{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:63WLC2VGHMS2YLPS3JGT2H2B26","short_pith_number":"pith:63WLC2VG","canonical_record":{"source":{"id":"0909.3801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-21T15:29:45Z","cross_cats_sorted":[],"title_canon_sha256":"8f36245705be7cf59e98252131ab8e24a3e9aab0d28e769a32e6bc786d42d3a8","abstract_canon_sha256":"d85f87c983c16a3570a22f57f92a01823adb2dc60e9e19964789f6ccb696b203"},"schema_version":"1.0"},"canonical_sha256":"f6ecb16aa63b25ac2df2da4d3d1f41d791ab291eb81b609550308dc8ef7e2ada","source":{"kind":"arxiv","id":"0909.3801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3801","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3801v1","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3801","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"63WLC2VGHMS2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"63WLC2VGHMS2YLPS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"63WLC2VG","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:63WLC2VGHMS2YLPS3JGT2H2B26","target":"record","payload":{"canonical_record":{"source":{"id":"0909.3801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-21T15:29:45Z","cross_cats_sorted":[],"title_canon_sha256":"8f36245705be7cf59e98252131ab8e24a3e9aab0d28e769a32e6bc786d42d3a8","abstract_canon_sha256":"d85f87c983c16a3570a22f57f92a01823adb2dc60e9e19964789f6ccb696b203"},"schema_version":"1.0"},"canonical_sha256":"f6ecb16aa63b25ac2df2da4d3d1f41d791ab291eb81b609550308dc8ef7e2ada","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:11:45.726340Z","signature_b64":"xJpnWq1arYK4jRx8/b+DYgUUhFCdcxw2iiGTd30b04vV3m00MaAPV2p9WU0KasFXsqcUDoOwKQGf5/eEibqZCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6ecb16aa63b25ac2df2da4d3d1f41d791ab291eb81b609550308dc8ef7e2ada","last_reissued_at":"2026-05-18T02:11:45.725382Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:11:45.725382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.3801","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":"2026-05-18T02:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oi82WHbyPYFUjWXXB/v56aqNVsz/RHQldjRBtYLKK6kM2rCYQ50W3/dKZnJ+cunWNZDRDYMaVlPDJNlWBj8MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:02:37.064950Z"},"content_sha256":"daa47c2f1ca5b469024038370d6c131d21284a3d4aae7a2eadfa3a432a48b6f8","schema_version":"1.0","event_id":"sha256:daa47c2f1ca5b469024038370d6c131d21284a3d4aae7a2eadfa3a432a48b6f8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:63WLC2VGHMS2YLPS3JGT2H2B26","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Stability of the Set of Hyperbolic Closed Orbits of a Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Celia Ferreira, Jorge Rocha, Mario Bessa","submitted_at":"2009-09-21T15:29:45Z","abstract_excerpt":"A Hamiltonian level, say a pair $(H,e)$ of a Hamiltonian $H$ and an energy $e \\in \\mathbb{R}$, is said to be Anosov if there exists a connected component $\\mathcal{E}_{H,e}$ of $H^{-1}({e})$ which is uniformly hyperbolic for the Hamiltonian flow $X_H^t$. The pair $(H,e)$ is said to be a Hamiltonian star system if there exists a connected component $\\mathcal{E}^\\star_{H,e}$ of the energy level $H^{-1}({{e}})$ such that all the closed orbits and all the critical points of $\\mathcal{E}^\\star_{H,e}$ are hyperbolic, and the same holds for a connected component of the energy level $\\tilde{H}^{-1}({\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3801","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":"2026-05-18T02:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GTi6cbtJiLjd2Ix5Yo6HKsjeGAB3qlQffCtDh5GuMyWZziF5uW8MNZfIX3Zc9292feELcNVpNFXFvNwrB3/TAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:02:37.066089Z"},"content_sha256":"c84fe712c55067f58c87f796a7d4f7e05215a6803277c0f1603bb4a730168deb","schema_version":"1.0","event_id":"sha256:c84fe712c55067f58c87f796a7d4f7e05215a6803277c0f1603bb4a730168deb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63WLC2VGHMS2YLPS3JGT2H2B26/bundle.json","state_url":"https://pith.science/pith/63WLC2VGHMS2YLPS3JGT2H2B26/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63WLC2VGHMS2YLPS3JGT2H2B26/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":"2026-06-08T17:02:37Z","links":{"resolver":"https://pith.science/pith/63WLC2VGHMS2YLPS3JGT2H2B26","bundle":"https://pith.science/pith/63WLC2VGHMS2YLPS3JGT2H2B26/bundle.json","state":"https://pith.science/pith/63WLC2VGHMS2YLPS3JGT2H2B26/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63WLC2VGHMS2YLPS3JGT2H2B26/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:63WLC2VGHMS2YLPS3JGT2H2B26","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":"d85f87c983c16a3570a22f57f92a01823adb2dc60e9e19964789f6ccb696b203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-21T15:29:45Z","title_canon_sha256":"8f36245705be7cf59e98252131ab8e24a3e9aab0d28e769a32e6bc786d42d3a8"},"schema_version":"1.0","source":{"id":"0909.3801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3801","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3801v1","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3801","created_at":"2026-05-18T02:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"63WLC2VGHMS2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"63WLC2VGHMS2YLPS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"63WLC2VG","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c84fe712c55067f58c87f796a7d4f7e05215a6803277c0f1603bb4a730168deb","target":"graph","created_at":"2026-05-18T02:11:45Z","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":"A Hamiltonian level, say a pair $(H,e)$ of a Hamiltonian $H$ and an energy $e \\in \\mathbb{R}$, is said to be Anosov if there exists a connected component $\\mathcal{E}_{H,e}$ of $H^{-1}({e})$ which is uniformly hyperbolic for the Hamiltonian flow $X_H^t$. The pair $(H,e)$ is said to be a Hamiltonian star system if there exists a connected component $\\mathcal{E}^\\star_{H,e}$ of the energy level $H^{-1}({{e}})$ such that all the closed orbits and all the critical points of $\\mathcal{E}^\\star_{H,e}$ are hyperbolic, and the same holds for a connected component of the energy level $\\tilde{H}^{-1}({\\","authors_text":"Celia Ferreira, Jorge Rocha, Mario Bessa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-21T15:29:45Z","title":"On the Stability of the Set of Hyperbolic Closed Orbits of a Hamiltonian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3801","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:daa47c2f1ca5b469024038370d6c131d21284a3d4aae7a2eadfa3a432a48b6f8","target":"record","created_at":"2026-05-18T02:11:45Z","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":"d85f87c983c16a3570a22f57f92a01823adb2dc60e9e19964789f6ccb696b203","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2009-09-21T15:29:45Z","title_canon_sha256":"8f36245705be7cf59e98252131ab8e24a3e9aab0d28e769a32e6bc786d42d3a8"},"schema_version":"1.0","source":{"id":"0909.3801","kind":"arxiv","version":1}},"canonical_sha256":"f6ecb16aa63b25ac2df2da4d3d1f41d791ab291eb81b609550308dc8ef7e2ada","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6ecb16aa63b25ac2df2da4d3d1f41d791ab291eb81b609550308dc8ef7e2ada","first_computed_at":"2026-05-18T02:11:45.725382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:11:45.725382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xJpnWq1arYK4jRx8/b+DYgUUhFCdcxw2iiGTd30b04vV3m00MaAPV2p9WU0KasFXsqcUDoOwKQGf5/eEibqZCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:11:45.726340Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daa47c2f1ca5b469024038370d6c131d21284a3d4aae7a2eadfa3a432a48b6f8","sha256:c84fe712c55067f58c87f796a7d4f7e05215a6803277c0f1603bb4a730168deb"],"state_sha256":"8fc31b1077079d0f2f6294c221fb6c7db9e1abe7a91694cc747d91d3df971a61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B+3kJEehFwXAC3qbBr5upD0NvEFxqW5KIDE/BhbJGrkpxJ6nehGpvCtn15OTWsc1xLXMZYB/RTnXnswC7vEpAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:02:37.070384Z","bundle_sha256":"966041ef5778530e87ff4a69791e15410c4a8c0ab1532ed06a34d970dc10ded9"}}