{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:25P76EK5Q2NQIGSAL3FIOFLKVS","short_pith_number":"pith:25P76EK5","canonical_record":{"source":{"id":"1009.3232","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-16T18:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"79e5b2c3a5b5c5b09f8c77c403c404c0e508c157ce7e08691b2258068e3a43f3","abstract_canon_sha256":"13c9580a03e4ec9fb91df73abf4393ccd34ea52265ce446c6de5151405be65dc"},"schema_version":"1.0"},"canonical_sha256":"d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be","source":{"kind":"arxiv","id":"1009.3232","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3232","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3232v3","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3232","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"25P76EK5Q2NQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"25P76EK5Q2NQIGSA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"25P76EK5","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:25P76EK5Q2NQIGSAL3FIOFLKVS","target":"record","payload":{"canonical_record":{"source":{"id":"1009.3232","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-16T18:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"79e5b2c3a5b5c5b09f8c77c403c404c0e508c157ce7e08691b2258068e3a43f3","abstract_canon_sha256":"13c9580a03e4ec9fb91df73abf4393ccd34ea52265ce446c6de5151405be65dc"},"schema_version":"1.0"},"canonical_sha256":"d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:52.219230Z","signature_b64":"EI9MjrKvct++RLHArQz6KeQioms0Z8i+mBiyoynRyP2yTRAUWMy0y40VtJTQcSEcxQPhCTKk+6ukTmwxmA5CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be","last_reissued_at":"2026-05-18T04:31:52.218558Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:52.218558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.3232","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":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xh8oQEx2WYmQpX8S1MfeWFaCAvJoABy5ro81PKrlg8VM76x3pqE3Tfwbq3XiCEPWEiF+gA5bTONi7nu+XQszCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:39:14.525324Z"},"content_sha256":"52a21048a30dc8dde5fdcf13b965023e8b783c71c8166df4d376789d0338b143","schema_version":"1.0","event_id":"sha256:52a21048a30dc8dde5fdcf13b965023e8b783c71c8166df4d376789d0338b143"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:25P76EK5Q2NQIGSAL3FIOFLKVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An H-theorem for the Brownian motion on the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"C. Vignat, P.W. Lamberti","submitted_at":"2010-09-16T18:03:32Z","abstract_excerpt":"We prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\\'enyi entropy, the parameter of which being related in a simple way to the value of the drift."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3232","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":""},"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":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0lX5PA32MhNKYIUL+bu5t9oaRGJR/BLgjeUiKlqz2FNwJ8u4uzwzqPO7QkQ9LSekXBl0a29N5/iVx0o7+CoVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:39:14.525937Z"},"content_sha256":"503c34268ef1a27485333803ffee8d5b0227928e297a8ed00fff87dd57e1830e","schema_version":"1.0","event_id":"sha256:503c34268ef1a27485333803ffee8d5b0227928e297a8ed00fff87dd57e1830e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/bundle.json","state_url":"https://pith.science/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/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":"2026-05-30T07:39:14Z","links":{"resolver":"https://pith.science/pith/25P76EK5Q2NQIGSAL3FIOFLKVS","bundle":"https://pith.science/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/bundle.json","state":"https://pith.science/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/25P76EK5Q2NQIGSAL3FIOFLKVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:25P76EK5Q2NQIGSAL3FIOFLKVS","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":"13c9580a03e4ec9fb91df73abf4393ccd34ea52265ce446c6de5151405be65dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-16T18:03:32Z","title_canon_sha256":"79e5b2c3a5b5c5b09f8c77c403c404c0e508c157ce7e08691b2258068e3a43f3"},"schema_version":"1.0","source":{"id":"1009.3232","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3232","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3232v3","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3232","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"25P76EK5Q2NQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"25P76EK5Q2NQIGSA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"25P76EK5","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:503c34268ef1a27485333803ffee8d5b0227928e297a8ed00fff87dd57e1830e","target":"graph","created_at":"2026-05-18T04:31:52Z","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 prove an $H-$theorem for the Brownian motion on the hyperbolic plane with a drift, as studied by Comtet and Monthus; the entropy used here is not the Boltzmann entropy but the R\\'enyi entropy, the parameter of which being related in a simple way to the value of the drift.","authors_text":"C. Vignat, P.W. Lamberti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-16T18:03:32Z","title":"An H-theorem for the Brownian motion on the hyperbolic plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3232","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":"sha256:52a21048a30dc8dde5fdcf13b965023e8b783c71c8166df4d376789d0338b143","target":"record","created_at":"2026-05-18T04:31:52Z","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":"13c9580a03e4ec9fb91df73abf4393ccd34ea52265ce446c6de5151405be65dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-09-16T18:03:32Z","title_canon_sha256":"79e5b2c3a5b5c5b09f8c77c403c404c0e508c157ce7e08691b2258068e3a43f3"},"schema_version":"1.0","source":{"id":"1009.3232","kind":"arxiv","version":3}},"canonical_sha256":"d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d75fff115d869b041a405eca87156aacb118a1dc09928953355e83d94f45e8be","first_computed_at":"2026-05-18T04:31:52.218558Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:52.218558Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EI9MjrKvct++RLHArQz6KeQioms0Z8i+mBiyoynRyP2yTRAUWMy0y40VtJTQcSEcxQPhCTKk+6ukTmwxmA5CDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:52.219230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3232","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a21048a30dc8dde5fdcf13b965023e8b783c71c8166df4d376789d0338b143","sha256:503c34268ef1a27485333803ffee8d5b0227928e297a8ed00fff87dd57e1830e"],"state_sha256":"c23272d63f60597d03d915c7f0c2feda762d301517fc12c420a507e690d7f330"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XnuBZzeEPNfWOijm37OtfNMHHdny0kuVy73OQ8Cpi4jvr0EHQl7bO0BF76s9ixeI6IHANGTXW/ml1+R5F3hfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:39:14.528671Z","bundle_sha256":"b6f3f9621a20246b7b385e9252b0e6539eb1ff342dd3c216c07303679954648d"}}