{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:N42WTPPUOBO6WBELNE3BEICDXX","short_pith_number":"pith:N42WTPPU","schema_version":"1.0","canonical_sha256":"6f3569bdf4705deb048b6936122043bde22c19a2c3bc1ff5adc419651af9a876","source":{"kind":"arxiv","id":"1510.06555","version":1},"attestation_state":"computed","paper":{"title":"On numerical Landau damping for splitting methods applied to the Vlasov-HMF model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erwan Faou (IPSO, Fr\\'ed\\'eric Rousset (LM-Orsay), IRMAR), Romain Horsin (IPSO","submitted_at":"2015-10-22T09:45:31Z","abstract_excerpt":"We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field) equation based on splitting methods between the linear and non-linear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect t"},"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":"1510.06555","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-10-22T09:45:31Z","cross_cats_sorted":[],"title_canon_sha256":"1820cfb03ca131cc3b12000dccef3aea4b2a1d434b961dcf410320112324e2f9","abstract_canon_sha256":"0d0d29519f675fe8ed626b05d4409e08989bfaebf8f7e14a55a1256cc675a250"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:30.644664Z","signature_b64":"EgVhShX08sP2k4WVt5dWB9/KY8IvzBb2ER7VRdoqixeW5XazAwPzd06JYvi0d4aXCfMpOTDVRjBzGlLiLyo6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f3569bdf4705deb048b6936122043bde22c19a2c3bc1ff5adc419651af9a876","last_reissued_at":"2026-05-18T01:29:30.644057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:30.644057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On numerical Landau damping for splitting methods applied to the Vlasov-HMF model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Erwan Faou (IPSO, Fr\\'ed\\'eric Rousset (LM-Orsay), IRMAR), Romain Horsin (IPSO","submitted_at":"2015-10-22T09:45:31Z","abstract_excerpt":"We consider time discretizations of the Vlasov-HMF (Hamiltonian Mean-Field) equation based on splitting methods between the linear and non-linear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06555","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":""},"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":"1510.06555","created_at":"2026-05-18T01:29:30.644141+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.06555v1","created_at":"2026-05-18T01:29:30.644141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06555","created_at":"2026-05-18T01:29:30.644141+00:00"},{"alias_kind":"pith_short_12","alias_value":"N42WTPPUOBO6","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_16","alias_value":"N42WTPPUOBO6WBEL","created_at":"2026-05-18T12:29:32.376354+00:00"},{"alias_kind":"pith_short_8","alias_value":"N42WTPPU","created_at":"2026-05-18T12:29:32.376354+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/N42WTPPUOBO6WBELNE3BEICDXX","json":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX.json","graph_json":"https://pith.science/api/pith-number/N42WTPPUOBO6WBELNE3BEICDXX/graph.json","events_json":"https://pith.science/api/pith-number/N42WTPPUOBO6WBELNE3BEICDXX/events.json","paper":"https://pith.science/paper/N42WTPPU"},"agent_actions":{"view_html":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX","download_json":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX.json","view_paper":"https://pith.science/paper/N42WTPPU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.06555&json=true","fetch_graph":"https://pith.science/api/pith-number/N42WTPPUOBO6WBELNE3BEICDXX/graph.json","fetch_events":"https://pith.science/api/pith-number/N42WTPPUOBO6WBELNE3BEICDXX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX/action/storage_attestation","attest_author":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX/action/author_attestation","sign_citation":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX/action/citation_signature","submit_replication":"https://pith.science/pith/N42WTPPUOBO6WBELNE3BEICDXX/action/replication_record"}},"created_at":"2026-05-18T01:29:30.644141+00:00","updated_at":"2026-05-18T01:29:30.644141+00:00"}