{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:OBB4RG7QHVOMRJVLMQWWQX2V5X","short_pith_number":"pith:OBB4RG7Q","canonical_record":{"source":{"id":"2109.13190","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-27T17:09:08Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"dc28714f8a34a5e4d5b6cdaab835f3821e759ab331e42e0cabef1b8424ead5db","abstract_canon_sha256":"00e9f4962b8272c02f3729752529334b3fb1901a7b2069b4f661ea95bd997fb6"},"schema_version":"1.0"},"canonical_sha256":"7043c89bf03d5cc8a6ab642d685f55edf138b57af1f6436d49558bc0178ac471","source":{"kind":"arxiv","id":"2109.13190","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13190","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13190v3","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13190","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"OBB4RG7QHVOM","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"OBB4RG7QHVOMRJVL","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"OBB4RG7Q","created_at":"2026-07-05T04:25:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:OBB4RG7QHVOMRJVLMQWWQX2V5X","target":"record","payload":{"canonical_record":{"source":{"id":"2109.13190","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-27T17:09:08Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"dc28714f8a34a5e4d5b6cdaab835f3821e759ab331e42e0cabef1b8424ead5db","abstract_canon_sha256":"00e9f4962b8272c02f3729752529334b3fb1901a7b2069b4f661ea95bd997fb6"},"schema_version":"1.0"},"canonical_sha256":"7043c89bf03d5cc8a6ab642d685f55edf138b57af1f6436d49558bc0178ac471","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:25:12.260781Z","signature_b64":"+x+vX5QwiPZ1l2NyYxMt7zke19X5sx+78CSE2M2B4+fJMBudnPCNS1nnjOBTlqBY1TWlFgrohXUb7w3X6rPgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7043c89bf03d5cc8a6ab642d685f55edf138b57af1f6436d49558bc0178ac471","last_reissued_at":"2026-07-05T04:25:12.260300Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:25:12.260300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.13190","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YP9HXCWirMRBmnaYIam8ingZuk+koiu1cBANCNWFVyoGLsDJNjIM9SUiSja6QM1nBUvhlxpLewyZSjU19xhPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T17:58:35.733381Z"},"content_sha256":"d2df118ea00fdebc0235c646b5fb8f0b6b8bc4c86b3c3ce8a3cbac908fcd51d1","schema_version":"1.0","event_id":"sha256:d2df118ea00fdebc0235c646b5fb8f0b6b8bc4c86b3c3ce8a3cbac908fcd51d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:OBB4RG7QHVOMRJVLMQWWQX2V5X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Claudia Strauch, Niklas Dexheimer","submitted_at":"2021-09-27T17:09:08Z","abstract_excerpt":"We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic smoothness assumptions on the unknown functions. The analysis is based on continuous observations of the process, and the estimators' performance is measured in terms of the sup-norm loss. Regarding invariant density estimation, we obtain highly nonclassical results for the rate of convergence, which reflect the inhomogeneous variance structure of the process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13190","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.13190/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:25:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTomloHMM1y2o/2FxQcCGb1Q4xu9mOR+PYy9L/tjPG7fknX2AGupMb/pWyPssi91XsT5e77ssRLYaQUtqtA9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T17:58:35.733967Z"},"content_sha256":"65e186435fb70bc87c3e468299ebfdfeb39f0d7cbaf3cff061a43c219c36a7d1","schema_version":"1.0","event_id":"sha256:65e186435fb70bc87c3e468299ebfdfeb39f0d7cbaf3cff061a43c219c36a7d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/bundle.json","state_url":"https://pith.science/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/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":"2026-08-21T17:58:35Z","links":{"resolver":"https://pith.science/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X","bundle":"https://pith.science/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/bundle.json","state":"https://pith.science/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OBB4RG7QHVOMRJVLMQWWQX2V5X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:OBB4RG7QHVOMRJVLMQWWQX2V5X","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":"00e9f4962b8272c02f3729752529334b3fb1901a7b2069b4f661ea95bd997fb6","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-27T17:09:08Z","title_canon_sha256":"dc28714f8a34a5e4d5b6cdaab835f3821e759ab331e42e0cabef1b8424ead5db"},"schema_version":"1.0","source":{"id":"2109.13190","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.13190","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"2109.13190v3","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.13190","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"OBB4RG7QHVOM","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_16","alias_value":"OBB4RG7QHVOMRJVL","created_at":"2026-07-05T04:25:12Z"},{"alias_kind":"pith_short_8","alias_value":"OBB4RG7Q","created_at":"2026-07-05T04:25:12Z"}],"graph_snapshots":[{"event_id":"sha256:65e186435fb70bc87c3e468299ebfdfeb39f0d7cbaf3cff061a43c219c36a7d1","target":"graph","created_at":"2026-07-05T04:25:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.13190/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic smoothness assumptions on the unknown functions. The analysis is based on continuous observations of the process, and the estimators' performance is measured in terms of the sup-norm loss. Regarding invariant density estimation, we obtain highly nonclassical results for the rate of convergence, which reflect the inhomogeneous variance structure of the process.","authors_text":"Claudia Strauch, Niklas Dexheimer","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-27T17:09:08Z","title":"Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.13190","kind":"arxiv","version":3},"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:d2df118ea00fdebc0235c646b5fb8f0b6b8bc4c86b3c3ce8a3cbac908fcd51d1","target":"record","created_at":"2026-07-05T04:25:12Z","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":"00e9f4962b8272c02f3729752529334b3fb1901a7b2069b4f661ea95bd997fb6","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2021-09-27T17:09:08Z","title_canon_sha256":"dc28714f8a34a5e4d5b6cdaab835f3821e759ab331e42e0cabef1b8424ead5db"},"schema_version":"1.0","source":{"id":"2109.13190","kind":"arxiv","version":3}},"canonical_sha256":"7043c89bf03d5cc8a6ab642d685f55edf138b57af1f6436d49558bc0178ac471","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7043c89bf03d5cc8a6ab642d685f55edf138b57af1f6436d49558bc0178ac471","first_computed_at":"2026-07-05T04:25:12.260300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:25:12.260300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+x+vX5QwiPZ1l2NyYxMt7zke19X5sx+78CSE2M2B4+fJMBudnPCNS1nnjOBTlqBY1TWlFgrohXUb7w3X6rPgAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:25:12.260781Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.13190","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2df118ea00fdebc0235c646b5fb8f0b6b8bc4c86b3c3ce8a3cbac908fcd51d1","sha256:65e186435fb70bc87c3e468299ebfdfeb39f0d7cbaf3cff061a43c219c36a7d1"],"state_sha256":"a9bc42ab3c490d30e9ff59d1d4f0174d021636374c61bbf063ab387ec8d59c53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Aev4oSVrXRoJe26RPyik/dFfOINJDQlvdyirMvYLar65dvf7F4Mx+SJvJp8U3KfIVnmNvzW2A4QfEUY8AQCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T17:58:35.738458Z","bundle_sha256":"330ff2cbdfde457008e8e1bfa4311ff1416ca75e861f04e29f96815d7ece0750"}}