{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4Z6AWRFOX6FJ4DGUV7VCDCNMHL","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":"7f6c0fec9b969bb576f30e112bd359943943d755404c483212e53fdac9c12a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T13:46:20Z","title_canon_sha256":"60795f6d3376b59866275d7a1595facbeed7fe22bf49f34d1f55ff5b64eb334e"},"schema_version":"1.0","source":{"id":"2505.24598","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.24598","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"2505.24598v1","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.24598","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"4Z6AWRFOX6FJ","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_16","alias_value":"4Z6AWRFOX6FJ4DGU","created_at":"2026-07-05T11:12:52Z"},{"alias_kind":"pith_short_8","alias_value":"4Z6AWRFO","created_at":"2026-07-05T11:12:52Z"}],"graph_snapshots":[{"event_id":"sha256:e1d5c3c582d1fc946bdd6c20f370fc1728b7f83ba733153b9a416f92150e63bc","target":"graph","created_at":"2026-07-05T11:12:52Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.24598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that an Anosov action of $\\mathbb{R}^k$ over a compact manifold $M$ transitive on regular sub-cones satisfies the dichotomy: each stable and unstable leaf is dense or the Anosov action is topologically conjugated to a suspension of a $\\mathbb{Z}^k$-Anosov action. This represents an important progress toward addressing Verjovsky's extended conjecture for Anosov actions, as developed by Barbot and Maquera.","authors_text":"Carlos Maquera, R\\'egis Var\\~ao, Rodrigo R. Lopes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T13:46:20Z","title":"Anosov actions: minimality of foliations or suspension action"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24598","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":"sha256:058458e05d2675d2b4a5f2f7f3f13410bdd70846bed3755ca3e0880e6baf9ebe","target":"record","created_at":"2026-07-05T11:12:52Z","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":"7f6c0fec9b969bb576f30e112bd359943943d755404c483212e53fdac9c12a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T13:46:20Z","title_canon_sha256":"60795f6d3376b59866275d7a1595facbeed7fe22bf49f34d1f55ff5b64eb334e"},"schema_version":"1.0","source":{"id":"2505.24598","kind":"arxiv","version":1}},"canonical_sha256":"e67c0b44aebf8a9e0cd4afea2189ac3add5b19ba6150ed062bcb59587b2f5272","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e67c0b44aebf8a9e0cd4afea2189ac3add5b19ba6150ed062bcb59587b2f5272","first_computed_at":"2026-07-05T11:12:52.961454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:12:52.961454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rxeo68VkJLx45bYYTja2fo55XsfIyjt3ee7EiQf0L1O7osRhpAjFLVWclw1BNpKIcbaYzVkT9FGWN7+li3hoBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:12:52.962010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.24598","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:058458e05d2675d2b4a5f2f7f3f13410bdd70846bed3755ca3e0880e6baf9ebe","sha256:e1d5c3c582d1fc946bdd6c20f370fc1728b7f83ba733153b9a416f92150e63bc"],"state_sha256":"32321bb49e4d32433ae3fb64d17309ce81070c9ae970a27bf5faef1515b8c302"}