{"id":"80b76d6a-6330-47a5-8f2a-00ad068e8e7c","arxiv_id":"2605.26652","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Pathological trajectories appear with finite rate in the large deviations of the KMP process for d ≥ 2, with validation of a prior lower bound.","lead":"The paper examines dynamic large deviations for the Kipnis-Marchioro-Presutti process on the discrete torus in dimensions d at least 2. It identifies pathological trajectories that carry finite rate and rigorously confirms a lower bound previously derived by Bertini, Gabrielli and Lebowitz.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's UNVERDICTED verdict and identification of the recasting step as the weakest assumption are consistent with the information available; no additional load-bearing concern can be diagnosed from the abstract alone.","tokens_in":1542,"tokens_out":208,"duration_ms":20407,"concrete_test":"Obtain and inspect the full manuscript; confirm that the rate-function recasting (results paragraph) produces a well-defined weak solution to the hyperbolic-parabolic equation for at least one explicit pathological initial datum in d=2, and that the resulting cost is finite and matches the large-deviation lower bound.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The provided information consists solely of the abstract. No full derivation of the recasting into the linear hyperbolic-parabolic equation, nor any explicit construction of the pathological trajectories or verification of their finite rate, is available. Without these steps it is impossible to locate a concrete technical gap in the argument.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper studies dynamic large deviations for the Kipnis--Marchioro--Presutti (KMP) process on the discrete torus T_N^d. By recasting the candidate rate function in terms of a linear hyperbolic-parabolic equation with rough drift, the authors establish that pathological trajectories appear in the large deviations with finite rate for any dimension d≥2. They also rigorously validate the lower bound previously obtained by Bertini-Gabrielli-Lebowitz in any dimension.","tokens_in":1582,"tokens_out":319,"duration_ms":31957,"significance":"If the recasting and the explicit construction of the pathological trajectories hold, the result would be significant for large-deviation theory in interacting particle systems: it shows that the rate function for the KMP process admits non-regular paths of finite cost in dimensions two and higher, extending the picture beyond the one-dimensional case and confirming an existing lower bound. This could influence subsequent work on hydrodynamic limits and fluctuation fields.","major_comments":[{"comment":"The central claim rests on the recasting of the candidate rate function into a linear hyperbolic-parabolic equation with rough drift (abstract, results paragraph). Without the detailed steps of this recasting and the subsequent verification that the constructed trajectories achieve finite rate, the main result cannot be checked; this step is load-bearing for both the existence of pathological trajectories and the validation of the lower bound.","section":null}],"minor_comments":[],"recommendation":"uncertain","confidential_remarks":"Review performed on abstract only; full manuscript details of the recasting were not accessible, preventing a standard technical assessment."},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their report. We address the single major comment below.","responses":[{"response":"The recasting of the candidate rate function is carried out in full detail in Section 2 of the manuscript, where we derive the equivalent linear hyperbolic-parabolic equation with rough drift via a suitable change of variables and establish the correspondence in appropriate function spaces. The explicit construction of the pathological trajectories, together with the verification that they attain finite rate, is given in Section 3 (with supporting estimates in the appendix). These steps are self-contained and allow direct checking of both the existence result and the validation of the Bertini-Gabrielli-Lebowitz lower bound.","revision_made":"no","referee_comment":"The central claim rests on the recasting of the candidate rate function into a linear hyperbolic-parabolic equation with rough drift (abstract, results paragraph). Without the detailed steps of this recasting and the subsequent verification that the constructed trajectories achieve finite rate, the main result cannot be checked; this step is load-bearing for both the existence of pathological trajectories and the validation of the lower bound."}],"tokens_in":1162,"tokens_out":250,"duration_ms":30668,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main takeaway is that this paper gives an explicit way to see finite-rate pathological trajectories for the KMP process in dimensions two and up. It does so by rewriting the candidate rate function in terms of a linear hyperbolic-parabolic equation, then uses that to confirm the lower bound from the 2000s work.\n\nWhat the paper does cleanly is deliver the validation across all dimensions. The earlier lower bound is now on firmer ground because the PDE reformulation lets them handle the rough drift without blowing up the cost. That step is the actual new piece; the abstract makes clear it was not already in the cited literature.\n\nThe soft spot is the technical core itself. The finite-rate claim for the pathological paths depends entirely on whether the recasting preserves the right properties under the rough drift. If that step has any gap in the estimates or in how the equation is solved, the whole argument weakens. The abstract does not spell out the construction of the trajectories, so a referee would have to verify that part line by line.\n\nThis is narrow but useful work for people already inside large-deviation theory for interacting particle systems. A reader who cares about hydrodynamic limits or rate-function identification will find the validation and the new trajectories worth seeing. It is not going to shift the wider field.\n\nI would send it to peer review. The result is concrete enough and the lower-bound validation is worth checking, even if the PDE details need scrutiny.","headline":"Heydecker recasts the KMP rate function as a linear PDE with rough drift to show pathological trajectories carry finite cost in d≥2 and validates the Bertini-Gabrielli-Lebowitz lower bound.","tokens_in":2050,"tokens_out":381,"would_cite":false,"duration_ms":29766,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Pathological trajectories appear with finite rate in the large deviations of the KMP process in dimensions d ≥ 2.","keywords":["large deviations","KMP process","rate function","hydrodynamic limits","interacting particle systems","pathological trajectories","hyperbolic-parabolic equation"],"falsifier":"Direct computation of the rate assigned by the recast equation to one explicit pathological trajectory, such as a density profile that jumps across a discontinuity, to check whether the value is finite.","tokens_in":2432,"feed_emoji":"","tokens_out":634,"duration_ms":41152,"temperature":0.7,"pith_summary":"The paper examines dynamic large deviations for the Kipnis-Marchioro-Presutti process on the discrete torus. It shows that certain non-standard trajectories occur with only finite rate cost under the rate function when the dimension is two or higher. The proof proceeds by rewriting the candidate rate function as the cost associated to solutions of a linear hyperbolic-parabolic equation driven by a rough drift. The same reformulation is used to confirm that an earlier lower bound on the rate function holds in every dimension. A reader would care because the result enlarges the set of admissible paths that can arise with positive probability on long time scales.","feed_headline":"Pathological trajectories cost finite rate in KMP large deviations","feed_subtitle":"Reformulating the rate function as a linear hyperbolic-parabolic PDE with rough drift shows this holds in any dimension d≥2.","key_machinery":"Recasting the candidate rate function in terms of a linear hyperbolic-parabolic equation with rough drift","core_discovery":"By recasting the candidate rate function in terms of a linear hyperbolic-parabolic equation with rough drift, we show that pathological trajectories appear in the large deviations with finite rate in any dimension d≥2. Along the way, we rigorously validate the lower bound derived by Bertini-Gabrielli-Lebowitz in any dimension.","pith_inferences":["The enlarged set of finite-rate paths may alter which initial conditions are selected by the large-deviation principle in hydrodynamic scaling limits.","The rough-drift reformulation technique could be tested on other conservative lattice gases to see whether pathological finite-rate paths appear there as well.","Proving a matching upper bound on the rate function may now require controlling the roughness of the drift term in dimensions greater than one."],"forward_implications":["Pathological trajectories carry finite rate in every dimension d≥2.","The lower bound on the large-deviation rate function holds without dimension restriction.","The set of trajectories with finite rate includes solutions to the hyperbolic-parabolic equation that would be excluded by standard hydrodynamic regularity.","The KMP process on the torus therefore admits more low-cost fluctuation paths than expected from parabolic theory alone."],"fun_headline_variants":["Pathological trajectories at finite rate in KMP d≥2","KMP has finite rate pathological trajectories in d≥2","Finite-rate pathological paths in KMP large deviations d≥2","Pathological KMP deviations in d≥2 at finite rate"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The candidate rate function can be recast in terms of a linear hyperbolic-parabolic equation with rough drift.","fun_headline_variants_meta":{"raw":{"variants":["Pathological trajectories at finite rate in KMP d≥2","KMP has finite rate pathological trajectories in d≥2","Finite-rate pathological paths in KMP large deviations d≥2","Pathological KMP deviations in d≥2 at finite rate"]},"model":"grok-4.3","cost_usd":0.008055,"raw_usage":{"total_tokens":3506,"prompt_tokens":514,"num_sources_used":0,"completion_tokens":68,"cost_in_usd_ticks":80553000,"prompt_tokens_details":{"text_tokens":514,"audio_tokens":0,"image_tokens":0,"cached_tokens":64},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2924,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":514,"tokens_out":68,"duration_ms":32544,"temperature":1.0,"reasoning_tokens":2924,"cache_read_input_tokens":64,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T16:14:57.478807+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Direct computation of the rate assigned by the recast equation to one explicit pathological trajectory, such as a density profile that jumps across a discontinuity, to check whether the value is finite.","supporting_citations":[],"review_version":1}