{"id":"0b4bea53-0f4e-485b-9c63-74b82af17883","arxiv_id":"2603.13727","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"CoSR discovers physical laws via progressive chains of symbolic knowledge units, recovering Kepler-to-Newton and improving scaling laws in convection, pipe flow, laser-metal interaction, and aircraft aerodynamics.","lead":"The paper introduces Chain of Symbolic Regression (CoSR), a framework that discovers physical laws by building them progressively as chains of simple symbolic units rather than in one end-to-end step. This aims to produce more interpretable, generalizable expressions that match how science historically builds from simple to complex laws.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Manuscript mismatch leaves CoSR's central progressive-discovery claim uncheckable; only the abstract is present.","rationale":"The Reader correctly diagnosed that only the abstract of the target paper is available and that the body belongs to a different work; the resulting UNVERDICTED / low-confidence assessment is therefore the only defensible stance. No additional internal inconsistency can be diagnosed because the algorithmic and experimental sections are simply absent. Once the correct manuscript appears the same weakest-assumption test (necessity and sufficiency of a fixed hierarchical chain) can be re-applied to the concrete examples; until then the verdict must stay UNVERDICTED.","tokens_in":36529,"tokens_out":394,"duration_ms":11937,"concrete_test":"Retrieve the genuine PDF of arXiv:2603.13727; extract the exact symbolic chain claimed for Kepler\to Newton and recompute the intermediate expressions on the same orbital data. If the recovered units do not match the classical progression or if the final expression fails to reduce to GMm/r^{2} under the stated logic, the central recapitulation claim collapses.","verdict_should_be":"UNVERDICTED","load_bearing_attack":"The strongest claim (CoSR forms a chain of physically meaningful symbolic units that recapitulates Kepler\to Newton and improves scaling laws) rests entirely on the abstract. The supplied full-text body is an unrelated CHI '26 UX/CA study (arXiv 2603.13717). Consequently every empirical assertion—successful recovery of the gravitational law, improved Rayleigh–Bénard / pipe-flow / laser-metal scalings, and new aircraft aerodynamic coefficients—cannot be inspected for method, data, intermediate expressions, or ablation. The motivating premise that physical laws universally admit a fixed hierarchical chain of discrete knowledge units therefore remains an untested assertion rather than a demonstrated algorithmic property.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The abstract proposes Chain of Symbolic Regression (CoSR), a framework that discovers physical laws by progressively combining discrete symbolic knowledge units with clear physical meanings, rather than one-shot end-to-end symbolic regression. It claims to recapitulate the historical path from Kepler’s third law to Newton’s law of universal gravitation, to improve classical scaling relations for turbulent Rayleigh–Bénard convection, pipe flow, and laser–metal interaction, and to discover new aerodynamic-coefficient scalings for aircraft. The supplied full manuscript body, however, is an entirely unrelated CHI ’26 multi-session HCI study of UX evaluators collaborating with novice versus experienced conversational AI assistants (arXiv:2603.13717). Consequently no methods, algorithms, intermediate expressions, datasets, error metrics, baselines, or ablations for CoSR are present.","tokens_in":36693,"tokens_out":671,"duration_ms":13810,"significance":"If the progressive-chain idea were correctly implemented and validated, CoSR would address a recognized failure mode of conventional symbolic regression (lengthy, unphysical expressions with poor generalization) and would constitute a meaningful methodological contribution to data-driven scientific discovery. The historical Kepler-to-Newton reconstruction and the claimed improvements to classical scaling laws would be especially valuable if independently recovered from data. None of these contributions can be assessed from the manuscript as supplied.","major_comments":[{"comment":"The full text provided under the CoSR title and abstract is the complete, unrelated CHI ’26 paper “It Became My Buddy, But I’m Not Afraid to Disagree” (arXiv:2603.13717). No section, equation, algorithm, figure, or table belonging to CoSR appears. Every empirical claim in the abstract—recovery of the gravitational law, improved Rayleigh–Bénard / pipe-flow / laser-metal scalings, and new aircraft aerodynamic coefficients—is therefore uninspectable.","section":null},{"comment":"Because the method body is absent, it is impossible to determine whether the “knowledge units” and the “specific logic” that combine them are recovered from data or are seeded by the same classical knowledge the method claims to rediscover. This circularity risk, already flagged by the abstract’s motivating premise, cannot be evaluated.","section":null},{"comment":"No datasets, intermediate symbolic expressions, quantitative error metrics, baselines (e.g., standard genetic-programming or sparse-regression SR), or ablation studies are supplied. The central claim that progressive chaining overcomes the unphysical expressions of one-step SR therefore rests solely on an unsupported abstract.","section":null}],"minor_comments":[{"comment":"The arXiv identifier printed in the body (2603.13717) does not match the identifier under review (2603.13727), confirming a manuscript-swap error.","section":null}],"recommendation":"reject","confidential_remarks":"The submission appears to be a complete manuscript mismatch (wrong PDF attached to the CoSR abstract). This is a desk-rejectable administrative error rather than a scientific flaw that can be repaired by revision of the present text. The authors should be asked to resubmit the correct CoSR manuscript; only then can a technical review proceed."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The situation is simple: the title and abstract describe Chain of Symbolic Regression (CoSR)—progressive composition of physically meaningful symbolic units, Kepler-to-Newton recovery, improved scalings in Rayleigh–Bénard, pipe flow, laser–metal interaction, and new aircraft aerodynamic coefficients. The body you were given is a different paper entirely (CHI multi-session study of UX evaluators with novice/experienced conversational assistants). So this is not an abstract-only review by choice; the manuscript for 2603.13727 is not present.\n\nFrom the abstract alone, the idea is clear and useful if true. Conventional one-shot symbolic regression often produces long, unphysical expressions; framing discovery as a chain of intermediate knowledge units with physical meaning is a sensible response, and the listed application domains matter for reduced-order modeling. Recapitulating Kepler → gravity is a strong sanity check if they actually show intermediate expressions and data, not just a narrative.\n\nNone of that can be verified here. No algorithm, no intermediate units, no datasets, no error metrics, no baselines, no ablations. The load-bearing premise—that physical laws admit a fixed hierarchical chain of discrete symbolic units that is necessary and sufficient to fix one-step SR—remains an assertion. There is also a real circularity risk: whether the “knowledge units” are recovered from data or seeded by the classical theories the method claims to improve. That is not a minor quibble; it is the whole claim.\n\nWho is this for? Symbolic regression and AI-for-science people who care about progressive / hierarchical discovery. Right now they get a pitch, not a paper. I would not bring this to reading group or cite it until the real CoSR manuscript appears. A serious editor should not send this package to referees; they should request the correct full text. If that text delivers the intermediate expressions, quantitative improvements over classical scalings, and honest ablations, then yes—it would deserve a full review. As submitted, it does not.","headline":"We only have the CoSR abstract; the supplied full text is an unrelated CHI UX paper, so every progressive-discovery claim is uncheckable.","tokens_in":37247,"tokens_out":503,"would_cite":false,"duration_ms":15684,"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":"Physical laws are recovered from data by chaining simple, meaningful symbolic units rather than inventing one long expression at once.","keywords":["symbolic regression","physical law discovery","progressive knowledge chain","scaling laws","interpretable machine learning","scientific discovery","aerodynamic coefficients"],"falsifier":"Apply CoSR and a standard one-step symbolic regressor to a system whose progressive discovery path is already known (for example the Kepler-to-Newton sequence) and check whether CoSR alone recovers the intermediate units and the final law while the one-step method produces only lengthy unphysical expressions.","tokens_in":37421,"feed_emoji":"🔗","tokens_out":514,"duration_ms":10978,"temperature":0.7,"pith_summary":"Conventional symbolic regression tries to invent a complete mathematical law in a single step and often produces long, unphysical formulas that fail to generalize. The paper argues that real physical discovery proceeds hierarchically, from simple relations to more complex ones, and therefore models discovery itself as a progressive chain of symbolic knowledge units that each carry clear physical meaning. By combining these units step by step along a logical path, the method recovers known laws (Kepler to Newton) and improves classical scaling relations in fluid and laser problems, while also extracting new scaling knowledge for aircraft aerodynamics. A sympathetic reader cares because the approach restores interpretability and generalization precisely where pure end-to-end search collapses into meaningless expressions.","feed_headline":"Laws emerge by chaining simple symbols, not one long formula","feed_subtitle":"CoSR recovers Kepler-to-Newton and improves scaling theories by building physical meaning step by step","key_machinery":"Chain of Symbolic Regression (CoSR): a progressive sequence of symbolic knowledge units that are combined along a fixed logical path, each unit remaining physically interpretable.","core_discovery":"The authors claim that physical laws do not appear as monolithic expressions but as hierarchical chains; their Chain of Symbolic Regression therefore discovers them by successively assembling discrete knowledge units that already possess clear physical meanings, ultimately recovering the correct underlying law from data.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Physical laws emerge as chains of simple symbolic units","CoSR assembles hierarchical knowledge units into true laws","From Kepler to Newton: progressive symbolic discovery works","Chaining meaningful symbols recovers physics from data","Laws form step by step not as one long expression"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"The claim rests on the premise that every physical law of interest can be broken into a fixed hierarchy of simple, physically meaningful symbolic units whose progressive combination is both necessary and sufficient to recover the true law.","fun_headline_variants_meta":{"raw":{"variants":["Physical laws emerge as chains of simple symbolic units","CoSR assembles hierarchical knowledge units into true laws","From Kepler to Newton: progressive symbolic discovery works","Chaining meaningful symbols recovers physics from data","Laws form step by step not as one long expression"]},"model":"grok-4.5","effort":"low","cost_usd":0.004868,"raw_usage":{"total_tokens":1338,"prompt_tokens":742,"num_sources_used":0,"completion_tokens":74,"cost_in_usd_ticks":48680000,"prompt_tokens_details":{"text_tokens":742,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":522,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":742,"tokens_out":74,"duration_ms":4115,"temperature":1.0,"reasoning_tokens":522,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T21:41:06.150457+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Apply CoSR and a standard one-step symbolic regressor to a system whose progressive discovery path is already known (for example the Kepler-to-Newton sequence) and check whether CoSR alone recovers the intermediate units and the final law while the one-step method produces only lengthy unphysical expressions.","supporting_citations":[],"review_version":1}