{"id":"8c316445-b0ae-4679-9730-4bb5cbc7acac","arxiv_id":"2603.29738","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Weak interactions yield discontinuous jumps between multiply-quantized vortices; stronger interactions yield continuous mixed states; hard-wall traps keep central density while power-law traps empty the center.","lead":"The paper maps the rotational phase diagram of a quasi-2D weakly interacting Bose-Einstein condensate in power-law versus hard-wall traps. It finds that trap shape qualitatively changes whether the cloud keeps density at the center or empties it as rotation increases, with experimentally observable consequences.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified: the supplied full text is an unrelated probability paper, so the BEC phase-diagram claim cannot be stress-tested.","rationale":"The reader's diagnosis is exact: the CACHEABLE PAPER SOURCE CONTEXT contains an entirely different manuscript. Under the hard rule that one must read the actual argument in good faith, no internal soft spot of the BEC claim can be identified, because that claim is not present. The only honest output is therefore a non-finding that leaves the reader's UNVERDICTED / LOW-confidence assessment untouched. The concrete test simply restores the correct document so that a genuine second-pass review can later be performed.","tokens_in":23240,"tokens_out":408,"duration_ms":3689,"concrete_test":"Retrieve the genuine PDF or source of arXiv:2603.29738 (Kavoulakis et al.) and confirm that its body contains the GP energy functional, the power-law/hard-wall potentials, and the claimed central-density dichotomy; if the body matches the abstract, re-run the stress test on that document.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The metadata and abstract describe a quasi-2D weakly-interacting rotating BEC phase diagram (power-law vs hard-wall traps, discontinuous-to-continuous vortex transitions, central-density dichotomy). The body that was supplied, however, is Nishiyama's martingale/empirical-process paper (arXiv:2603.29739). No Gross-Pitaevskii functional, no energy minimization, no vortex ansätze, and no phase-diagram figures for the BEC problem appear. Consequently there is no load-bearing mathematical step inside the actual BEC argument that can be examined or attacked. The reader's weakest-assumption remark (mean-field quasi-2D regime) is formally correct for the abstract, but cannot be located or verified in any equation of the supplied text.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The submission metadata and abstract claim a study of the rotational phase diagram of a quasi-two-dimensional, weakly interacting Bose–Einstein condensate in power-law and hard-wall traps. The abstract asserts discontinuous transitions between multiply quantized vortex states at weak interactions, continuous transitions to mixed singly/multiply quantized states at stronger interactions, a qualitative dichotomy in central density between the two confinements, and associated scaling properties of the phase diagrams. The body of the manuscript that was supplied, however, is an unrelated probability paper (Nishiyama, arXiv:2603.29739) on oracle maximal inequalities for submartingales, finite approximation devices, infinite-dimensional Lenglart inequalities, and Donsker theorems for separable martingale random fields and empirical processes. No Gross–Pitaevskii energy functional, vortex ansätze, numerical phase diagrams, or BEC-related derivations appear.","tokens_in":23386,"tokens_out":692,"duration_ms":11267,"significance":"If the abstract’s claims were supported by a correct manuscript, the reported qualitative distinction between power-law and hard-wall traps (central density vanishing versus remaining finite) would be of genuine experimental interest for rotating ultracold gases. Because the supplied full text belongs to a different paper, none of those claims can be verified, and the scientific significance of the actual submission cannot be assessed.","major_comments":[{"comment":"Title, abstract and arXiv identifier (2603.29738, cond-mat.quant-gas) describe a BEC phase-diagram paper, yet the entire body (Sections 1–5, Lemmas 4–8, Theorems 10–18, Appendix) is the unrelated martingale/empirical-process manuscript arXiv:2603.29739. No energy functional, rotation term, vortex trial wave functions, or phase-diagram figures for the claimed BEC problem are present. The central scientific claims of the abstract are therefore unsupported by any verifiable derivation or data in the submitted text.","section":null},{"comment":"Because the body does not treat rotating BECs, the load-bearing assertions of the abstract—discontinuous-to-continuous transition with interaction strength, the hard-wall versus power-law central-density dichotomy, and the claimed scaling properties—cannot be checked for correctness, completeness of the mean-field regime, or experimental observability. A referee report on the physics content is impossible until the correct manuscript is supplied.","section":null}],"minor_comments":[{"comment":"The supplied text itself (the probability paper) contains ordinary presentation issues (occasional typographical slips such as “puseudomentirc”, “indistinguishability” conventions, and dense notation), but these are irrelevant to the BEC submission under review.","section":null}],"recommendation":"reject","confidential_remarks":"The mismatch between metadata/abstract (BEC phase diagram) and full text (martingale inequalities) appears to be a systematic packaging or caching error rather than an authorial attempt to submit the wrong paper. The authors should be asked to resubmit the correct PDF of arXiv:2603.29738; until then the manuscript is not reviewable. I have not attempted to evaluate the probability paper on its own merits, as that is outside the stated scope of this review."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The arXiv number, title and abstract point to a quasi-2D mean-field study of rotating BECs in power-law versus hard-wall traps, claiming discontinuous-to-continuous vortex transitions and a clean central-density diagnostic that distinguishes the two confinements. That contrast, if real, would be a useful experimental handle and a modest organizational advance inside an already well-mapped subfield.\n\nWhat actually arrived as the full text is Nishiyama’s paper on oracle maximal inequalities, finite approximation of martingale random fields, and Donsker theorems without entropy assumptions. The math there looks carefully done: the OMIs via integration by parts, the finite-approximation device, the infinite-dimensional Lenglart inequality, and the resulting CLTs for separable fields are all spelled out with explicit proofs. Citations are standard and the technical development is coherent on its own terms.\n\nNone of that material, however, contains a Gross-Pitaevskii functional, a vortex ansatz, an energy minimization, or a phase diagram. Consequently the BEC claims—scaling properties, the discontinuous-versus-continuous transition, the central-density dichotomy—sit unsupported. The weakest assumption flagged by the reader (strict quasi-2D weak-interaction regime) cannot even be located, let alone stress-tested.\n\nUntil the correct manuscript is supplied, the BEC work cannot be evaluated for soundness or novelty beyond the abstract’s self-description. The probability paper is a different object and should be judged separately. For the stated title I would not bring it to reading group, would not cite it, and would not send it to referees in its present mismatched state. If the real BEC manuscript appears and matches the abstract, it would then deserve a normal condensed-matter referee look.","headline":"Metadata and abstract describe a rotating-BEC vortex phase diagram, but the supplied body is an unrelated martingale paper; nothing in the BEC claims can be checked.","tokens_in":23987,"tokens_out":454,"would_cite":false,"duration_ms":12258,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Power-law and hard-wall traps produce opposite central-density behavior in rotating Bose-Einstein condensates as rotation frequency rises.","keywords":["Bose-Einstein condensate","rotating condensate","vortex phase diagram","power-law trap","hard-wall trap","multiply quantized vortices","quasi-two-dimensional"],"falsifier":"Measure the central column density of a rotating quasi-two-dimensional condensate while ramping rotation frequency: hard-wall confinement must keep finite central density at the first instability, while power-law confinement must empty the center; any opposite behavior falsifies the claimed dichotomy.","tokens_in":24119,"feed_emoji":"🌀","tokens_out":598,"duration_ms":9743,"temperature":0.7,"pith_summary":"This paper maps the rotational phase diagram of a quasi-two-dimensional, weakly interacting Bose-Einstein condensate in two families of traps: smooth power-law potentials and hard-wall containers. At weak interactions the condensate jumps discontinuously between multiply quantized vortex states as the trap rotation frequency is raised. Stronger interactions turn those jumps into continuous transitions into mixed states that combine singly and multiply quantized vortices. The central, experimentally accessible distinction is that hard-wall traps always destabilize first into states that keep nonzero density at the origin, while power-law traps empty the center as rotation increases. The two confinement types also produce distinct scaling laws that collapse their respective phase diagrams.","feed_headline":"Hard-wall traps keep the center full; power-law traps empty it","feed_subtitle":"Rotating Bose condensates show opposite central-density behavior under the two confinements","key_machinery":"The rotational energy functional (or equivalent mean-field Gross-Pitaevskii description) of a quasi-two-dimensional condensate in a rotating frame, whose minimization with respect to vortex multiplicity and density profile produces the phase boundaries and the central-density dichotomy.","core_discovery":"In the weakly interacting, quasi-two-dimensional regime the rotational phase diagram of a Bose-Einstein condensate is qualitatively different under power-law versus hard-wall confinement: hard-wall traps always lose stability first to states with finite central density, whereas power-law traps drive the density at the origin to zero with increasing rotation frequency; weak interactions produce discontinuous transitions between multiply quantized vortices, while stronger interactions produce continuous transitions into mixed singly- and multiply-quantized states, and each confinement class yields its own scaling properties for the phase diagram.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Hard-wall traps retain center density; power-law ones empty it","Power-law traps drive BEC density to zero at the origin","Confinement flips central-density fate in rotating condensates","Weak interactions trigger jumps between multiquantized vortices","Hard-wall versus power-law traps produce opposite phase diagrams"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"Everything is calculated inside the quasi-two-dimensional, weakly interacting mean-field regime; if three-dimensional excitations or strong-interaction corrections become important the predicted transitions and central-density contrast can change.","fun_headline_variants_meta":{"raw":{"variants":["Hard-wall traps retain center density; power-law ones empty it","Power-law traps drive BEC density to zero at the origin","Confinement flips central-density fate in rotating condensates","Weak interactions trigger jumps between multiquantized vortices","Hard-wall versus power-law traps produce opposite phase diagrams"]},"model":"grok-4.5","effort":"low","cost_usd":0.006836,"raw_usage":{"total_tokens":1682,"prompt_tokens":718,"num_sources_used":0,"completion_tokens":87,"cost_in_usd_ticks":68360000,"prompt_tokens_details":{"text_tokens":718,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":877,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":718,"tokens_out":87,"duration_ms":6635,"temperature":1.0,"reasoning_tokens":877,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-13T15:34:38.595285+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure the central column density of a rotating quasi-two-dimensional condensate while ramping rotation frequency: hard-wall confinement must keep finite central density at the first instability, while power-law confinement must empty the center; any opposite behavior falsifies the claimed dichotomy.","supporting_citations":[],"review_version":1}