{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HX7ALZIWPNMPSBVNIG3U43SFID","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":"8504a1403be43eb7f37fd6859b53e4d8714f71760630ff984546a9b4042c4487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-16T21:35:46Z","title_canon_sha256":"0809e06e97d42dcc6753b10651de0add01879f398f8f76e342969a915c3936e8"},"schema_version":"1.0","source":{"id":"1011.3836","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.3836","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1011.3836v1","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3836","created_at":"2026-05-18T04:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"HX7ALZIWPNMP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HX7ALZIWPNMPSBVN","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HX7ALZIW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:2cb0edf1f319e7f2f5b818021fe789ce42f751a1232350618ba1b7f53e6b4135","target":"graph","created_at":"2026-05-18T04:35:47Z","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 that any diffeomorphism of a compact manifold can be approximated in topology C1 by another diffeomorphism exhibiting a homoclinic bifurcation (a homoclinic tangency or a heterodimensional cycle) or by one which is essentially hyperbolic (it has a finite number of transitive hyperbolic attractors with open and dense basin of attraction).","authors_text":"Enrique R. Pujals, Sylvain Crovisier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-16T21:35:46Z","title":"Essential hyperbolicity and homoclinic bifurcations: a dichotomy phenomenon/mechanism for diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3836","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":"sha256:13023f74f2e5920830a91965a462e3224c5871bd40794122e1060d702a3584ac","target":"record","created_at":"2026-05-18T04:35:47Z","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":"8504a1403be43eb7f37fd6859b53e4d8714f71760630ff984546a9b4042c4487","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-16T21:35:46Z","title_canon_sha256":"0809e06e97d42dcc6753b10651de0add01879f398f8f76e342969a915c3936e8"},"schema_version":"1.0","source":{"id":"1011.3836","kind":"arxiv","version":1}},"canonical_sha256":"3dfe05e5167b58f906ad41b74e6e4540d080e989d6aba7b8a33a74efe5864dd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3dfe05e5167b58f906ad41b74e6e4540d080e989d6aba7b8a33a74efe5864dd8","first_computed_at":"2026-05-18T04:35:47.479822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:47.479822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWMVx3EYFho3+kvMjoK/h5iGfR7mVIIGrQOjYus619cZtvFqW63T3/UUzfwBi0zzw2hhQBJorueZo4dcB1IkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:47.480383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.3836","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13023f74f2e5920830a91965a462e3224c5871bd40794122e1060d702a3584ac","sha256:2cb0edf1f319e7f2f5b818021fe789ce42f751a1232350618ba1b7f53e6b4135"],"state_sha256":"aa16cc32e7887e30e70914fecb9d2b697418b5d1f978727bb33a3f6e9aa35b31"}