{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4Z6AWRFOX6FJ4DGUV7VCDCNMHL","short_pith_number":"pith:4Z6AWRFO","canonical_record":{"source":{"id":"2505.24598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T13:46:20Z","cross_cats_sorted":[],"title_canon_sha256":"60795f6d3376b59866275d7a1595facbeed7fe22bf49f34d1f55ff5b64eb334e","abstract_canon_sha256":"7f6c0fec9b969bb576f30e112bd359943943d755404c483212e53fdac9c12a31"},"schema_version":"1.0"},"canonical_sha256":"e67c0b44aebf8a9e0cd4afea2189ac3add5b19ba6150ed062bcb59587b2f5272","source":{"kind":"arxiv","id":"2505.24598","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4Z6AWRFOX6FJ4DGUV7VCDCNMHL","target":"record","payload":{"canonical_record":{"source":{"id":"2505.24598","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2025-05-30T13:46:20Z","cross_cats_sorted":[],"title_canon_sha256":"60795f6d3376b59866275d7a1595facbeed7fe22bf49f34d1f55ff5b64eb334e","abstract_canon_sha256":"7f6c0fec9b969bb576f30e112bd359943943d755404c483212e53fdac9c12a31"},"schema_version":"1.0"},"canonical_sha256":"e67c0b44aebf8a9e0cd4afea2189ac3add5b19ba6150ed062bcb59587b2f5272","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:52.962010Z","signature_b64":"Rxeo68VkJLx45bYYTja2fo55XsfIyjt3ee7EiQf0L1O7osRhpAjFLVWclw1BNpKIcbaYzVkT9FGWN7+li3hoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e67c0b44aebf8a9e0cd4afea2189ac3add5b19ba6150ed062bcb59587b2f5272","last_reissued_at":"2026-07-05T11:12:52.961454Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:52.961454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.24598","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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+/fJR8SdCCNBpfbgbQhMGTkcaoL1qQTRQp7eU+s6fVXlz/bMuvDPoaNgEsYTNswMtNUCBO/W1UyE/e9VXQoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:01:53.263728Z"},"content_sha256":"058458e05d2675d2b4a5f2f7f3f13410bdd70846bed3755ca3e0880e6baf9ebe","schema_version":"1.0","event_id":"sha256:058458e05d2675d2b4a5f2f7f3f13410bdd70846bed3755ca3e0880e6baf9ebe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4Z6AWRFOX6FJ4DGUV7VCDCNMHL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anosov actions: minimality of foliations or suspension action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Carlos Maquera, R\\'egis Var\\~ao, Rodrigo R. Lopes","submitted_at":"2025-05-30T13:46:20Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.24598","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.24598/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ajlmMn5aRtVeffPj08me3/XAn7u7S4yVB9Eq1Sox6pzUdqpjWKUrrocEI+75UuE5g2oXW26YfUXs9N1eRGuaCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T17:01:53.264723Z"},"content_sha256":"e1d5c3c582d1fc946bdd6c20f370fc1728b7f83ba733153b9a416f92150e63bc","schema_version":"1.0","event_id":"sha256:e1d5c3c582d1fc946bdd6c20f370fc1728b7f83ba733153b9a416f92150e63bc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/bundle.json","state_url":"https://pith.science/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/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":"2026-08-08T17:01:53Z","links":{"resolver":"https://pith.science/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL","bundle":"https://pith.science/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/bundle.json","state":"https://pith.science/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4Z6AWRFOX6FJ4DGUV7VCDCNMHL/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+sPvZ71+p0Tc7St6RC6dMW29IDmqkUAzuUfWV20EH+fbxDTWbQA8h/1mSfaTv67fs4wW5QAzmKhEEDLMaJdZDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T17:01:53.270690Z","bundle_sha256":"87487be520b6d5c8a81b4b2b3b2a46df8b0f5e88c686cf10c31e4b52359c846b"}}