{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RN3TOO66QQLJF2TNT77LOKJBSR","short_pith_number":"pith:RN3TOO66","canonical_record":{"source":{"id":"1710.01610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T14:10:11Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"5dad4cc613de46aaf33eb355b9a27681b256c4e9d50f0d4a298eacd5a3dde006","abstract_canon_sha256":"0f2f9cb65869c78aea748fa81a52cadd55885f76c45e0b46485a033ed5df23e0"},"schema_version":"1.0"},"canonical_sha256":"8b77373bde841692ea6d9ffeb72921945ee97aff1b75b3b4018a45631b2a9008","source":{"kind":"arxiv","id":"1710.01610","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01610","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01610v1","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01610","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"RN3TOO66QQLJ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RN3TOO66QQLJF2TN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RN3TOO66","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RN3TOO66QQLJF2TNT77LOKJBSR","target":"record","payload":{"canonical_record":{"source":{"id":"1710.01610","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T14:10:11Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"5dad4cc613de46aaf33eb355b9a27681b256c4e9d50f0d4a298eacd5a3dde006","abstract_canon_sha256":"0f2f9cb65869c78aea748fa81a52cadd55885f76c45e0b46485a033ed5df23e0"},"schema_version":"1.0"},"canonical_sha256":"8b77373bde841692ea6d9ffeb72921945ee97aff1b75b3b4018a45631b2a9008","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:40.696971Z","signature_b64":"rbqLySmgGHX3mmBbd5O0tkLuNMXNKimEyL+qM/fBNPfeOm5WGKteWOv6E1/3tQlc1m55Ve7jPftC846IBWk0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b77373bde841692ea6d9ffeb72921945ee97aff1b75b3b4018a45631b2a9008","last_reissued_at":"2026-05-18T00:11:40.696235Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:40.696235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.01610","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2pr40VycGV8dudgfIYA4P1wUS3t36/uqx2f5149NtUlH1yqz0b5t9zH8VVzMh5xkN0eh6UpB6+88rEHo0ZnCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:29:49.608038Z"},"content_sha256":"72df73da4bad82b0fbe666ebd324a92d474eebe2c406e6b5da7efe7492353b07","schema_version":"1.0","event_id":"sha256:72df73da4bad82b0fbe666ebd324a92d474eebe2c406e6b5da7efe7492353b07"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RN3TOO66QQLJF2TNT77LOKJBSR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.AP","authors_text":"(2) DMA, (3) UMPA-ENSL), Isabelle Gallagher (2), Laure Saint-Raymond (3) ((1) CMAP, Thierry Bodineau (1), UPD7","submitted_at":"2017-10-04T14:10:11Z","abstract_excerpt":"We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01610","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:11:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZKEvNvaC2uN+nMpaOrn3JElLOw4ipX093DUTj6e0WunUXnaFRiXQEROT/aAZ9p5x6TXPjKLkoJH/TsCtWum4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T00:29:49.608771Z"},"content_sha256":"9d1658d2aa9c000986dd1ef707cee460316fe8c0da9c40b4bdebbef8f53bb36a","schema_version":"1.0","event_id":"sha256:9d1658d2aa9c000986dd1ef707cee460316fe8c0da9c40b4bdebbef8f53bb36a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RN3TOO66QQLJF2TNT77LOKJBSR/bundle.json","state_url":"https://pith.science/pith/RN3TOO66QQLJF2TNT77LOKJBSR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RN3TOO66QQLJF2TNT77LOKJBSR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T00:29:49Z","links":{"resolver":"https://pith.science/pith/RN3TOO66QQLJF2TNT77LOKJBSR","bundle":"https://pith.science/pith/RN3TOO66QQLJF2TNT77LOKJBSR/bundle.json","state":"https://pith.science/pith/RN3TOO66QQLJF2TNT77LOKJBSR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RN3TOO66QQLJF2TNT77LOKJBSR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RN3TOO66QQLJF2TNT77LOKJBSR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f2f9cb65869c78aea748fa81a52cadd55885f76c45e0b46485a033ed5df23e0","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T14:10:11Z","title_canon_sha256":"5dad4cc613de46aaf33eb355b9a27681b256c4e9d50f0d4a298eacd5a3dde006"},"schema_version":"1.0","source":{"id":"1710.01610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.01610","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.01610v1","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.01610","created_at":"2026-05-18T00:11:40Z"},{"alias_kind":"pith_short_12","alias_value":"RN3TOO66QQLJ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RN3TOO66QQLJF2TN","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RN3TOO66","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:9d1658d2aa9c000986dd1ef707cee460316fe8c0da9c40b4bdebbef8f53bb36a","target":"graph","created_at":"2026-05-18T00:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We consider the statistical motion of a convex rigid body in a gas of N smaller (spherical) atoms close to thermodynamic equilibrium. Because the rigid body is much bigger and heavier, it undergoes a lot of collisions leading to small deflections. We prove that its velocity is described, in a suitable limit, by an Ornstein-Uhlenbeck process. The strategy of proof relies on Lanford's arguments [17] together with the pruning procedure from [3] to reach diffusive times, much larger than the mean free time. Furthermore, we need to introduce a modified dynamics to avoid pathological collisions of a","authors_text":"(2) DMA, (3) UMPA-ENSL), Isabelle Gallagher (2), Laure Saint-Raymond (3) ((1) CMAP, Thierry Bodineau (1), UPD7","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T14:10:11Z","title":"Derivation of an ornstein-uhlenbeck process for a massive particle in a rarified gas of particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.01610","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:72df73da4bad82b0fbe666ebd324a92d474eebe2c406e6b5da7efe7492353b07","target":"record","created_at":"2026-05-18T00:11:40Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f2f9cb65869c78aea748fa81a52cadd55885f76c45e0b46485a033ed5df23e0","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-10-04T14:10:11Z","title_canon_sha256":"5dad4cc613de46aaf33eb355b9a27681b256c4e9d50f0d4a298eacd5a3dde006"},"schema_version":"1.0","source":{"id":"1710.01610","kind":"arxiv","version":1}},"canonical_sha256":"8b77373bde841692ea6d9ffeb72921945ee97aff1b75b3b4018a45631b2a9008","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b77373bde841692ea6d9ffeb72921945ee97aff1b75b3b4018a45631b2a9008","first_computed_at":"2026-05-18T00:11:40.696235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:40.696235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rbqLySmgGHX3mmBbd5O0tkLuNMXNKimEyL+qM/fBNPfeOm5WGKteWOv6E1/3tQlc1m55Ve7jPftC846IBWk0CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:40.696971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.01610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72df73da4bad82b0fbe666ebd324a92d474eebe2c406e6b5da7efe7492353b07","sha256:9d1658d2aa9c000986dd1ef707cee460316fe8c0da9c40b4bdebbef8f53bb36a"],"state_sha256":"e370a2710416f1f278054c8e1feaf3c08a9ab64815ea9423c77f2f8d8ac68fa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KsyIghhawu5vVwv/Bxl2m2f8lvdgJQ/VD9jj6IHfINtth7Q53Ta0ucbr7I6WkOETwOKG+lA1RuAnJB1qsQAtBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T00:29:49.612466Z","bundle_sha256":"8900efafcf175a9fc7688c3b75a533c5201dad1e6081bf088f9d677196c520b9"}}