{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:MRQ24XKQ6TNPHKPAXOMOTJ252U","short_pith_number":"pith:MRQ24XKQ","canonical_record":{"source":{"id":"0912.0591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-03T08:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"04920f8a3d53037637b4a8ce826d44d093160cda7aea6c02e68013b0ff9af4f6","abstract_canon_sha256":"ff3dcdde1982fd15e4411d3df49121d84793c941eb87a0ad889000b53b84ecc6"},"schema_version":"1.0"},"canonical_sha256":"6461ae5d50f4daf3a9e0bb98e9a75dd53e006aa987ea166eb43965d594ce5d67","source":{"kind":"arxiv","id":"0912.0591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0591","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0591v2","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0591","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"MRQ24XKQ6TNP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MRQ24XKQ6TNPHKPA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MRQ24XKQ","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:MRQ24XKQ6TNPHKPAXOMOTJ252U","target":"record","payload":{"canonical_record":{"source":{"id":"0912.0591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-03T08:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"04920f8a3d53037637b4a8ce826d44d093160cda7aea6c02e68013b0ff9af4f6","abstract_canon_sha256":"ff3dcdde1982fd15e4411d3df49121d84793c941eb87a0ad889000b53b84ecc6"},"schema_version":"1.0"},"canonical_sha256":"6461ae5d50f4daf3a9e0bb98e9a75dd53e006aa987ea166eb43965d594ce5d67","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:34.371580Z","signature_b64":"EqDnPnFyK7vbCDMnmTBa31gZrT9ctF/D55kBsvT4N+i4Xeh7agJz+j14KYlIQosPy7wJNxCKm+VwaV5v10QkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6461ae5d50f4daf3a9e0bb98e9a75dd53e006aa987ea166eb43965d594ce5d67","last_reissued_at":"2026-05-18T02:10:34.370939Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:34.370939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.0591","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f38SU+TcQEaOz9ARCwVEn0B6PFCrw9zOSKDii5aZKMbCVC6GZDHCkX8w6vZ4+tNPk2kwnX4WV6TaX+0Kb0KUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:45:10.004419Z"},"content_sha256":"e43136e7bd862ad8343d96d6fbf256c3c25c98310faa9f881dfaa2025c4308b7","schema_version":"1.0","event_id":"sha256:e43136e7bd862ad8343d96d6fbf256c3c25c98310faa9f881dfaa2025c4308b7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:MRQ24XKQ6TNPHKPAXOMOTJ252U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large normally hyperbolic cylinders in a priori stable Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Patrick Bernard (CEREMADE)","submitted_at":"2009-12-03T08:01:09Z","abstract_excerpt":"We prove the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0591","kind":"arxiv","version":2},"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":"2026-05-18T02:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"huIle7WZ8YwSplqEbr0OYT/XNRljdHEBx26bpii6TgrkJm1w+OvHyCIE4jspFH+pv6KbEYrzOY8E+IVqGeSVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:45:10.004822Z"},"content_sha256":"1d92b92a2dfa6bba5853ae227fb4b42a660dedc57beecb0bacff0ef683c4b9b8","schema_version":"1.0","event_id":"sha256:1d92b92a2dfa6bba5853ae227fb4b42a660dedc57beecb0bacff0ef683c4b9b8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/bundle.json","state_url":"https://pith.science/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/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":"2026-06-06T15:45:10Z","links":{"resolver":"https://pith.science/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U","bundle":"https://pith.science/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/bundle.json","state":"https://pith.science/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MRQ24XKQ6TNPHKPAXOMOTJ252U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:MRQ24XKQ6TNPHKPAXOMOTJ252U","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":"ff3dcdde1982fd15e4411d3df49121d84793c941eb87a0ad889000b53b84ecc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-03T08:01:09Z","title_canon_sha256":"04920f8a3d53037637b4a8ce826d44d093160cda7aea6c02e68013b0ff9af4f6"},"schema_version":"1.0","source":{"id":"0912.0591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.0591","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"0912.0591v2","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.0591","created_at":"2026-05-18T02:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"MRQ24XKQ6TNP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"MRQ24XKQ6TNPHKPA","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"MRQ24XKQ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:1d92b92a2dfa6bba5853ae227fb4b42a660dedc57beecb0bacff0ef683c4b9b8","target":"graph","created_at":"2026-05-18T02:10:34Z","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 the existence of normally hyperbolic invariant cylinders in nearly integrable hamiltonian systems.","authors_text":"Patrick Bernard (CEREMADE)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-03T08:01:09Z","title":"Large normally hyperbolic cylinders in a priori stable Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.0591","kind":"arxiv","version":2},"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:e43136e7bd862ad8343d96d6fbf256c3c25c98310faa9f881dfaa2025c4308b7","target":"record","created_at":"2026-05-18T02:10:34Z","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":"ff3dcdde1982fd15e4411d3df49121d84793c941eb87a0ad889000b53b84ecc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-12-03T08:01:09Z","title_canon_sha256":"04920f8a3d53037637b4a8ce826d44d093160cda7aea6c02e68013b0ff9af4f6"},"schema_version":"1.0","source":{"id":"0912.0591","kind":"arxiv","version":2}},"canonical_sha256":"6461ae5d50f4daf3a9e0bb98e9a75dd53e006aa987ea166eb43965d594ce5d67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6461ae5d50f4daf3a9e0bb98e9a75dd53e006aa987ea166eb43965d594ce5d67","first_computed_at":"2026-05-18T02:10:34.370939Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:10:34.370939Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EqDnPnFyK7vbCDMnmTBa31gZrT9ctF/D55kBsvT4N+i4Xeh7agJz+j14KYlIQosPy7wJNxCKm+VwaV5v10QkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:10:34.371580Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.0591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e43136e7bd862ad8343d96d6fbf256c3c25c98310faa9f881dfaa2025c4308b7","sha256:1d92b92a2dfa6bba5853ae227fb4b42a660dedc57beecb0bacff0ef683c4b9b8"],"state_sha256":"61331373a4efe81f470b12d585d23a4a396952e4ff03cac0950035141e1b0f33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNg+5ed58nGicShfCLz9udiLworYBPcnY/Yx48jZA/50NhPlpiasjxefqU/JEDdB6uA0Rh5XCpFfDRW5bYi9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:45:10.008007Z","bundle_sha256":"13160aa79b51d9ba3282a8226b2c15c43710cdd4d33c7795ee3c2cbc905002dc"}}