{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:R4BN5FVD4YADVLAZ6P5V7LN4ZM","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":"183d12b57ee69a7297c9c35d6b3a35fc908d01029f7f5041140aa5f5af5330e9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2005-04-11T05:20:18Z","title_canon_sha256":"0302544654e00911a94d7a6c19c161c213f60b703895312e03e202e82d4f9ad3"},"schema_version":"1.0","source":{"id":"math/0504208","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504208","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504208v4","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504208","created_at":"2026-05-18T04:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"R4BN5FVD4YAD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"R4BN5FVD4YADVLAZ","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"R4BN5FVD","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9aedf823cbbf5f940bef8dae68e8c25d85961c2cd2e9d1ae6969ae7470993f02","target":"graph","created_at":"2026-05-18T04:13:46Z","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 give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2 \\times I$-models. We also apply our method to rigidity problems of some group actions.","authors_text":"Masayuki Asaoka","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2005-04-11T05:20:18Z","title":"Regular projectively Anosov flows on three-dimensional manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504208","kind":"arxiv","version":4},"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:ee6416c9b1b090e22d532e0b66fff5c269782c2aa850afba3b4e01af24ffa7f3","target":"record","created_at":"2026-05-18T04:13:46Z","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":"183d12b57ee69a7297c9c35d6b3a35fc908d01029f7f5041140aa5f5af5330e9","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2005-04-11T05:20:18Z","title_canon_sha256":"0302544654e00911a94d7a6c19c161c213f60b703895312e03e202e82d4f9ad3"},"schema_version":"1.0","source":{"id":"math/0504208","kind":"arxiv","version":4}},"canonical_sha256":"8f02de96a3e6003aac19f3fb5fadbccb2fc3966848f8c37a5ec8fb6ff8ff274a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f02de96a3e6003aac19f3fb5fadbccb2fc3966848f8c37a5ec8fb6ff8ff274a","first_computed_at":"2026-05-18T04:13:46.156990Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:13:46.156990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kkN5EJZS7XmmJ0Hf5uRm91JAyLVvTlBoABmHJH5q77shxEqR1cqkJbKm/w0Ceq2jI7DDMK5Gb6M6U8RnIH6WDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:13:46.157550Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504208","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee6416c9b1b090e22d532e0b66fff5c269782c2aa850afba3b4e01af24ffa7f3","sha256:9aedf823cbbf5f940bef8dae68e8c25d85961c2cd2e9d1ae6969ae7470993f02"],"state_sha256":"213b791d5e3c4a9b2986adb82f59ccc0a93b663fc2ee29274ffb5328082c3246"}