{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JVM7ANXDVWDS3E3HSOFZ6BYQWP","short_pith_number":"pith:JVM7ANXD","canonical_record":{"source":{"id":"1212.1931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-09T22:52:15Z","cross_cats_sorted":[],"title_canon_sha256":"6fab7aeadaf7056c322776fa43bd9f381fe1fda8879bdaab1fa6bd0e804b712e","abstract_canon_sha256":"0ba889fe096168c3ee9fdca4b919f55c8814158c5f24f8af71285306d1007ea4"},"schema_version":"1.0"},"canonical_sha256":"4d59f036e3ad872d9367938b9f0710b3e7bea2e3606b97b82e26be6354754cca","source":{"kind":"arxiv","id":"1212.1931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1931","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1931v1","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1931","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"JVM7ANXDVWDS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JVM7ANXDVWDS3E3H","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JVM7ANXD","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JVM7ANXDVWDS3E3HSOFZ6BYQWP","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-09T22:52:15Z","cross_cats_sorted":[],"title_canon_sha256":"6fab7aeadaf7056c322776fa43bd9f381fe1fda8879bdaab1fa6bd0e804b712e","abstract_canon_sha256":"0ba889fe096168c3ee9fdca4b919f55c8814158c5f24f8af71285306d1007ea4"},"schema_version":"1.0"},"canonical_sha256":"4d59f036e3ad872d9367938b9f0710b3e7bea2e3606b97b82e26be6354754cca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:54.730381Z","signature_b64":"RMTb+sqfLr5KM2csG/V+w+vCktC6ncNKFmuTiTHX3wop440xQK2JXXSfAJdLr12IK42WUSXr7NEOj9FOB9MwBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d59f036e3ad872d9367938b9f0710b3e7bea2e3606b97b82e26be6354754cca","last_reissued_at":"2026-05-18T03:38:54.729700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:54.729700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1931","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":"2026-05-18T03:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z4TQ3XO6SLlVQLn54eZCJ+zSfA7okdu+ucqnuXEagt6ALjH3xt9UnJueZ3SZH2LshethwCxaXefLrPY2aPtaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:42:34.773755Z"},"content_sha256":"5f5ffba15cca43c76826afd505f68a9020115c3e802b795cd5dd03c22e752970","schema_version":"1.0","event_id":"sha256:5f5ffba15cca43c76826afd505f68a9020115c3e802b795cd5dd03c22e752970"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JVM7ANXDVWDS3E3HSOFZ6BYQWP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Attractors and repellers near generic elliptic points of reversible maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Dmitry Turaev, Isabel Rios, Jeroen Lamb, Sergey Gonchenko","submitted_at":"2012-12-09T22:52:15Z","abstract_excerpt":"We show that resonance zones near an elliptic periodic point of a reversible map must, generically, contain asymptotically stable and asymptotically unstable periodic orbits, along with wild hyperbolic sets."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1931","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":"2026-05-18T03:38:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zs+aFHUDvK1bqBJx2YERuCKPhhIt2DRv65m8hGs2rO/Hv7axkI8PjyEn9NGk345O4dsqML3raGa1vqXNI2i/Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:42:34.774092Z"},"content_sha256":"221b3a05df310ccaab9b2d9a4e526ccf7f76d9360c167b042e5fd7258b1215a4","schema_version":"1.0","event_id":"sha256:221b3a05df310ccaab9b2d9a4e526ccf7f76d9360c167b042e5fd7258b1215a4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/bundle.json","state_url":"https://pith.science/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/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":"2026-06-01T20:42:34Z","links":{"resolver":"https://pith.science/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP","bundle":"https://pith.science/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/bundle.json","state":"https://pith.science/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JVM7ANXDVWDS3E3HSOFZ6BYQWP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JVM7ANXDVWDS3E3HSOFZ6BYQWP","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":"0ba889fe096168c3ee9fdca4b919f55c8814158c5f24f8af71285306d1007ea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-09T22:52:15Z","title_canon_sha256":"6fab7aeadaf7056c322776fa43bd9f381fe1fda8879bdaab1fa6bd0e804b712e"},"schema_version":"1.0","source":{"id":"1212.1931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1931","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1931v1","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1931","created_at":"2026-05-18T03:38:54Z"},{"alias_kind":"pith_short_12","alias_value":"JVM7ANXDVWDS","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JVM7ANXDVWDS3E3H","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JVM7ANXD","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:221b3a05df310ccaab9b2d9a4e526ccf7f76d9360c167b042e5fd7258b1215a4","target":"graph","created_at":"2026-05-18T03:38:54Z","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 show that resonance zones near an elliptic periodic point of a reversible map must, generically, contain asymptotically stable and asymptotically unstable periodic orbits, along with wild hyperbolic sets.","authors_text":"Dmitry Turaev, Isabel Rios, Jeroen Lamb, Sergey Gonchenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-09T22:52:15Z","title":"Attractors and repellers near generic elliptic points of reversible maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1931","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":"sha256:5f5ffba15cca43c76826afd505f68a9020115c3e802b795cd5dd03c22e752970","target":"record","created_at":"2026-05-18T03:38:54Z","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":"0ba889fe096168c3ee9fdca4b919f55c8814158c5f24f8af71285306d1007ea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-12-09T22:52:15Z","title_canon_sha256":"6fab7aeadaf7056c322776fa43bd9f381fe1fda8879bdaab1fa6bd0e804b712e"},"schema_version":"1.0","source":{"id":"1212.1931","kind":"arxiv","version":1}},"canonical_sha256":"4d59f036e3ad872d9367938b9f0710b3e7bea2e3606b97b82e26be6354754cca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d59f036e3ad872d9367938b9f0710b3e7bea2e3606b97b82e26be6354754cca","first_computed_at":"2026-05-18T03:38:54.729700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:54.729700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RMTb+sqfLr5KM2csG/V+w+vCktC6ncNKFmuTiTHX3wop440xQK2JXXSfAJdLr12IK42WUSXr7NEOj9FOB9MwBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:54.730381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f5ffba15cca43c76826afd505f68a9020115c3e802b795cd5dd03c22e752970","sha256:221b3a05df310ccaab9b2d9a4e526ccf7f76d9360c167b042e5fd7258b1215a4"],"state_sha256":"5f2c16b04b6c56f3280eebe5fbaab2279732b2c1adb5946c0d53dcd1e15df333"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GdHs4N+AcxUZWAo2J50RBVVuaeJcPuU1Z0Me8TnenXaJQw2KJhEUozKTyWAh/NdRYPM/rAnf2LLumeUYtYF3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:42:34.775905Z","bundle_sha256":"b14e6638d2e1a4e991981d3daf04e341c7d715ef39015c161ae3785b9085d2b2"}}