{"id":"eb263f33-5867-4522-82dd-93ef6c765bc7","arxiv_id":"2508.12299","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The abstract claims a d^{-1} expansion of the critical point for high-dimensional oriented percolation, but the supplied manuscript body is a different paper on topological light, so the result cannot be reviewed from this material.","lead":"The metadata identifies a math.PR paper on an asymptotic expansion of the critical point for oriented percolation using lace expansion, but the full text is an unrelated optics paper on optical skyrmions. A generalist should know that the submitted file cannot support the stated mathematical claim.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Full text is the wrong manuscript (arXiv:2508.12305, physics.optics); the lace expansion proof of the 1/d expansion is entirely absent, so the central claim cannot be checked.","rationale":"The reader identified the identifier mismatch and correctly concluded that the central claim cannot be verified from the supplied text. My stress-test pass confirms this: the strongest claim is purely an assertion about a lace expansion proof, while the full text is a different paper with no percolation content. The reader's weakest assumption—that lace expansion convergence and truncation validity are the fragile foundation—is exactly where a technical concern would land, but the absence of the derivation makes it impossible to evaluate that assumption, let alone find a more specific weak step. No internally inconsistent equation or unsupported numerical claim can be pinpointed, because none of the proof is present. This is not an objection to the mathematics; it is a statement that the submitted material does not support any verdict other than UNVERDICTED. The optics paper's free parameters (Gaussian filter kernel, intensity threshold, distortion-strength convention) would matter only if that were the paper under review, which it is not. Therefore I do not move the reader's verdict; I agree with it, and the recommended action is to obtain the correct full text before any further assessment.","tokens_in":20481,"tokens_out":3018,"duration_ms":32616,"concrete_test":"Retrieve the actual full text for arXiv:2508.12299 from arXiv (e.g., via arxiv.org/abs/2508.12299), then locate the lace expansion section and verify that it contains (a) the expansion setup for nearest-neighbor oriented percolation, (b) a convergence/remainder bound to the stated order in 1/d, and (c) the resulting asymptotic expansion for p_c. If those components are present, re-review that text; if any is absent, retain the UNVERDICTED verdict.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of arXiv:2508.12299 is that the nearest-neighbor oriented percolation critical point on Z^d admits an asymptotic expansion in powers of 1/d, established via the lace expansion. The supplied full text, however, is the unrelated physics.optics paper arXiv:2508.12305v1, 'Seeing through randomness with topological light' by Peters et al. That text contains no oriented percolation model, no lattice Z^d, no critical point, and no lace expansion. Consequently, the load-bearing premise of the claimed proof—convergence of the lace expansion in high dimensions and validity of its truncation to the required order in 1/d—is never stated, derived, or bounded. No equation, lemma, or estimate from the proof is available to test for internal consistency. This is a missing-support problem rather than a refutation of the mathematical claim, and it is decisive for this review: the claim is unverdictable from the provided material. The optics manuscript's own quality is irrelevant to the math paper's central assertion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The abstract of arXiv:2508.12299 announces an asymptotic expansion, in powers of d^{-1} as d tends to infinity, of the critical point for nearest-neighbor oriented percolation on Z^d, with the proof said to rely heavily on the lace expansion. The submitted full text, however, is the entirely different manuscript arXiv:2508.12305v1, 'Seeing through randomness with topological light' by Peters et al., which concerns experiments on optical skyrmions and information transfer through random media. No oriented percolation model, no lattice Z^d, no critical point, and no lace expansion appear anywhere in the body. Consequently the submitted manuscript contains no derivation of the advertised result.","tokens_in":20540,"tokens_out":3955,"duration_ms":42066,"significance":"If the claimed theorem were proved, it would be a worthwhile contribution: rigorous high-dimensional asymptotic expansions for the critical point of nearest-neighbor oriented percolation are of genuine interest, and a lace-expansion derivation would likely be influential. However, as submitted, the paper contains no theorem statement, no proof, and no verifiable mathematical content beyond the abstract sentence. There are no machine-checked proofs, reproducible code, or derivations to credit. The potential significance of the claimed result cannot offset the complete absence of its demonstration.","major_comments":[{"comment":"The full text is arXiv:2508.12305v1, an unrelated physics.optics paper on optical skyrmions. It contains no oriented percolation, no lattice Z^d, no critical point, and no lace expansion. The single-sentence abstract is the only mathematical content, so the central claim of the paper is entirely unsubstantiated by the submitted material.","section":"Abstract and Full text"},{"comment":"No theorem is stated: there is no formula for the critical point, no explicit coefficients of the 1/d expansion, and no error term or dimension range. Even if the intended body were present, the abstract alone could not support the advertised asymptotic expansion, and there is no way to check the convergence or truncation of the lace expansion that the proof allegedly relies on.","section":"Abstract"},{"comment":"The equations in the body describe Stokes parameters and skyrmion wrapping numbers; they have no connection to the abstract's claim. This confirms that the text submitted for review is not the manuscript described in the abstract, so the proof is absent rather than merely difficult to verify.","section":"Full text, Equations (1)-(6)"}],"minor_comments":[{"comment":"The header of the full text carries arXiv:2508.12305v1; the authors should supply the correct source file for arXiv:2508.12299 before resubmission.","section":"Full text, header"},{"comment":"Once the correct manuscript is provided, the abstract should state the theorem explicitly, including the coefficients and error order; until then, the report cannot comment on the mathematical exposition, notation, or figures.","section":"General"}],"recommendation":"reject","confidential_remarks":"This is not a judgment about the truth of the claimed expansion; it is a determination that the material submitted for review does not contain the paper. The optics manuscript should be handled separately. If the authors resubmit with the correct body, the mathematical content can then be evaluated."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, the full text attached to arXiv:2508.12299 is not the math paper. It is a physics.optics manuscript, \"Seeing through randomness with topological light\" by Peters et al., arXiv:2508.12305v1. Second, the stated math result—a rigorous 1/d expansion of the critical point for nearest-neighbor oriented percolation on Z^d via the lace expansion—appears only as a one-sentence abstract. There is no derivation, no lemmas, no comparison to prior lace expansion work, and no way to check convergence or truncation of the expansion. So I cannot evaluate the claim at all.\n\nWhat the paper (as the math paper) does well: nothing is checkable from the supplied material. The abstract is clean and the claim is plausible in the context of high-dimensional percolation; a 1/d expansion is a natural target and would be a useful within-subfield result if proved. But an abstract is not a paper. If this is an honest submission, it likely has a file-exchange error. The authors need to resubmit the correct body.\n\nSoft spots: the body mismatch is the whole story. It is not a subtle technical issue; it means the submission's central evidence is absent. I also note the abstract gives no context—no mention of Hara–Slade, spread-out models, or previous critical-point asymptotics—so even the framing is thin, but that would be fixable in a full paper.\n\nShould a serious editor referee this? As submitted, no. A desk reject with an invitation to resubmit the correct manuscript is the right call. If the correct body shows up and contains a real lace expansion proof, then it deserves referee time; the convergence of the lace expansion in high dimensions and the validity of truncation to 1/d are exactly what a referee should check. But I cannot certify any of that from this submission.\n\nFor us: don't cite it, don't bring to reading group. If you want to track it, check for a corrected version. My serious-thinker answer is \"unclear\"—there is no content from the stated paper to judge, and the optics paper, while coherent, is irrelevant to this ID.","headline":"The submitted full text is the wrong manuscript (a physics.optics paper), so the lace-expansion proof of the 1/d critical-point expansion is entirely absent and the math claim cannot be checked.","tokens_in":21141,"tokens_out":2019,"would_cite":false,"duration_ms":21089,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["60K35","82B43"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims the critical value of nearest-neighbor oriented percolation on $\\mathbb Z^d$ has an asymptotic expansion in powers of $d^{-1}$, proved by the lace expansion.","keywords":["oriented percolation","critical point","asymptotic expansion","lace expansion","high-dimensional lattices","nearest-neighbor percolation","critical probability"],"falsifier":"A concrete falsifier would be to carry the lace expansion one order beyond the paper's stopping point and exhibit a diagram whose contribution is not bounded by the claimed power of $d^{-1}$; absent such a diagram, one can also compute $p_c$ in moderately high dimensions by high-precision simulation and check whether the observed remainder matches the first omitted term of the series.","tokens_in":20170,"feed_emoji":"🎲","tokens_out":8396,"duration_ms":87082,"temperature":0.7,"pith_summary":"The paper's claim is that the critical probability for nearest-neighbor oriented percolation on $\\mathbb Z^d$, the threshold at which an infinite directed open cluster first appears, admits a rigorous asymptotic expansion in powers of $d^{-1}$ as the dimension grows. The announced proof route is the lace expansion, a diagrammatic method that in high dimensions controls the connectivity function well enough to extract the threshold order by order. A precise critical-point expansion matters because it turns a non-perturbative lattice problem into a systematic computation and gives quantitative benchmarks for large-dimensional connectivity. The supplied full text is a different manuscript on optical skyrmions, so the derivation announced in the abstract is not present in the provided material; the summary above follows the paper's stated claim.","feed_headline":"Percolation threshold gains a systematic inverse-dimension expansion","feed_subtitle":"A lace-expansion proof expands the critical value on Z^d to arbitrary order in inverse dimension.","key_machinery":"The load-bearing object is the lace expansion, a diagrammatic expansion for the two-point function of a random spatial process: the probability that occupation spreads from one site to another is written as a sum over 'laces,' configurations of mutually intersecting paths, and in high dimensions only sufficiently sparse diagrams survive at each order. In this paper the expansion is meant to convert the non-perturbative connectivity problem for oriented percolation into a power series in $1/d$, from which the critical point can be extracted order by order. The specific lace structures and their bounds are not visible in the supplied text.","core_discovery":"The paper's central claim, stated in its abstract, is that the critical point of nearest-neighbor oriented percolation on $\\mathbb Z^d$ admits an asymptotic expansion in powers of $d^{-1}$ as $d\\to\\infty$. In this setting, each directed bond between neighboring lattice sites is open with probability $p$, and the critical value $p_c(\\mathbb Z^d)$ is the threshold below which every connected cluster dies out almost surely and above which an infinite directed cluster exists. The announcement says the proof relies heavily on the lace expansion, meaning the argument is expected to show, diagram by diagram, that the threshold differs from its leading approximation by a series of corrections suppressed by inverse powers of the dimension. No coefficients are quoted in the abstract, and the supplied full text is a different manuscript, so this paragraph records the claim as made rather than a derivation that can be inspected.","pith_inferences":["A natural extension, not claimed by the paper, is that the same order-by-order lace-expansion scheme would yield analogous $d^{-1}$ expansions for related high-dimensional stochastic models, such as the contact process, whose critical point is computed by similar diagrammatic methods.","Readers could test the asymptotic claim numerically by estimating $p_c(\\mathbb Z^d)$ for $d=5$ through $d=12$ and checking that the remainder after the leading terms shrinks at the rate predicted by the first omitted power of $d^{-1}$; agreement would support the expansion, while a stable nonvanishing remainder would put pressure on it.","Because the supplied material contains none of the derivation, the expansion's coefficients should be treated for now as announced rather than established; this caution is an editorial observation about the available text, not a finding about the mathematics."],"forward_implications":["If the expansion holds, $p_c(\\mathbb Z^d)$ can in principle be computed to any fixed order in $1/d$ by extending the lace expansion, so the threshold becomes a systematic series rather than a single limiting value.","The series makes quantitative the sense in which high-dimensional oriented percolation is close to its branching-process limit, with the gap between the two expressed as computable corrections.","The rigorous expansion supplies a calibration target for numerical simulations of oriented percolation in moderately high dimensions, where finite-size extrapolations can be checked against the asymptotic series."],"supporting_citations":[],"fun_headline_variants":["Critical point for oriented percolation gets full inverse-dimension expansion","Asymptotic series for critical percolation point proven via lace expansion","Lace expansion yields full inverse-dimension expansion for percolation threshold","Oriented percolation critical point: full expansion in 1/d"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the lace expansion converges in the high-dimensional nearest-neighbor setting and that its truncation to the required order in $1/d$ is valid; the supplied text does not include the proof of that premise.","fun_headline_variants_meta":{"raw":{"variants":["Critical point for oriented percolation gets full inverse-dimension expansion","Asymptotic series for critical percolation point proven via lace expansion","Lace expansion yields full inverse-dimension expansion for percolation threshold","Oriented percolation critical point: full expansion in 1/d"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00139,"raw_usage":{"total_tokens":5523,"prompt_tokens":741,"completion_tokens":4782,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":357,"completion_tokens_details":{"reasoning_tokens":4704}},"tokens_in":357,"tokens_out":4782,"duration_ms":35748,"temperature":1.0,"reasoning_tokens":4704,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:23:13.306452+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A concrete falsifier would be to carry the lace expansion one order beyond the paper's stopping point and exhibit a diagram whose contribution is not bounded by the claimed power of $d^{-1}$; absent such a diagram, one can also compute $p_c$ in moderately high dimensions by high-precision simulation and check whether the observed remainder matches the first omitted term of the series.","supporting_citations":[],"review_version":1}