{"paper":{"title":"Percolation representations of additive particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Additive interacting particle systems with finite distributive lattice state spaces admit percolation representations via open paths.","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jan M. Swart","submitted_at":"2026-05-13T11:28:54Z","abstract_excerpt":"It is well-known that additive interacting particle systems with a local state space of cardinality two have a percolation representation in terms of open paths in a graphical representation. In this paper, it is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice. The theory is demonstrated on Krone's two-stage contact process."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"It is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The interacting particle system must be additive and the local state space must be a finite distributive lattice.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A percolation representation is constructed for additive particle systems with finite distributive lattice state spaces, demonstrated on Krone's two-stage contact process.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Additive interacting particle systems with finite distributive lattice state spaces admit percolation representations via open paths.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8111118c90dc59dac8fa3673d8d54afc4d805c63dc3f4746cc0c300a44b15887"},"source":{"id":"2605.13371","kind":"arxiv","version":1},"verdict":{"id":"86807a18-e444-4eaf-b63d-a2b4e8f3e7d9","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T18:36:30.934832Z","strongest_claim":"It is shown how such a percolation representation can be constructed more generally when the local state space is a finite distributive lattice.","one_line_summary":"A percolation representation is constructed for additive particle systems with finite distributive lattice state spaces, demonstrated on Krone's two-stage contact process.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The interacting particle system must be additive and the local state space must be a finite distributive lattice.","pith_extraction_headline":"Additive interacting particle systems with finite distributive lattice state spaces admit percolation representations via open paths."},"references":{"count":6,"sample":[{"doi":"","year":2016,"title":"E. Foxall. Duality and complete convergence for multi-type additive growth models. Adv.\\ Appl.\\ Probab. 48(1) (2016), 32--51","work_id":"9fadaf46-ec86-4fc4-84d3-337213888773","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1979,"title":"D. Griffeath. Additive and Cancellative Interacting Particle Systems. Lecture Notes in Math. 724, Springer, Berlin, 1979","work_id":"c40fa24c-2c8e-4fee-8798-85164e827515","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1978,"title":"T.E. Harris. Additive set-valued Markov processes and graphical methods. Ann.\\ Probab. 6 (1978), 355--378","work_id":"cd663f1c-bb48-4d9d-8244-d21623736ba7","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"S. Krone. The two-stage contact process. Ann.\\ Appl.\\ Probab. 9(2) (1999), 331--351","work_id":"512a902a-2647-4553-b946-1910cba5877b","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"A. Sturm and J.M. Swart. Pathwise duals of monotone and additive Markov processes. J.\\ Theor.\\ Probab. 31(2) (2018), 932--983","work_id":"3a730bab-91ec-4557-bcb7-9ba7543c86c4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":6,"snapshot_sha256":"0e20636978c68f99563aae15828c135bd1480764ff459e525bc6de23e4901dd4","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"954270c37a3c310d85217a862f5e0c211c013961a28a5ae1588bb059aa19858e"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}