{"id":"677581f5-c87c-41b5-82de-81c73103a735","arxiv_id":"2603.13158","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"PhaseJumps recovers zeros of complex planar functions from grid samples via phase jumps, with Wasserstein accuracy √δ and failure probability O(log²(1/δ)·δ) under a stochastic model.","lead":"PhaseJumps is an algorithm that finds zeros of complex-valued functions from samples on a planar grid by tracking phase jumps and local oscillations between neighbors. It aims to make zero-finding for short-time Fourier transforms practical for general windows, not only analytic ones, with a smoothed-analysis guarantee.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Wrong full manuscript supplied; PhaseJumps claims remain unverifiable from abstract alone.","rationale":"The reader correctly diagnosed the manuscript mismatch and set UNVERDICTED with low confidence. The strongest claim and weakest assumption extracted from the abstract are accurate given the available text. No further load-bearing technical objection to PhaseJumps itself can be raised until the correct paper is supplied; manufacturing a critique of the clustering paper under the PhaseJumps ID would be invalid. Verdict remains UNVERDICTED; agreement with the reader is full.","tokens_in":20874,"tokens_out":481,"duration_ms":11650,"concrete_test":"Replace the cached full text with the actual arXiv 2603.13158 PDF/source and re-run the Pith pass. Confirm that § on the stochastic model and the smoothed-analysis theorem state the precise algorithm variant, the noise model, and the Wasserstein/√δ bound; if those match the abstract, lift UNVERDICTED; if the bound is only for a non-STFT proxy or the model is far from STFT residuals, flag the gap.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (zeros recovered to Wasserstein accuracy √δ with failure probability O(log²(1/δ)·δ) under a stochastic model, for a PhaseJumps variant that also handles non-analytic STFT zeros) cannot be stress-tested. The CACHEABLE full text is an unrelated paper (Catanzaro–van der Hofstad–Garlaschelli, clustering without geometry, arXiv 2603.13159). Only the PhaseJumps abstract is present. That abstract asserts a smoothed-analysis guarantee for “(a variant of) PhaseJumps” but does not define the stochastic input model, state whether the bound applies to the exact STFT algorithm or a simplified proxy, or give the proof. Without those, the load-bearing conditions of the strongest claim are inaccessible; no internal inconsistency or fragile assumption inside PhaseJumps can be checked.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The submission is labeled as PhaseJumps (arXiv 2603.13158, math.NA): an algorithm that recovers zeros of complex-valued planar functions from finite grid samples by comparing phase changes and local oscillations among neighbors, works for non-analytic inputs (including general-window STFT zeros), returns phase-winding direction, and—under a stochastic model motivated by signal processing—achieves Wasserstein accuracy √δ with failure probability O(log²(1/δ)·δ) via smoothed analysis. The body of the supplied manuscript, however, is an entirely different paper (Catanzaro–van der Hofstad–Garlaschelli, clustering without geometry in sparse networks with independent edges, arXiv 2603.13159): it proves that the multi-scale / Norros–Reittu model with infinite-mean Pareto (or α-stable) fitness yields positive local clustering without geometry or higher-order edge dependence, derives the annealed clustering function, leaf/hub asymptotics, and non-self-averaging of r_{0/1} and of the average clustering coefficient.","tokens_in":21043,"tokens_out":1143,"duration_ms":19475,"significance":"If the PhaseJumps claims were substantiated, the work would be significant for numerical analysis and time-frequency analysis: a practical, non-analytic method for STFT zeros with general windows, plus a concrete smoothed-analysis rate, would remove a long-standing analytic-window restriction and make recent signal-processing insights more widely usable. Separately, the clustering manuscript that actually appears in the full text is itself a substantial contribution to network science: it rigorously shows that sparsity + strong local clustering + power-law degrees can arise from edge-independent models with infinite-mean fitness (node-aggregation invariance), without latent geometry, and it carefully characterizes non-self-averaging—directly addressing a debated implication that “clustering implies geometry.” Neither contribution can be properly credited or stress-tested under the present mismatched materials.","major_comments":[{"comment":"Title/abstract vs. full text mismatch: the abstract and paper_id describe PhaseJumps (zeros from grid samples, STFT application, smoothed-analysis Wasserstein bound √δ with failure O(log²(1/δ)·δ)), but the entire FULL MANUSCRIPT TEXT is the unrelated clustering paper (MSM/Norros–Reittu with Pareto/α-stable fitness, annealed clustering function (6), leaf/hub asymptotics (7)–(8), average clustering (10), non-self-averaging of r_{0/1}). No definition of PhaseJumps, no stochastic input model, no proof of the claimed rate, and no STFT experiments appear. The central PhaseJumps claim is therefore unverifiable from the supplied package.","section":null},{"comment":"Because the load-bearing objects for PhaseJumps (algorithm pseudocode, precise variant used in the bound, definition of the stochastic model and additive noise, Wasserstein distance on zero sets, and the smoothed-analysis argument) are absent, the performance guarantee and the “first effective means” claim for general-window STFT zeros cannot be checked for correctness, restrictiveness of assumptions, or applicability to the stated STFT setting. This is not a presentation issue; it blocks assessment of the paper as submitted under the PhaseJumps title.","section":null},{"comment":"If the intended submission were instead the clustering manuscript that occupies the full text, its main theorems (annealed clustering function, lim C̄ = 1 or 1−r_{0/1}, hub contribution vanishing, non-self-averaging via α-stable total weight S_n) appear carefully derived in the SI and supported by numerics (Figs. 1–2, S1–S8). Even then, the package would need a matching title/abstract and a clear statement that the PhaseJumps abstract is erroneous; as currently assembled, the submission is not reviewable as either paper.","section":null}],"minor_comments":[{"comment":"Abstract (PhaseJumps): the phrase “(a variant of) PhaseJumps” already flags that the proved bound may not apply to the exact algorithm used for STFT; that distinction must be made explicit once the correct manuscript is supplied.","section":null},{"comment":"Clustering full text: figure captions and some SI labels contain garbled/placeholder characters (e.g., sequences of black squares in Fig. 1 and SI figure titles), which should be cleaned for production.","section":null},{"comment":"Clustering full text: the claim that a second-moment argument would show C(k) and C̄(k) coincide w.h.p. is left unproved (footnote [38]); either prove it or clearly mark it as a conjecture.","section":null}],"recommendation":"uncertain","confidential_remarks":"The supplied package mixes the abstract of 2603.13158 (PhaseJumps) with the full text of 2603.13159 (clustering without geometry). This looks like a production/cache error rather than author misconduct, but it makes a normal technical review impossible. I recommend returning the submission to the authors (or correcting the source) and reassigning only after a consistent manuscript is provided. I have not attempted to referee PhaseJumps from the abstract alone, nor to treat the clustering paper as the official submission under the PhaseJumps title."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The package for 2603.13158 is broken. The abstract describes PhaseJumps, a grid-based phase-jump method for locating zeros of complex functions (including non-analytic ones) and, specifically, STFT zeros for general windows. It claims a smoothed-analysis guarantee: Wasserstein accuracy √δ with failure probability O(log^{2}(1/δ)·δ) under a signal-processing-motivated stochastic model. That would be useful if true; prior STFT-zero work was largely restricted to analytic windows, so a practical general-window tool plus a non-asymptotic robustness statement would matter to time-frequency people.\n\nWhat arrived as “full manuscript,” however, is the entirely different Catanzaro–van der Hofstad–Garlaschelli paper on clustering without geometry (2603.13159). No algorithm pseudocode, no definition of the stochastic model, no proof of the √δ rate, no experiments for PhaseJumps. I therefore cannot verify soundness, check whether the bound applies to the exact STFT procedure or only a proxy, or assess how restrictive the noise model is. The abstract alone is clean and non-tautological, but that is all we have.\n\nSoft spots are therefore total for the claimed contribution: everything load-bearing is missing. The clustering paper that was supplied instead looks carefully written and mathematically serious on its own topic, but that is irrelevant here.\n\nThis is for numerical analysts and signal-processing researchers who need reliable zero finders on grids. Right now it does not deserve referee time until the correct PDF is supplied. Once that happens I would re-read; until then I would not bring it to reading group or cite it.","headline":"Materials mismatch: only the PhaseJumps abstract is present; the full text is an unrelated clustering paper, so the claimed algorithm and smoothed-analysis bound cannot be checked.","tokens_in":21685,"tokens_out":466,"would_cite":false,"duration_ms":11777,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65H05","65T50","94A12"],"pacs":[],"model":"grok-4.5","headline":"PhaseJumps recovers zeros of complex-valued functions from planar grid samples by tracking phase changes between neighbors, with √δ Wasserstein accuracy and vanishing failure probability even for non-analytic inputs.","keywords":["PhaseJumps","zero finding","grid samples","complex phase","short-time Fourier transform","Wasserstein metric","smoothed analysis","non-analytic functions"],"falsifier":"Draw many independent realizations from the paper’s stochastic input model on grids of spacing δ, run the analyzed variant of PhaseJumps, and check whether the empirical Wasserstein error stays order √δ and the observed failure rate remains bounded by a constant times log²(1/δ)·δ; systematic violation of either bound falsifies the claim.","tokens_in":21720,"feed_emoji":"🌀","tokens_out":874,"duration_ms":24338,"temperature":0.7,"pith_summary":"The paper introduces PhaseJumps, an algorithm that locates the zeros of a complex-valued function given only its samples on a finite planar grid. It works by comparing how the complex phase jumps and how the function oscillates from one grid point to its neighbors, and it also returns the sense of phase winding around each detected zero. Because the method never assumes analyticity, it applies directly to the short-time Fourier transform of an analog signal under a completely general analysis window—the first practical way to extract those zeros. Under a stochastic model drawn from signal-processing noise, a variant of the algorithm is proved to return a zero set accurate to order √δ in the Wasserstein metric, with failure probability only O(log²(1/δ)·δ); the rare bad instances are fragile and are regularized by additive noise (smoothed analysis). Numerical experiments indicate still better practical rates. The result therefore removes an analyticity barrier that had limited several recent time-frequency techniques.","feed_headline":"Phase jumps find complex zeros from grid samples to √δ","feed_subtitle":"Works for non-analytic functions and unlocks general-window STFT zeros with vanishing failure rate","key_machinery":"The PhaseJumps algorithm: it detects zeros by comparing phase changes and local oscillations among neighboring grid points, simultaneously recovering the direction of phase winding.","core_discovery":"Given samples of a complex-valued function on a grid of spacing δ, PhaseJumps (or a stated variant) computes the zeros to accuracy √δ in the Wasserstein metric with failure probability O(log²(1/δ)·δ) under a signal-processing-motivated stochastic model, while also returning phase-winding directions and applying to non-analytic functions such as general-window short-time Fourier transforms.","pith_inferences":["The same local phase-jump test may extend, with suitable modifications, to higher-order zeros or to branch points of multi-valued functions sampled on grids.","If the √δ Wasserstein rate is essentially sharp under the model, it quantifies a fundamental resolution limit for zero recovery without derivative information.","Spectrogram pipelines that currently discard non-Gaussian windows can now extract and exploit zero sets that were previously inaccessible."],"forward_implications":["Zeros of the short-time Fourier transform become computable for arbitrary analysis windows, not only analytic ones.","Recent signal-processing insights that previously required analyticity can now be applied more broadly.","Pathological inputs that defeat zero recovery are shown to be fragile under additive noise, so practical spectrograms are typically well-behaved.","Both location and orientation (winding direction) of zeros are recovered from discrete samples alone."],"fun_headline_variants":["PhaseJumps finds complex zeros from δ-grid samples to √δ accuracy","Phase jumps compute non-analytic zeros and STFT zeros from grids","Grid phase jumps recover zeros to √δ with failure O(δ log²(1/δ))","PhaseJumps extracts zeros and winding from planar complex samples","Fast phase-jump zero finding works for general-window STFT grids"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The accuracy and failure-probability guarantees rest on a specific random model of the input function (motivated by signal processing) together with the claim that ordinary additive noise will smooth away the fragile bad cases.","fun_headline_variants_meta":{"raw":{"variants":["PhaseJumps finds complex zeros from δ-grid samples to √δ accuracy","Phase jumps compute non-analytic zeros and STFT zeros from grids","Grid phase jumps recover zeros to √δ with failure O(δ log²(1/δ))","PhaseJumps extracts zeros and winding from planar complex samples","Fast phase-jump zero finding works for general-window STFT grids"]},"model":"grok-4.5","effort":"low","cost_usd":0.004752,"raw_usage":{"total_tokens":1372,"prompt_tokens":774,"num_sources_used":0,"completion_tokens":100,"cost_in_usd_ticks":47520000,"prompt_tokens_details":{"text_tokens":774,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":498,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":774,"tokens_out":100,"duration_ms":4692,"temperature":1.0,"reasoning_tokens":498,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T21:51:02.455116+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Draw many independent realizations from the paper’s stochastic input model on grids of spacing δ, run the analyzed variant of PhaseJumps, and check whether the empirical Wasserstein error stays order √δ and the observed failure rate remains bounded by a constant times log²(1/δ)·δ; systematic violation of either bound falsifies the claim.","supporting_citations":[],"review_version":1}