{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HXZUA6Q37TZIYJQ5OJ4KFKX52U","short_pith_number":"pith:HXZUA6Q3","canonical_record":{"source":{"id":"1106.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T08:03:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"804513e9c8acd914f204ddfb6c3122e3d29f26196f7c42bb77af8ab65cfe5251","abstract_canon_sha256":"92980b0d2ecf3d5a0d0818998feeb4602af5ed8c9c1f3b28d2b3e8b6bbd949ca"},"schema_version":"1.0"},"canonical_sha256":"3df3407a1bfcf28c261d7278a2aafdd50f2a2d721fed3d23bad92f7128271615","source":{"kind":"arxiv","id":"1106.5867","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5867","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5867v1","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5867","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"pith_short_12","alias_value":"HXZUA6Q37TZI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HXZUA6Q37TZIYJQ5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HXZUA6Q3","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HXZUA6Q37TZIYJQ5OJ4KFKX52U","target":"record","payload":{"canonical_record":{"source":{"id":"1106.5867","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T08:03:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"804513e9c8acd914f204ddfb6c3122e3d29f26196f7c42bb77af8ab65cfe5251","abstract_canon_sha256":"92980b0d2ecf3d5a0d0818998feeb4602af5ed8c9c1f3b28d2b3e8b6bbd949ca"},"schema_version":"1.0"},"canonical_sha256":"3df3407a1bfcf28c261d7278a2aafdd50f2a2d721fed3d23bad92f7128271615","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:27.136982Z","signature_b64":"uhd/9Lo5dkC5Q0db1Xt0lTU8WdDM1E3rP4qq3NYxov3re1nZD6bTpwloniYpyeDL9rR86jTOhLoz8ZeY0fONCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3df3407a1bfcf28c261d7278a2aafdd50f2a2d721fed3d23bad92f7128271615","last_reissued_at":"2026-05-18T02:01:27.136482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:27.136482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.5867","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":"2026-05-18T02:01:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p6elm2gmAUrlRm15Z6WWkr+WgW52/aIzp/RqK1gaHg2WYytShw5RyOuwn3KOdBAs092ZqG5K4yrjwVSi5h00DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:18:13.116638Z"},"content_sha256":"5486124ab20482541b59073f526aea856b8a62d4dff18a74174fb8841d020849","schema_version":"1.0","event_id":"sha256:5486124ab20482541b59073f526aea856b8a62d4dff18a74174fb8841d020849"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HXZUA6Q37TZIYJQ5OJ4KFKX52U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trends to equilibrium for a class of relativistic diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"J\\\"urgen Angst","submitted_at":"2011-06-29T08:03:53Z","abstract_excerpt":"We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L2-norm and in total variation. A similar result was obtained recently in arXiv:1009.5086 for a particular process of the class C."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5867","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":"2026-05-18T02:01:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5OrKcXc/1xY1AnZA54IiFOMReMYN6/J9muruBa242Ztz4dxM2yKubhNoM7OyQGRq9wtS2XkJm/iYUyhROFDyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T05:18:13.116988Z"},"content_sha256":"41f8d6ac06f508a36bddd1b3562b2f80284fcac8a9338ffdb1abfba5dcfd744a","schema_version":"1.0","event_id":"sha256:41f8d6ac06f508a36bddd1b3562b2f80284fcac8a9338ffdb1abfba5dcfd744a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/bundle.json","state_url":"https://pith.science/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/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":"2026-06-25T05:18:13Z","links":{"resolver":"https://pith.science/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U","bundle":"https://pith.science/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/bundle.json","state":"https://pith.science/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXZUA6Q37TZIYJQ5OJ4KFKX52U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HXZUA6Q37TZIYJQ5OJ4KFKX52U","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":"92980b0d2ecf3d5a0d0818998feeb4602af5ed8c9c1f3b28d2b3e8b6bbd949ca","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T08:03:53Z","title_canon_sha256":"804513e9c8acd914f204ddfb6c3122e3d29f26196f7c42bb77af8ab65cfe5251"},"schema_version":"1.0","source":{"id":"1106.5867","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.5867","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"arxiv_version","alias_value":"1106.5867v1","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5867","created_at":"2026-05-18T02:01:27Z"},{"alias_kind":"pith_short_12","alias_value":"HXZUA6Q37TZI","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HXZUA6Q37TZIYJQ5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HXZUA6Q3","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:41f8d6ac06f508a36bddd1b3562b2f80284fcac8a9338ffdb1abfba5dcfd744a","target":"graph","created_at":"2026-05-18T02:01:27Z","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 address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L2-norm and in total variation. A similar result was obtained recently in arXiv:1009.5086 for a particular process of the class C.","authors_text":"J\\\"urgen Angst","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T08:03:53Z","title":"Trends to equilibrium for a class of relativistic diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5867","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":"sha256:5486124ab20482541b59073f526aea856b8a62d4dff18a74174fb8841d020849","target":"record","created_at":"2026-05-18T02:01:27Z","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":"92980b0d2ecf3d5a0d0818998feeb4602af5ed8c9c1f3b28d2b3e8b6bbd949ca","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-29T08:03:53Z","title_canon_sha256":"804513e9c8acd914f204ddfb6c3122e3d29f26196f7c42bb77af8ab65cfe5251"},"schema_version":"1.0","source":{"id":"1106.5867","kind":"arxiv","version":1}},"canonical_sha256":"3df3407a1bfcf28c261d7278a2aafdd50f2a2d721fed3d23bad92f7128271615","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3df3407a1bfcf28c261d7278a2aafdd50f2a2d721fed3d23bad92f7128271615","first_computed_at":"2026-05-18T02:01:27.136482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:27.136482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uhd/9Lo5dkC5Q0db1Xt0lTU8WdDM1E3rP4qq3NYxov3re1nZD6bTpwloniYpyeDL9rR86jTOhLoz8ZeY0fONCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:27.136982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5867","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5486124ab20482541b59073f526aea856b8a62d4dff18a74174fb8841d020849","sha256:41f8d6ac06f508a36bddd1b3562b2f80284fcac8a9338ffdb1abfba5dcfd744a"],"state_sha256":"09eced6e29b7e3a46415fc0d858d8e9e761e89784bb62afe16ae8baea18cec38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wAGT1KDDiKHtNcKOJutyHE8zQyL/Bfblqz56c28JvlbGUJYAENVbF96AR/7BKkt68GbNBANlWfgyaDEbkt+nBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T05:18:13.118961Z","bundle_sha256":"38ce245dde823ff195cdb0760ac570ba0bf52f0679cef6536aacf9e15c91d103"}}