{"id":"d4783830-b7c4-4335-9e9d-477ba70e0351","arxiv_id":"2505.14063","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"PolyDiM is a new open-source C++ library that implements Virtual Element and other polytopal discretizations for PDEs in 2D and 3D on complex meshes.","lead":"This paper presents PolyDiM, an open-source C++ library for solving partial differential equations on complex polygonal and polyhedral meshes, with a focus on the Virtual Element Method. The library is a practical toolkit for researchers working on complicated geometries such as fractured rocks and coupled soil-root systems.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim that PolyDiM is a usable open-source library is not independently verifiable from the paper: no GitHub URL, commit hash, license, or reproduction script is given, and the numerical evidence is largely drawn from prior publications.","rationale":"The reader's weakest assumption is exactly the one I consider most load-bearing: the paper claims a publicly available, functional software library, but the preprint does not contain enough information to verify that claim. The mathematical descriptions of the virtual element spaces, projections, and stabilization are standard and appear internally consistent; no fatal mathematical error emerges from the formulas as presented. The risk is therefore concentrated on the artifact: whether the released code exists, matches the paper, builds, and reproduces the reported numerical results. This is not a manufactured objection; the paper itself repeatedly makes availability claims in Section 5 without supplying the repository address, a version identifier, or a minimal reproduction script. The proposed concrete test, cloning and running the examples against reference errors and convergence rates, would settle the concern. If the code is present and runnable, the central claim is supported; if not, the paper cannot be fully accepted as a software announcement. Since this concern is the same one the reader identified and the verdict CONDITIONAL already reflects it, no change to the verdict is needed.","tokens_in":22441,"tokens_out":6314,"duration_ms":77237,"concrete_test":"Clone the repository from the GitHub link reachable at https://polydim.it/ (or directly from the GitHub page referenced in Section 5), check out the exact commit or tag corresponding to this preprint (if none exists, the claim of a matching release fails), build with the documented CMake procedure, and run the supplied example for Test 1 of [10] in two dimensions. Compare the H1 and L2 errors against the values in Figure 5 (left) and against a hand-computed manufactured solution, checking the reported convergence rates O(h^{k+1}) and O(h^k). Also run the Cook's membrane example from Section 5.2 and the Navier-Stokes example from Test 5.2 of [41] to confirm they execute without modification. If any of these steps cannot be completed using only the instructions in the paper, the central claim is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"PolyDiM's central claim is that it is an open-source C++ library implementing polytopal discretization methods, especially VEM in 2D and 3D, with the features described in Sections 3 to 5. The weakest point is not the mathematics, which is standard and correctly cited, but the existence and usability of the released artifact. Section 5.2 asserts that 'All examples are fully implemented and publicly available on GitHub,' and Section 5.1 similarly states 'All these examples are implemented and available to the reader on GitHub.' Yet the manuscript provides no repository URL, no commit or version identifier, and no license. Table 1 gives only https://polydim.it/ as a website, and the MATLAB/Python interfaces are listed as 'Upon Request.' A reader therefore cannot check whether the code used to produce Figures 5, 9, and 10 is the same as the released code, nor whether the examples build and run as claimed. Because the paper's value proposition is a software artifact, this omission makes the core claim unverifiable from the preprint alone.","agreement_with_reader":"agree"},"referee_report":null,"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe thing to know about this paper is that it is a software announcement for PolyDiM, a C++ library for virtual element methods, and the math is not the issue—it is mostly a correctly cited recap of standard VEM theory. The new contribution is the library itself, which looks like a substantive engineering effort. The soft spot is that the preprint never gives a repository URL, commit hash, or license, even though Section 5 twice says all examples are 'publicly available on GitHub.' That makes the central claim unverifiable from the preprint alone.\n\nWhat the paper does well: the design choices are sensible and clearly described—modular element-wise assembly, multiple polynomial bases (monomial, orthonormal, inertial), a DOFsManager for local-to-global mapping, integration via GeDiM, and interfaces to MATLAB/Python. The code snippets are short and readable. The numerical experiments, while mostly reproduced from the authors' prior work, do cover non-convex geometries, hanging nodes, DFNs, mixed-dimensional coupling, and a couple of external benchmarks. If the code actually builds and runs as described, this would be a useful tool for the VEM community.\n\nWhere it is soft: the missing artifact metadata is a load-bearing flaw for a software paper. A reader cannot check whether the released code matches the convergence plots, whether the examples build, or whether the MATLAB/Python interfaces exist—those are listed as 'Upon Request,' which conflicts with the abstract's promise of open-source. There are also no quantitative tables in this preprint, only convergence plots from earlier papers, so a referee cannot easily assess accuracy without digging into the cited papers. The heavy reliance on the authors' own prior work is not itself a problem, since the math is standard and the external benchmarks are cited.\n\nBottom line: the paper deserves peer review, but the referee instructions should require the authors to supply the repository URL, a commit hash, a license, and a minimal reproduction script. If the code checks out, I would cite it. As it stands, I wouldn't yet, purely because I cannot verify it. A reading group could still find it useful as a case study in software-paper reproducibility.","headline":"Software announcement with solid math but missing repository details; worth refereeing if the authors can make the artifact verifiable.","tokens_in":23149,"tokens_out":2705,"would_cite":false,"duration_ms":27481,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-07T15:40:42.421214+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}