{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FZ2NSK7WOVXL62Y3FZFDU64JUK","short_pith_number":"pith:FZ2NSK7W","canonical_record":{"source":{"id":"1302.5333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T16:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"563e96bf9ebdc76c663085005bf387abf7c21290ef491499505aeacec66b046c","abstract_canon_sha256":"4d1a4830f729f70f7deba6bcdc472949a1eafc583504680e8a72116fa1ed91d4"},"schema_version":"1.0"},"canonical_sha256":"2e74d92bf6756ebf6b1b2e4a3a7b89a2b5b431514fbb763d76e7755fdc348161","source":{"kind":"arxiv","id":"1302.5333","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5333","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5333v1","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5333","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"pith_short_12","alias_value":"FZ2NSK7WOVXL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZ2NSK7WOVXL62Y3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZ2NSK7W","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FZ2NSK7WOVXL62Y3FZFDU64JUK","target":"record","payload":{"canonical_record":{"source":{"id":"1302.5333","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T16:50:16Z","cross_cats_sorted":[],"title_canon_sha256":"563e96bf9ebdc76c663085005bf387abf7c21290ef491499505aeacec66b046c","abstract_canon_sha256":"4d1a4830f729f70f7deba6bcdc472949a1eafc583504680e8a72116fa1ed91d4"},"schema_version":"1.0"},"canonical_sha256":"2e74d92bf6756ebf6b1b2e4a3a7b89a2b5b431514fbb763d76e7755fdc348161","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:57.988563Z","signature_b64":"PAeGZpi8ETdAFPU63rhD8Tg85OFy3QFG2LBQIzcKoXQstIU5YO2FBaq8e22recBoDGWVlweOWJ5b6SQSsnrWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e74d92bf6756ebf6b1b2e4a3a7b89a2b5b431514fbb763d76e7755fdc348161","last_reissued_at":"2026-05-18T03:32:57.987657Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:57.987657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.5333","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":"2026-05-18T03:32:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YvFcbHa0KXa7NPBhbMLQ2ZFv9/h3ZvtLyFlPpbNkpm2JiC8FYTTHv1A9V8nmzwOrVaJ/SPVcCEQZwSU0L7hQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:53:48.420654Z"},"content_sha256":"e6c5240e501718d9a9468d53320be6d8a8e525e0e391b0f1ff4a7db0b038e8bd","schema_version":"1.0","event_id":"sha256:e6c5240e501718d9a9468d53320be6d8a8e525e0e391b0f1ff4a7db0b038e8bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FZ2NSK7WOVXL62Y3FZFDU64JUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial symmetry breaking and heteroclinic tangencies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alexandre A. P. Rodrigues, Isabel S. Labouriau","submitted_at":"2013-02-21T16:50:16Z","abstract_excerpt":"We study some global aspects of the bifurcation of an equivariant family of volume-contracting vector fields on the three-dimensional sphere. When part of the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the symmetry, we investigate the mechanism of the emergence of heteroclinic tangencies coexisting with transverse connections. We find persistent suspended horseshoes accompanied by attracting periodic trajectories with long periods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5333","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":"2026-05-18T03:32:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGWwEroNpAM5R2Exgt2DjK/560mHs0L9YkEiB8KR3buVNqisxooMmZ7eH0oRPE5D/wSyGUls5orVXVhHvmN5Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:53:48.420998Z"},"content_sha256":"17f9d8d305da3ac1ac5d6a3db71e23d6ffbf1d4629e18fc41c0b3a443a4095f2","schema_version":"1.0","event_id":"sha256:17f9d8d305da3ac1ac5d6a3db71e23d6ffbf1d4629e18fc41c0b3a443a4095f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/bundle.json","state_url":"https://pith.science/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/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":"2026-06-23T14:53:48Z","links":{"resolver":"https://pith.science/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK","bundle":"https://pith.science/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/bundle.json","state":"https://pith.science/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZ2NSK7WOVXL62Y3FZFDU64JUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FZ2NSK7WOVXL62Y3FZFDU64JUK","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":"4d1a4830f729f70f7deba6bcdc472949a1eafc583504680e8a72116fa1ed91d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T16:50:16Z","title_canon_sha256":"563e96bf9ebdc76c663085005bf387abf7c21290ef491499505aeacec66b046c"},"schema_version":"1.0","source":{"id":"1302.5333","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.5333","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"arxiv_version","alias_value":"1302.5333v1","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.5333","created_at":"2026-05-18T03:32:57Z"},{"alias_kind":"pith_short_12","alias_value":"FZ2NSK7WOVXL","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FZ2NSK7WOVXL62Y3","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FZ2NSK7W","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:17f9d8d305da3ac1ac5d6a3db71e23d6ffbf1d4629e18fc41c0b3a443a4095f2","target":"graph","created_at":"2026-05-18T03:32:57Z","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 study some global aspects of the bifurcation of an equivariant family of volume-contracting vector fields on the three-dimensional sphere. When part of the symmetry is broken, the vector fields exhibit Bykov cycles. Close to the symmetry, we investigate the mechanism of the emergence of heteroclinic tangencies coexisting with transverse connections. We find persistent suspended horseshoes accompanied by attracting periodic trajectories with long periods.","authors_text":"Alexandre A. P. Rodrigues, Isabel S. Labouriau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T16:50:16Z","title":"Partial symmetry breaking and heteroclinic tangencies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.5333","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:e6c5240e501718d9a9468d53320be6d8a8e525e0e391b0f1ff4a7db0b038e8bd","target":"record","created_at":"2026-05-18T03:32:57Z","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":"4d1a4830f729f70f7deba6bcdc472949a1eafc583504680e8a72116fa1ed91d4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-21T16:50:16Z","title_canon_sha256":"563e96bf9ebdc76c663085005bf387abf7c21290ef491499505aeacec66b046c"},"schema_version":"1.0","source":{"id":"1302.5333","kind":"arxiv","version":1}},"canonical_sha256":"2e74d92bf6756ebf6b1b2e4a3a7b89a2b5b431514fbb763d76e7755fdc348161","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e74d92bf6756ebf6b1b2e4a3a7b89a2b5b431514fbb763d76e7755fdc348161","first_computed_at":"2026-05-18T03:32:57.987657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:57.987657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PAeGZpi8ETdAFPU63rhD8Tg85OFy3QFG2LBQIzcKoXQstIU5YO2FBaq8e22recBoDGWVlweOWJ5b6SQSsnrWAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:57.988563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.5333","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6c5240e501718d9a9468d53320be6d8a8e525e0e391b0f1ff4a7db0b038e8bd","sha256:17f9d8d305da3ac1ac5d6a3db71e23d6ffbf1d4629e18fc41c0b3a443a4095f2"],"state_sha256":"d1914c8235eeaa5bf54c7af36b93ed67c524ea04e677bc3de42652997d52dc18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhfFYbGKpVdLrV6MbZZ3hIgb1On17VjhBiSYltAx4h1jf0PnvXG/QzsTNCQ7LpbHaHWvXzqNfoloPBDXgQLsAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:53:48.422947Z","bundle_sha256":"5881093f37b0a5799e22e4de741897996ab446c2257f308515096d0277ad9b87"}}