{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:L4MZ7OUGKFBT5NIMA6LFOZLIG3","short_pith_number":"pith:L4MZ7OUG","schema_version":"1.0","canonical_sha256":"5f199fba8651433eb50c079657656836c5fe9de228c1631c4caae649efb89f3d","source":{"kind":"arxiv","id":"1610.06966","version":2},"attestation_state":"computed","paper":{"title":"Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Bruno Marcos, Fernanda P. C. Benetti","submitted_at":"2016-10-21T22:20:23Z","abstract_excerpt":"Systems of particles with long range interactions present two important processes: first, the formation of out-of-equilibrium quasi-stationary states (QSS), and the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much longer timescale. In this paper, we study the collisional relaxation in the Hamiltonian-Mean-Field model (HMF) using the appropriate kinetic equations for a system of $N$ particles at order $1/N$ : the Landau equation when collective effects are neglected and the Lenard-Balescu equation when they are taken into account. We derive explicit expressions for the dif"},"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":"1610.06966","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-10-21T22:20:23Z","cross_cats_sorted":[],"title_canon_sha256":"623441b5d3799a826e48f22e04dc06f4eef47943516e5f8a0fe570cd9191eb9a","abstract_canon_sha256":"dd45df7f29f6a733dbd7db2bce457ae77b5448ecad4766cf79fd93523ce95b45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:14.708569Z","signature_b64":"dh0gDVYmONlgw2t5mfKB2s7hdJ9sXqiocwcCpxcexLnyhmB2pckIIHRFPpovw8LIbqIx2gn+DGsq5rOqgQp6AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f199fba8651433eb50c079657656836c5fe9de228c1631c4caae649efb89f3d","last_reissued_at":"2026-05-18T00:49:14.707893Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:14.707893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Collisional relaxation in the inhomogeneous Hamiltonian-Mean-Field model: diffusion coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Bruno Marcos, Fernanda P. C. Benetti","submitted_at":"2016-10-21T22:20:23Z","abstract_excerpt":"Systems of particles with long range interactions present two important processes: first, the formation of out-of-equilibrium quasi-stationary states (QSS), and the collisional relaxation towards Maxwell-Boltzmann equilibrium in a much longer timescale. In this paper, we study the collisional relaxation in the Hamiltonian-Mean-Field model (HMF) using the appropriate kinetic equations for a system of $N$ particles at order $1/N$ : the Landau equation when collective effects are neglected and the Lenard-Balescu equation when they are taken into account. We derive explicit expressions for the dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06966","kind":"arxiv","version":2},"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":"1610.06966","created_at":"2026-05-18T00:49:14.708001+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06966v2","created_at":"2026-05-18T00:49:14.708001+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06966","created_at":"2026-05-18T00:49:14.708001+00:00"},{"alias_kind":"pith_short_12","alias_value":"L4MZ7OUGKFBT","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"L4MZ7OUGKFBT5NIM","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"L4MZ7OUG","created_at":"2026-05-18T12:30:29.479603+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/L4MZ7OUGKFBT5NIMA6LFOZLIG3","json":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3.json","graph_json":"https://pith.science/api/pith-number/L4MZ7OUGKFBT5NIMA6LFOZLIG3/graph.json","events_json":"https://pith.science/api/pith-number/L4MZ7OUGKFBT5NIMA6LFOZLIG3/events.json","paper":"https://pith.science/paper/L4MZ7OUG"},"agent_actions":{"view_html":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3","download_json":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3.json","view_paper":"https://pith.science/paper/L4MZ7OUG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06966&json=true","fetch_graph":"https://pith.science/api/pith-number/L4MZ7OUGKFBT5NIMA6LFOZLIG3/graph.json","fetch_events":"https://pith.science/api/pith-number/L4MZ7OUGKFBT5NIMA6LFOZLIG3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3/action/storage_attestation","attest_author":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3/action/author_attestation","sign_citation":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3/action/citation_signature","submit_replication":"https://pith.science/pith/L4MZ7OUGKFBT5NIMA6LFOZLIG3/action/replication_record"}},"created_at":"2026-05-18T00:49:14.708001+00:00","updated_at":"2026-05-18T00:49:14.708001+00:00"}