{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TKOGW3PY5TL4D4NNVTAXD6JNYJ","short_pith_number":"pith:TKOGW3PY","canonical_record":{"source":{"id":"1106.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T13:56:21Z","cross_cats_sorted":[],"title_canon_sha256":"6d3a51274ebf5881d61273922155f229601cb68eb51098694f8eed06e71c106e","abstract_canon_sha256":"eb943ea96b3ed88190051074cd9447511e66efd233b04d63eeb41af657c4386c"},"schema_version":"1.0"},"canonical_sha256":"9a9c6b6df8ecd7c1f1adacc171f92dc259210562ef315b32aed95fc5cb8d0132","source":{"kind":"arxiv","id":"1106.3905","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3905","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3905v1","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3905","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"TKOGW3PY5TL4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKOGW3PY5TL4D4NN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKOGW3PY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TKOGW3PY5TL4D4NNVTAXD6JNYJ","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3905","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T13:56:21Z","cross_cats_sorted":[],"title_canon_sha256":"6d3a51274ebf5881d61273922155f229601cb68eb51098694f8eed06e71c106e","abstract_canon_sha256":"eb943ea96b3ed88190051074cd9447511e66efd233b04d63eeb41af657c4386c"},"schema_version":"1.0"},"canonical_sha256":"9a9c6b6df8ecd7c1f1adacc171f92dc259210562ef315b32aed95fc5cb8d0132","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:41.881178Z","signature_b64":"+mS4rc91/g3i/lVct7Kh9S4MibLy6wYxd7uzJE46MJ7hPGBHU+smlzDsEon9LKmti16+GRv+Lqo9jEpsNt7jCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a9c6b6df8ecd7c1f1adacc171f92dc259210562ef315b32aed95fc5cb8d0132","last_reissued_at":"2026-05-18T04:19:41.880740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:41.880740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3905","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":"2026-05-18T04:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvjRrNJgE9/jmqWyUddzT850HUBYFZzRQavq20RjTt3VgYfPqCrwUJr+5CG64iOsPxR5I2BsXcoxSgDZ32A3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:18:06.761005Z"},"content_sha256":"9f2219c1ee66a0e7b3d1795092ecc961b23fd5c4361fd96f7d5abd12976e6bf8","schema_version":"1.0","event_id":"sha256:9f2219c1ee66a0e7b3d1795092ecc961b23fd5c4361fd96f7d5abd12976e6bf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TKOGW3PY5TL4D4NNVTAXD6JNYJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dominated chain recurrent class with singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, Dawei Yang, Shaobo Gan","submitted_at":"2011-06-20T13:56:21Z","abstract_excerpt":"We prove that for generic three-dimensional vector fields, domination implies singular hyperbolicity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3905","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":"2026-05-18T04:19:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbfilfxXlIWMhieFhGwtv+ex8vCi4o9w4xOwdorVMVWTHTRJQ+cQhqe6upONnB3CeV059gTa6RHAr7kl6ADWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:18:06.761676Z"},"content_sha256":"7e3f9e81ea07abec62f2d64b191c4e8b54c20f17a23a27466399b443ca3f2249","schema_version":"1.0","event_id":"sha256:7e3f9e81ea07abec62f2d64b191c4e8b54c20f17a23a27466399b443ca3f2249"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/bundle.json","state_url":"https://pith.science/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/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":"2026-05-26T03:18:06Z","links":{"resolver":"https://pith.science/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ","bundle":"https://pith.science/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/bundle.json","state":"https://pith.science/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TKOGW3PY5TL4D4NNVTAXD6JNYJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TKOGW3PY5TL4D4NNVTAXD6JNYJ","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":"eb943ea96b3ed88190051074cd9447511e66efd233b04d63eeb41af657c4386c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T13:56:21Z","title_canon_sha256":"6d3a51274ebf5881d61273922155f229601cb68eb51098694f8eed06e71c106e"},"schema_version":"1.0","source":{"id":"1106.3905","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3905","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3905v1","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3905","created_at":"2026-05-18T04:19:41Z"},{"alias_kind":"pith_short_12","alias_value":"TKOGW3PY5TL4","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TKOGW3PY5TL4D4NN","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TKOGW3PY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:7e3f9e81ea07abec62f2d64b191c4e8b54c20f17a23a27466399b443ca3f2249","target":"graph","created_at":"2026-05-18T04:19:41Z","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 for generic three-dimensional vector fields, domination implies singular hyperbolicity.","authors_text":"Christian Bonatti, Dawei Yang, Shaobo Gan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T13:56:21Z","title":"Dominated chain recurrent class with singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3905","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":"sha256:9f2219c1ee66a0e7b3d1795092ecc961b23fd5c4361fd96f7d5abd12976e6bf8","target":"record","created_at":"2026-05-18T04:19:41Z","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":"eb943ea96b3ed88190051074cd9447511e66efd233b04d63eeb41af657c4386c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-06-20T13:56:21Z","title_canon_sha256":"6d3a51274ebf5881d61273922155f229601cb68eb51098694f8eed06e71c106e"},"schema_version":"1.0","source":{"id":"1106.3905","kind":"arxiv","version":1}},"canonical_sha256":"9a9c6b6df8ecd7c1f1adacc171f92dc259210562ef315b32aed95fc5cb8d0132","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a9c6b6df8ecd7c1f1adacc171f92dc259210562ef315b32aed95fc5cb8d0132","first_computed_at":"2026-05-18T04:19:41.880740Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:41.880740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+mS4rc91/g3i/lVct7Kh9S4MibLy6wYxd7uzJE46MJ7hPGBHU+smlzDsEon9LKmti16+GRv+Lqo9jEpsNt7jCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:41.881178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3905","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f2219c1ee66a0e7b3d1795092ecc961b23fd5c4361fd96f7d5abd12976e6bf8","sha256:7e3f9e81ea07abec62f2d64b191c4e8b54c20f17a23a27466399b443ca3f2249"],"state_sha256":"7ed239507aafaae8a391afd6c9aaed064231c9022ac602880b28dd054bed71df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xGOJ9tBH0ESUv0J3xbpUBgtteZxTe3y4TsPWzdRUihrEXUIv8AvQDNlMmqRZxjrY3v9NHSQ4pNwU1Hz04eDDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:18:06.764964Z","bundle_sha256":"de9d99211ef8c7283cf98ec8eeecf0a764da4cc90c6556c6e9184ac58b5c50dc"}}