{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YHSZPNR4YDW56SCPKI5KQSYATD","short_pith_number":"pith:YHSZPNR4","schema_version":"1.0","canonical_sha256":"c1e597b63cc0eddf484f523aa84b0098ff86a75736b586fffec4714098ad8f67","source":{"kind":"arxiv","id":"1312.4301","version":2},"attestation_state":"computed","paper":{"title":"Propagation of chaos for the thermostatted Kac master equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bernt Wennberg, Dawan Mustafa, Eric Carlen","submitted_at":"2013-12-16T10:44:48Z","abstract_excerpt":"The Kac model is a simplified model of an $N$-particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an $N$-particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model."},"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":"1312.4301","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-12-16T10:44:48Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"3a94e31ab35295c9108c70ea945e0f26f7d044f01f1e7593a8bccf01e5b28667","abstract_canon_sha256":"4c985e135c61665fd42afb3f99a1e60009818037d17c5eb572299921f97d6d1d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:50.321767Z","signature_b64":"vFtuaCyROUQWeFLFq9cUwXtv5i3sFybRGr7aSWSSjuk112SdZROIar94lPr5TyV1f5JBTt1yZ5XWSFJr7q7JBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1e597b63cc0eddf484f523aa84b0098ff86a75736b586fffec4714098ad8f67","last_reissued_at":"2026-05-18T01:45:50.321289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:50.321289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Propagation of chaos for the thermostatted Kac master equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bernt Wennberg, Dawan Mustafa, Eric Carlen","submitted_at":"2013-12-16T10:44:48Z","abstract_excerpt":"The Kac model is a simplified model of an $N$-particle system in which the collisions of a real particle system are modeled by random jumps of pairs of particle velocities. Kac proved propagation of chaos for this model, and hence provided a rigorous validation of the corresponding Boltzmann equation. Starting with the same model we consider an $N$-particle system in which the particles are accelerated between the jumps by a constant uniform force field which conserves the total energy of the system. We show propagation of chaos for this model."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4301","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":"1312.4301","created_at":"2026-05-18T01:45:50.321395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4301v2","created_at":"2026-05-18T01:45:50.321395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4301","created_at":"2026-05-18T01:45:50.321395+00:00"},{"alias_kind":"pith_short_12","alias_value":"YHSZPNR4YDW5","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"YHSZPNR4YDW56SCP","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"YHSZPNR4","created_at":"2026-05-18T12:28:06.772260+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/YHSZPNR4YDW56SCPKI5KQSYATD","json":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD.json","graph_json":"https://pith.science/api/pith-number/YHSZPNR4YDW56SCPKI5KQSYATD/graph.json","events_json":"https://pith.science/api/pith-number/YHSZPNR4YDW56SCPKI5KQSYATD/events.json","paper":"https://pith.science/paper/YHSZPNR4"},"agent_actions":{"view_html":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD","download_json":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD.json","view_paper":"https://pith.science/paper/YHSZPNR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4301&json=true","fetch_graph":"https://pith.science/api/pith-number/YHSZPNR4YDW56SCPKI5KQSYATD/graph.json","fetch_events":"https://pith.science/api/pith-number/YHSZPNR4YDW56SCPKI5KQSYATD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD/action/storage_attestation","attest_author":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD/action/author_attestation","sign_citation":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD/action/citation_signature","submit_replication":"https://pith.science/pith/YHSZPNR4YDW56SCPKI5KQSYATD/action/replication_record"}},"created_at":"2026-05-18T01:45:50.321395+00:00","updated_at":"2026-05-18T01:45:50.321395+00:00"}