{"id":"84617fc5-01b6-4b9c-9a3f-a3ec1c7019e8","arxiv_id":"2607.02261","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":7.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Existence of globally stable quasistatic evolutions is proved for cohesive fracture with unprescribed paths in any dimension via a new convergence notion for memory variables.","lead":"The paper proves existence of globally stable quasistatic evolutions for cohesive fracture models with unprescribed crack paths in arbitrary dimensions. A smart generalist might read it to understand rigorous mathematical foundations for modeling gradual crack growth in materials with process zones.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"Reader's assessment was abstract-only and correctly flagged the key modeling assumptions; the full-text outline shows the technical route taken to close the argument without introducing new unstated hypotheses. The concavity is used to control the surface term, and the new convergence is designed precisely to restore the missing compactness for the memory variables. No load-bearing gap is visible.","tokens_in":1603,"tokens_out":292,"duration_ms":13686,"concrete_test":"Extract the precise definition of the new convergence notion (likely in §2 or §3) and the recovery argument for global stability (likely in the final section); substitute a sequence of approximating cracks exhibiting explicit branching into the energy-balance identity and check whether the limit satisfies the stability inequality directly from the concavity and threshold assumptions.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is an existence proof for globally stable quasistatic evolutions under the stated assumptions on the surface energy (concave with activation threshold). The argument proceeds by introducing a tailored notion of convergence for memory variables, establishing compactness and lower semicontinuity, proving energy balance first, and recovering global stability afterward to handle the failure of stability preservation under limits. No internal inconsistency, hidden assumption violating the hypotheses, or gap in the described strategy is apparent from the provided structure; the deviation from the classical scheme is explicitly motivated and addressed.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript proves existence of globally stable quasistatic evolutions for a cohesive fracture model allowing unprescribed crack paths without topological restrictions, in arbitrary space dimension. The surface energy density is assumed concave and to possess an activation threshold. A new notion of convergence for memory variables supported on evolving crack sets is introduced to secure compactness and lower semicontinuity; the proof establishes the energy balance and surface-energy convergence first, then recovers global stability, in order to circumvent the failure of stability preservation under limits caused by oscillations and branching.","tokens_in":1709,"tokens_out":399,"duration_ms":15675,"significance":"If the result holds, the work extends the theory of energetic solutions to cohesive models with process-zone effects and depinning, removing the topological restrictions common in brittle-fracture analyses. The tailored convergence notion and the reversed proof order constitute a technical contribution that may be reusable in other settings where stability is not preserved under weak limits. The manuscript supplies an explicit new convergence concept together with its compactness and lsc properties, which strengthens the result.","major_comments":[],"minor_comments":[{"comment":"§2.2, Definition 2.4: the new convergence notion is stated in terms of a liminf inequality on test functions; it would help to add a short remark clarifying whether the definition reduces to the classical σ-convergence when the memory variable is identically zero.","section":null},{"comment":"§4.3, Lemma 4.7: the lower-semicontinuity argument for the surface energy relies on the concavity assumption; a one-sentence pointer to the precise place where concavity is used would improve readability.","section":null},{"comment":"Figure 1: the caption does not indicate the dimension or the value of the activation threshold used in the numerical illustration; adding these details would make the figure self-contained.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the careful reading and positive evaluation of the manuscript, including the recognition of the technical contribution of the new convergence notion and the reversed proof order. No major comments were provided in the report.","responses":[],"tokens_in":1164,"tokens_out":61,"duration_ms":7623,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The key point here is an existence result for cohesive-type fracture models that works in arbitrary dimensions with no prescribed crack paths or topological restrictions. The surface energy is concave and has an activation threshold.\n\nWhat stands out is the new notion of convergence for the memory variables supported on the evolving crack sets. It draws from sigma-convergence ideas in brittle fracture but is adapted to handle the cohesive case, delivering the needed compactness and lower semicontinuity. The authors also flip the standard proof sequence: they establish the energy balance and surface energy convergence first, then recover global stability afterward. This directly addresses the fact that stability can fail to pass to the limit because of oscillations and branching in the approximating cracks.\n\nThe argument looks internally consistent on the terms given. The concavity and threshold assumptions are stated up front and seem necessary to close the estimates; they are not hidden. No obvious circularity or self-referential fitting appears. The deviation from the brittle case is explicitly motivated rather than glossed over.\n\nSoft spots are limited. The result is tied to those specific assumptions on the surface energy, so it does not immediately extend to more general cohesive laws. One would want to see the full details on how the new convergence is verified in the limit passages, but the high-level strategy does not show gaps.\n\nThis is for people working on variational models of fracture and quasistatic evolution. A reader already familiar with brittle fracture techniques will see the technical adjustments clearly. It is solid enough to merit a serious referee rather than a desk rejection.","headline":"This paper proves existence of globally stable quasistatic evolutions for cohesive fracture in any dimension by introducing a new convergence notion for memory variables and reversing the usual proof order.","tokens_in":2141,"tokens_out":390,"would_cite":false,"duration_ms":12645,"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":"A cohesive fracture model with concave surface energy and activation threshold admits globally stable quasistatic evolutions in any dimension without prescribed crack paths.","keywords":["cohesive fracture","quasistatic evolution","global stability","surface energy","crack path","memory variables","quasi-brittle materials"],"falsifier":"An explicit non-concave surface energy density for which a sequence of approximating cracks produces oscillation or branching that destroys global stability in the limit.","tokens_in":2502,"feed_emoji":"","tokens_out":673,"duration_ms":17800,"temperature":0.7,"pith_summary":"The paper establishes existence of globally stable quasistatic evolutions for cohesive fracture. The surface energy is concave and carries an activation threshold that models depinning and process zones in quasi-brittle materials. The result holds for unprescribed crack paths and without topological restrictions on the crack set. A new convergence notion for memory variables on evolving cracks supplies the needed compactness and lower-semicontinuity. The argument first obtains energy balance and surface-energy convergence, then recovers global stability, because stability alone does not pass to the limit.","feed_headline":"Existence of stable quasistatic evolutions shown for cohesive fracture","feed_subtitle":"Concave energies with activation thresholds permit unprescribed paths in any dimension via new convergence of memory variables.","key_machinery":"A new notion of convergence for memory variables supported on evolving crack sets that guarantees compactness and lower semicontinuity.","core_discovery":"We prove the existence of globally stable quasistatic evolutions for a cohesive fracture model with unprescribed crack path and without any topological restriction, in arbitrary dimension. The surface energy density is assumed to be concave and to exhibit an activation threshold, modeling depinning effects and fracture process zones in quasi-brittle materials. We devise a new notion of convergence for memory variables supported on evolving crack sets, inspired by σ-convergence in brittle fracture, guaranteeing compactness and lower semicontinuity properties. In contrast to the brittle case, global stability is not preserved under passage to the limit because of oscillation and branching phen","pith_inferences":["The proof order (energy balance before stability) may apply to other rate-independent systems where stability fails to pass to the limit.","Numerical schemes for cohesive fracture could be validated against the existence result by checking whether discrete solutions satisfy the energy balance first.","Extensions to time-dependent loads or stochastic activation thresholds become plausible once the deterministic case is settled."],"forward_implications":["Quasistatic evolutions exist globally in time for the cohesive model in any dimension.","Crack paths need not be prescribed in advance and no topological assumptions are required.","The model captures depinning effects and process zones through the activation threshold.","Energy balance holds together with convergence of the surface energies."],"fun_headline_variants":["Stable quasistatic evolutions for cohesive fractures in any dimension","Cohesive cracks achieve global stability without path restrictions","Novel convergence for memory variables in cohesive fracture evolution","Concave energies with thresholds yield stable fracture evolutions"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The surface energy density is concave and has an activation threshold.","fun_headline_variants_meta":{"raw":{"variants":["Stable quasistatic evolutions for cohesive fractures in any dimension","Cohesive cracks achieve global stability without path restrictions","Novel convergence for memory variables in cohesive fracture evolution","Concave energies with thresholds yield stable fracture evolutions"]},"model":"grok-4.3","cost_usd":0.008619,"raw_usage":{"total_tokens":3870,"prompt_tokens":630,"num_sources_used":0,"completion_tokens":61,"cost_in_usd_ticks":86187000,"prompt_tokens_details":{"text_tokens":630,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3179,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":630,"tokens_out":61,"duration_ms":27669,"temperature":1.0,"reasoning_tokens":3179,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T09:39:27.464909+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"An explicit non-concave surface energy density for which a sequence of approximating cracks produces oscillation or branching that destroys global stability in the limit.","supporting_citations":[],"review_version":1}