both.

3.4 Construction A's advertised adaptivity has no inferential content, and two supporting results are disconnected

The manuscript presents as a contribution that Theorem 4.1 permits score-dependent selection, but the permission appears inferentially empty. Family, scores, and weights are fixed before deployment, and Section 4 requires each score to be defined on all documents including those where the action is not executed, so the whole rank vector is determined independently of the selection rule. An exhaustive analyst alerts exactly when some rank clears its allocated threshold; a selective analyst alerts on a subset of those occasions and never otherwise. Selection therefore cannot raise the alert probability — which is why the theorem holds — but neither can it raise power; the sole gain is computational and is never quantified. Separately, Theorem 6.1 and Proposition 6.2 reproduce standard results the authors themselves declare inapplicable to their constructions; they should either be deleted or made load-bearing, for instance by positing an effective independent-replicate count and setting the resulting budget against the required calibration count. The induced-sequential-test passage likewise concedes that Construction B is a conservative lower bound on an existing construction without characterizing when the gap is small.

Minor Issues

1. The Section 6.2 heading misspells Hoeffding as "Hoefding," and reference [3] gives Schwarzschild as "Schwarzchild." References [11] and [13] carry 2026 dates with incomplete volume and page details, [6] lacks the DOI or URL carried by every other conference entry, and [19] cites software documentation, with a future access date, for a claim about Kolmogorov–Smirnov test assumptions.

2. Ramdas, Ruf, Larsson, and Koolen are cited in Section 6.5 as the source for the general e-process definition, yet no corresponding entry appears in the numbered list. Unresolved placeholders also remain throughout: the MSC line defers classification, the competing-interests and ethics statements defer confirmation, and the AI-assistance statement records that the authors must still verify the claims, proofs, references, and final text.

3. Section 7 carries the heading "Discussion: scope and limits" with no body text, and the six items that follow are typeset as top-level sections rather than subsections. Two unnumbered passages also sit between the end of the Section 5 development and Corollary 5.3, detaching the corollary from the construction it describes.

4. Notation is inconsistent: the action family alternates between $\mathcal{A}$ and $A$; $K$ serves both the repeated-looks count and the audit count; "alert," "flag for review," and "rejection" are used interchangeably; and $N_\tau$ and $C_\tau$ are defined carefully and never used again. The stopping index "$\rho = \tau \leq T_\pi(X)$" is ambiguous as a definition, and several displays render with corrupted spacing.

5. The manuscript contains no figures or tables. A schematic contrasting the two constructions, and a summary table of required calibration count, threshold, offline cost, and audit size at several values of $\alpha$, would do substantial work for a reader deciding between them.

6. Three conditions are stated too casually for their weight: that revisited actions must reuse a frozen seed and that fresh replicates require their own registered action are conditions of Theorem 4.1 yet appear as trailing sentences; the futility rules should be stated explicitly as part of the fixed object $\pi$; and "or their summaries" in Remark 5.2 is undefined, though an analyst who has seen aggregate alert rates from a prior deployment arguably has seen a summary.

7. Several passages stop short of their consequences: the empty-routes illustration does not note that frequent empty termination yields a degenerate reference distribution; the shared-authorship caveat to Proposition 6.5 is a closing clause though it is central for a cohort answering a common prompt; and the point that deployment need not compute a route's unvisited actions is buried in a trailing clause.

8. Smaller matters: the abstract runs to roughly 210 words and its phrase "necessary calibration counts" invites a sufficiency misreading; Proposition 6.2 is labelled illustrative yet contains no illustration; $\sum_a w_a \leq 1$ rather than $= 1$ is never explained; Theorem 6.1 is stated for product laws although the identity is general; and the monotonicity relation driving Theorem 5.1 is unnumbered despite being referenced later.

Missing and Inadequately Integrated Literature

Cited but Inadequately Integrated

Bates, Candès, Lei, Romano, and Sesia [8] are cited for the marginal-versus-conditional distinction and the conservative rank argument, but only their simplest content is used; the same work treats the joint behaviour of conformal p-values sharing a calibration set and calibration-conditional corrections, bearing directly on whether Construction A's union bound can be sharpened and whether the gap in Example 6.4 can be bounded rather than merely displayed. Barber, Candès, Ramdas, and Tibshirani [16] appear in one closing sentence, although their coverage-gap bound competes with Proposition 6.3 and does not require the product-law condition the authors identify as an additional assumption. Zhu and coauthors [6] are the closest methodological antecedent, yet the asserted gap is never demonstrated; readers need to know whether Construction A subsumes multiscale conformal prediction under a particular family and weighting, and Xie and coauthors [13] are likewise set aside in a single sentence despite being the nearest neighbour in the literature. Chen and Wang [7] are distinguished on the ground that a stream-level setting differs from inspecting one document's segments, but that concerns the data rather than the machinery, and a betting construction over within-document prefixes is the natural competitor.

Truly Missing Papers

Lan and DeMets (1983) is a direct antecedent for Construction A: alpha-spending allocates a fixed error budget across looks whose timing need not be pre-specified, structurally what the weights accomplish, and that literature supplies allocation shapes answering the question Remark 4.2 raises but does not resolve. Bian and Barber (2023) addresses when distribution-free methods admit training-conditional guarantees and at what cost, and Vovk (2012) supplies the standard taxonomy of conditional validity notions; together they would let the authors locate their result within an established classification and convert Example 6.4 from a warning into a quantified statement. Jin and Candès (2023) develops multiple testing with conformal p-values for screening a candidate pool with false-discovery-rate control, exactly the deployment-wide accounting Section 7 identifies as missing. Simes (1986) is the standard improvement on Bonferroni under positive dependence, and Vovk, Gammerman, and Shafer (2005) should appear as the foundational conformal reference, since smoothed conformal p-values bear on the tie conservativeness accepted in Lemma 3.1. On the application side, Krishna and coauthors (2023) quantify the paraphrase vulnerability the manuscript treats qualitatively, reporting a fall in DetectGPT's detection rate from 70.3% to 4.6% at a fixed 1% false positive rate. All entries below except Simes and Vovk, Gammerman, and Shafer were verified via web search.

Bian, M., and R. F. Barber. 2023. Training-conditional coverage for distribution-free predictive
    inference. Electronic Journal of Statistics 17(2):2044-2066.
Jin, Y., and E. J. Candes. 2023. Selection by prediction with conformal p-values. JMLR 24(244):1-41.
Krishna, K., Y. Song, M. Karpinska, J. Wieting, and M. Iyyer. 2023. Paraphrasing evades detectors
    of AI-generated text, but retrieval is an effective defense. NeurIPS 36:27469-27500.
Lan, K. K. G., and D. L. DeMets. 1983. Discrete sequential boundaries for clinical trials.
    Biometrika 70(3):659-663.
Simes, R. J. 1986. An improved Bonferroni procedure for multiple tests. Biometrika 73(3):751-754.
Vovk, V. 2012. Conditional validity of inductive conformal predictors. PMLR 25:475-490.
Vovk, V., A. Gammerman, and G. Shafer. 2005. Algorithmic Learning in a Random World. Springer.

Conclusion and Path Forward

The manuscript identifies a genuine gap between fixed-decision conformal guarantees and the adaptive inspection that document screening actually involves, and both constructions close that gap within their stated scope. The proofs are correct, the assumptions are well chosen, degenerate cases are handled with unusual care, and the refusal to overstate is a real virtue in a literature where overstatement is common. Complete-path calibration in particular obtains stopping validity from a containment relation rather than from martingale structure, which is simpler and more transparent than the alternatives.

The revisions required fall into three groups. The paper needs an evidentiary basis: a simulation reporting realized size and power, a unified treatment of the calibration, audit, and development-reference requirements, and a comparison that lets a reader choose between the constructions. It needs to close, or at least price, the distance between what it controls and what a deployer operates, through a calibration-conditional version of its theorems, an operationalization of the exchangeability premise with diagnostics, and a discussion of how the error target should be chosen. And it needs design-level additions: length stratification, formal requirements on the transformations, a pre-screening step for detector failure, and a plain statement that Construction A's selection permission trades power for computation. The question the authors have posed is worth answering, and the manuscript has the right skeleton for answering it.