{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:J62ZGQDWWXEZGOW4AWYZ6PUAPY","short_pith_number":"pith:J62ZGQDW","schema_version":"1.0","canonical_sha256":"4fb5934076b5c9933adc05b19f3e807e05d7a266b4ffbc5103d812772f93a6f7","source":{"kind":"arxiv","id":"2105.05637","version":1},"attestation_state":"computed","paper":{"title":"A Mathematical Definition of Particle Methods","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"cs.DS","authors_text":"Ivo F. Sbalzarini, Johannes Bamme","submitted_at":"2021-05-12T13:09:31Z","abstract_excerpt":"We provide a formal definition for a class of algorithms known as \"particle methods\". Particle methods are used in scientific computing. They include popular simulation methods, such as Discrete Element Methods (DEM), Molecular Dynamics (MD), Particle Strength Exchange (PSE), and Smoothed Particle Hydrodynamics (SPH), but also particle-based image processing methods, point-based computer graphics, and computational optimization algorithms using point samples. All of these rest on a common concept, which we here formally define. The presented definition of particle methods makes it possible to "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2105.05637","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2021-05-12T13:09:31Z","cross_cats_sorted":["cs.CE"],"title_canon_sha256":"b876c71022b32d3712734c977358ee80d6ab8e7cf7546160f7b925ccf006d464","abstract_canon_sha256":"fc1ce7b18cead0076f94e6ffb00a09758e8f504ab6fb69c46e53b52b164e13e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:53.016865Z","signature_b64":"DnQRVcQh+m38qSJH3VMhcwgxS4iDBBwFWXrM23feVeyd5uy1YpMh5wsa7IPyKrYFKNgJ9g9CVSQ8lG+jlGZcCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fb5934076b5c9933adc05b19f3e807e05d7a266b4ffbc5103d812772f93a6f7","last_reissued_at":"2026-07-05T02:39:53.016520Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:53.016520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Mathematical Definition of Particle Methods","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.CE"],"primary_cat":"cs.DS","authors_text":"Ivo F. Sbalzarini, Johannes Bamme","submitted_at":"2021-05-12T13:09:31Z","abstract_excerpt":"We provide a formal definition for a class of algorithms known as \"particle methods\". Particle methods are used in scientific computing. They include popular simulation methods, such as Discrete Element Methods (DEM), Molecular Dynamics (MD), Particle Strength Exchange (PSE), and Smoothed Particle Hydrodynamics (SPH), but also particle-based image processing methods, point-based computer graphics, and computational optimization algorithms using point samples. All of these rest on a common concept, which we here formally define. The presented definition of particle methods makes it possible to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.05637","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.05637/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2105.05637","created_at":"2026-07-05T02:39:53.016573+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.05637v1","created_at":"2026-07-05T02:39:53.016573+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.05637","created_at":"2026-07-05T02:39:53.016573+00:00"},{"alias_kind":"pith_short_12","alias_value":"J62ZGQDWWXEZ","created_at":"2026-07-05T02:39:53.016573+00:00"},{"alias_kind":"pith_short_16","alias_value":"J62ZGQDWWXEZGOW4","created_at":"2026-07-05T02:39:53.016573+00:00"},{"alias_kind":"pith_short_8","alias_value":"J62ZGQDW","created_at":"2026-07-05T02:39:53.016573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY","json":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY.json","graph_json":"https://pith.science/api/pith-number/J62ZGQDWWXEZGOW4AWYZ6PUAPY/graph.json","events_json":"https://pith.science/api/pith-number/J62ZGQDWWXEZGOW4AWYZ6PUAPY/events.json","paper":"https://pith.science/paper/J62ZGQDW"},"agent_actions":{"view_html":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY","download_json":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY.json","view_paper":"https://pith.science/paper/J62ZGQDW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.05637&json=true","fetch_graph":"https://pith.science/api/pith-number/J62ZGQDWWXEZGOW4AWYZ6PUAPY/graph.json","fetch_events":"https://pith.science/api/pith-number/J62ZGQDWWXEZGOW4AWYZ6PUAPY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY/action/storage_attestation","attest_author":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY/action/author_attestation","sign_citation":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY/action/citation_signature","submit_replication":"https://pith.science/pith/J62ZGQDWWXEZGOW4AWYZ6PUAPY/action/replication_record"}},"created_at":"2026-07-05T02:39:53.016573+00:00","updated_at":"2026-07-05T02:39:53.016573+00:00"}