{"paper":{"title":"The Directed Abelian Sandpile Model on Cylinders","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"The sandpile group on a directed cylindrical lattice reduces exactly to a transverse problem.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Abdul Quadir, Nikita Kalinin, Ram Ramaswamy","submitted_at":"2026-05-15T12:52:20Z","abstract_excerpt":"We study the abelian sandpile model in two dimensions on a directed cylindrical lattice with periodic transverse boundary conditions in the transverse direction and dissipation at one boundary. Recurrent configurations form a finite abelian group, and repeated grain addition at a specific site generates deterministic dynamics on this group. Using Dhar's formulation, the sandpile group is identified with the co-kernel of the reduced directed Laplacian. We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The directed cylindrical lattice with periodic transverse boundary conditions and dissipation at one boundary permits an exact reduction of the sandpile group to a purely transverse problem without residual longitudinal contributions (as invoked when applying Dhar's formulation to identify the group with the co-kernel of the reduced directed Laplacian).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The sandpile group on directed cylinders reduces exactly to a transverse problem, fully determining its cyclic decomposition and linking it to the periodicity of driven dynamics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The sandpile group on a directed cylindrical lattice reduces exactly to a transverse problem.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8800a32d09f702bca72d8c02fdcecabda4bedee9d741260534a0595960d1ca8f"},"source":{"id":"2605.15914","kind":"arxiv","version":1},"verdict":{"id":"ed7e6801-5bd2-4cac-b02c-e3baa8689c7c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:08:05.762728Z","strongest_claim":"We show that the group structure admits an exact reduction to a transverse problem, allowing complete determination of its cyclic decomposition.","one_line_summary":"The sandpile group on directed cylinders reduces exactly to a transverse problem, fully determining its cyclic decomposition and linking it to the periodicity of driven dynamics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The directed cylindrical lattice with periodic transverse boundary conditions and dissipation at one boundary permits an exact reduction of the sandpile group to a purely transverse problem without residual longitudinal contributions (as invoked when applying Dhar's formulation to identify the group with the co-kernel of the reduced directed Laplacian).","pith_extraction_headline":"The sandpile group on a directed cylindrical lattice reduces exactly to a transverse problem."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15914/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.060209Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:21:19.829262Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:46.556475Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:01:55.759241Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"5219f6a0830c0aacb085314a02a0b6e6ca82d0014cda5410423fc7ea29095e02"},"references":{"count":14,"sample":[{"doi":"","year":null,"title":"In particu- lar, odd and even transverse widths lead to qualitatively different algebraic structures","work_id":"298fbb2a-1557-4cb2-9530-aeadc9434777","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"The directed ladder [8, 9] is a special limit of the cylin- drical construction","work_id":"e8e427ac-d27f-4bb4-a615-b866cbc5b1bd","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1987,"title":"P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A38, 364 (1988)","work_id":"476a5ab1-cdee-421e-9408-0610b46b89ca","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1988,"title":"C. Tang and P. Bak, Phys. Rev. Lett.60, 2347 (1988); J. Stat. Phys.51, 797 (1988)","work_id":"bb0c83fd-8166-401b-b055-f4220de7ba72","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1989,"title":"D. Dhar and R. Ramaswamy, Phys. Rev. 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