{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AV23AJ5AX4M5RDZFJMSPXH34JM","short_pith_number":"pith:AV23AJ5A","canonical_record":{"source":{"id":"1608.07889","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T02:02:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a60c3107a2fb2adaa22a966bb1a27a3de94d37285e60c997ed12555291e12c1","abstract_canon_sha256":"59df3768f07bbf3a2b037bad7350b05076fee711a3c495288e2a3b70ecf15ed6"},"schema_version":"1.0"},"canonical_sha256":"0575b027a0bf19d88f254b24fb9f7c4b26a8558e1db2926d01f7e8bf0fd939eb","source":{"kind":"arxiv","id":"1608.07889","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07889","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07889v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07889","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"AV23AJ5AX4M5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AV23AJ5AX4M5RDZF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AV23AJ5A","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AV23AJ5AX4M5RDZFJMSPXH34JM","target":"record","payload":{"canonical_record":{"source":{"id":"1608.07889","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T02:02:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"3a60c3107a2fb2adaa22a966bb1a27a3de94d37285e60c997ed12555291e12c1","abstract_canon_sha256":"59df3768f07bbf3a2b037bad7350b05076fee711a3c495288e2a3b70ecf15ed6"},"schema_version":"1.0"},"canonical_sha256":"0575b027a0bf19d88f254b24fb9f7c4b26a8558e1db2926d01f7e8bf0fd939eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:49.676416Z","signature_b64":"UgSYvZZKvLfaewHv11CCWsAY27/0ofzmcEUJ7Zy+ULvJvozCAFM4IcdFLpxlrXoKT+Kn2o3VmPtnUwrn3FcrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0575b027a0bf19d88f254b24fb9f7c4b26a8558e1db2926d01f7e8bf0fd939eb","last_reissued_at":"2026-05-18T01:07:49.675909Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:49.675909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.07889","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nf5PDMGqbtJGl1yoyMnP9Qga/o6Ieyi3DGVzq8L2M4hd2QSzPFyrVLgCpWpjaKCt+Npv3PhjY4mTCgJjXjEIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:00:23.900141Z"},"content_sha256":"2f4b829f805303dfd5e042b555071c5f47a79aa32d9d0072ac34c9c05afb2d1d","schema_version":"1.0","event_id":"sha256:2f4b829f805303dfd5e042b555071c5f47a79aa32d9d0072ac34c9c05afb2d1d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AV23AJ5AX4M5RDZFJMSPXH34JM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hilbert space hypocoercivity for the Langevin dynamics revisited","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Martin Grothaus, Patrik Stilgenbauer","submitted_at":"2016-08-29T02:02:41Z","abstract_excerpt":"We provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics via studying the longtime behavior of the strongly continuous contraction semigroup solving the associated Kolmogorov (backward) equation as an abstract Cauchy problem. This hypocoercivity result is proven in previous works before by Dolbeault, Mouhot and Schmeiser in the corresponding dual Fokker-Planck framework, but without including domain issues of the appearing operators. In our elaboration, we include the domain issues and additionally compute the rate of convergence "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07889","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":"2026-05-18T01:07:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lO+xrRcQXSfrweudiPjew7AuXxyXkiqNucap1D7rOLkiRdmnbxeCmaLmND9jRfdLIQZYLjStKa3CSkvnkhX8Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:00:23.900647Z"},"content_sha256":"7265bf93ab09405148437ebc3be4cd241a80a6cb1128ded941df05681cf1eb87","schema_version":"1.0","event_id":"sha256:7265bf93ab09405148437ebc3be4cd241a80a6cb1128ded941df05681cf1eb87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/bundle.json","state_url":"https://pith.science/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/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":"2026-06-24T11:00:23Z","links":{"resolver":"https://pith.science/pith/AV23AJ5AX4M5RDZFJMSPXH34JM","bundle":"https://pith.science/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/bundle.json","state":"https://pith.science/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AV23AJ5AX4M5RDZFJMSPXH34JM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AV23AJ5AX4M5RDZFJMSPXH34JM","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":"59df3768f07bbf3a2b037bad7350b05076fee711a3c495288e2a3b70ecf15ed6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T02:02:41Z","title_canon_sha256":"3a60c3107a2fb2adaa22a966bb1a27a3de94d37285e60c997ed12555291e12c1"},"schema_version":"1.0","source":{"id":"1608.07889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07889","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07889v1","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07889","created_at":"2026-05-18T01:07:49Z"},{"alias_kind":"pith_short_12","alias_value":"AV23AJ5AX4M5","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AV23AJ5AX4M5RDZF","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AV23AJ5A","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:7265bf93ab09405148437ebc3be4cd241a80a6cb1128ded941df05681cf1eb87","target":"graph","created_at":"2026-05-18T01:07:49Z","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 provide a complete elaboration of the $L^2$-Hilbert space hypocoercivity theorem for the degenerate Langevin dynamics via studying the longtime behavior of the strongly continuous contraction semigroup solving the associated Kolmogorov (backward) equation as an abstract Cauchy problem. This hypocoercivity result is proven in previous works before by Dolbeault, Mouhot and Schmeiser in the corresponding dual Fokker-Planck framework, but without including domain issues of the appearing operators. In our elaboration, we include the domain issues and additionally compute the rate of convergence ","authors_text":"Martin Grothaus, Patrik Stilgenbauer","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T02:02:41Z","title":"Hilbert space hypocoercivity for the Langevin dynamics revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07889","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":"sha256:2f4b829f805303dfd5e042b555071c5f47a79aa32d9d0072ac34c9c05afb2d1d","target":"record","created_at":"2026-05-18T01:07:49Z","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":"59df3768f07bbf3a2b037bad7350b05076fee711a3c495288e2a3b70ecf15ed6","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.FA","submitted_at":"2016-08-29T02:02:41Z","title_canon_sha256":"3a60c3107a2fb2adaa22a966bb1a27a3de94d37285e60c997ed12555291e12c1"},"schema_version":"1.0","source":{"id":"1608.07889","kind":"arxiv","version":1}},"canonical_sha256":"0575b027a0bf19d88f254b24fb9f7c4b26a8558e1db2926d01f7e8bf0fd939eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0575b027a0bf19d88f254b24fb9f7c4b26a8558e1db2926d01f7e8bf0fd939eb","first_computed_at":"2026-05-18T01:07:49.675909Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:49.675909Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UgSYvZZKvLfaewHv11CCWsAY27/0ofzmcEUJ7Zy+ULvJvozCAFM4IcdFLpxlrXoKT+Kn2o3VmPtnUwrn3FcrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:49.676416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f4b829f805303dfd5e042b555071c5f47a79aa32d9d0072ac34c9c05afb2d1d","sha256:7265bf93ab09405148437ebc3be4cd241a80a6cb1128ded941df05681cf1eb87"],"state_sha256":"02f9510de3600122e8f77b3c5de0fa34f1eed7b3ec736a706b20d7a4570d0193"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E2e29S8Z4yNFzbA+/QT/rdwcGUv3Th/9ZdL9pA2KRAdTp0HUm5zIlVAs39T5iRlIW4DFzhyem+y7ELMRl2tgBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:00:23.903247Z","bundle_sha256":"630543fdbdc788e9cea230d3b800124e2a8909e68d64ac4706572d82ce057b1a"}}