{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:NJFRSV3B3GIVAFCHR2MGKUSKZT","short_pith_number":"pith:NJFRSV3B","canonical_record":{"source":{"id":"1706.04962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-15T16:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"115ef2f7a47ed1443b530156ed3e835b6f45a41f566e50aa0c68bfc27d38ff15","abstract_canon_sha256":"a8c322587287d1ca799b27e6659bdc97b17058000d3c2a55c5d65a7de504dc7c"},"schema_version":"1.0"},"canonical_sha256":"6a4b195761d9915014478e9865524acce96d682da2a26245accb79413e93c4a1","source":{"kind":"arxiv","id":"1706.04962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04962","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04962v2","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04962","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"NJFRSV3B3GIV","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_16","alias_value":"NJFRSV3B3GIVAFCH","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_8","alias_value":"NJFRSV3B","created_at":"2026-07-05T01:52:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:NJFRSV3B3GIVAFCHR2MGKUSKZT","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-15T16:49:41Z","cross_cats_sorted":[],"title_canon_sha256":"115ef2f7a47ed1443b530156ed3e835b6f45a41f566e50aa0c68bfc27d38ff15","abstract_canon_sha256":"a8c322587287d1ca799b27e6659bdc97b17058000d3c2a55c5d65a7de504dc7c"},"schema_version":"1.0"},"canonical_sha256":"6a4b195761d9915014478e9865524acce96d682da2a26245accb79413e93c4a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:52:13.804598Z","signature_b64":"i3/HgUFuG6WefpjGvdHt/7X7+g6gqd7/G8WvMSFf/B59RP9/7embZYaYhetERHc02GC4IvM9/JY7tRIj6x42Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a4b195761d9915014478e9865524acce96d682da2a26245accb79413e93c4a1","last_reissued_at":"2026-07-05T01:52:13.804135Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:52:13.804135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04962","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wuKkMuBLgYsXbf2g1BrwzG0g9f5aESUAt2iFS4Ve5qoMV/gxlgNt4BNClp3sGF5AQTXfoaq9JmWOxPMUh8JdBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:46:26.876735Z"},"content_sha256":"eefbb63f98db2b6f6e6777b5664a8bd303038aec43329781f521e2d16d6156d6","schema_version":"1.0","event_id":"sha256:eefbb63f98db2b6f6e6777b5664a8bd303038aec43329781f521e2d16d6156d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:NJFRSV3B3GIVAFCHR2MGKUSKZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andrey Gogolev, Andy Hammerlindl, Christian Bonatti, Rafael Potrie","submitted_at":"2017-06-15T16:49:41Z","abstract_excerpt":"Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic flows on closed hyperbolic surfaces and for Anosov flows which admit transverse tori. We emphasize the similarity of both constructions through the concept of $h$-transversality, a tool which allows us to compose different mapping classes while retaining partial hyperbolicity.\n  In the case of the geodesic flow of a closed hyperbolic surface $S$ we build stab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04962","kind":"arxiv","version":2},"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/1706.04962/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":"2026-07-05T01:52:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tedPoPKSrFOTwhmH1OomKxmnMlbWeMLmuJq5Wg806I4tP1KQqG6xzSSL4CHZCYA3+ffuvbEXdMQIQY3hzHebDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T18:46:26.877537Z"},"content_sha256":"69b71c3066009856fc4f7d972dec6dec18fe622b15c0eefa16584d640f6acb99","schema_version":"1.0","event_id":"sha256:69b71c3066009856fc4f7d972dec6dec18fe622b15c0eefa16584d640f6acb99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/bundle.json","state_url":"https://pith.science/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/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":"2026-08-17T18:46:26Z","links":{"resolver":"https://pith.science/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT","bundle":"https://pith.science/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/bundle.json","state":"https://pith.science/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJFRSV3B3GIVAFCHR2MGKUSKZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:NJFRSV3B3GIVAFCHR2MGKUSKZT","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":"a8c322587287d1ca799b27e6659bdc97b17058000d3c2a55c5d65a7de504dc7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-15T16:49:41Z","title_canon_sha256":"115ef2f7a47ed1443b530156ed3e835b6f45a41f566e50aa0c68bfc27d38ff15"},"schema_version":"1.0","source":{"id":"1706.04962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04962","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04962v2","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04962","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"NJFRSV3B3GIV","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_16","alias_value":"NJFRSV3B3GIVAFCH","created_at":"2026-07-05T01:52:13Z"},{"alias_kind":"pith_short_8","alias_value":"NJFRSV3B","created_at":"2026-07-05T01:52:13Z"}],"graph_snapshots":[{"event_id":"sha256:69b71c3066009856fc4f7d972dec6dec18fe622b15c0eefa16584d640f6acb99","target":"graph","created_at":"2026-07-05T01:52:13Z","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/1706.04962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $M$ be a closed 3-manifold which admits an Anosov flow. In this paper we develop a technique for constructing partially hyperbolic representatives in many mapping classes of $M$. We apply this technique both in the setting of geodesic flows on closed hyperbolic surfaces and for Anosov flows which admit transverse tori. We emphasize the similarity of both constructions through the concept of $h$-transversality, a tool which allows us to compose different mapping classes while retaining partial hyperbolicity.\n  In the case of the geodesic flow of a closed hyperbolic surface $S$ we build stab","authors_text":"Andrey Gogolev, Andy Hammerlindl, Christian Bonatti, Rafael Potrie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-15T16:49:41Z","title":"Anomalous partially hyperbolic diffeomorphisms III: abundance and incoherence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04962","kind":"arxiv","version":2},"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:eefbb63f98db2b6f6e6777b5664a8bd303038aec43329781f521e2d16d6156d6","target":"record","created_at":"2026-07-05T01:52:13Z","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":"a8c322587287d1ca799b27e6659bdc97b17058000d3c2a55c5d65a7de504dc7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-06-15T16:49:41Z","title_canon_sha256":"115ef2f7a47ed1443b530156ed3e835b6f45a41f566e50aa0c68bfc27d38ff15"},"schema_version":"1.0","source":{"id":"1706.04962","kind":"arxiv","version":2}},"canonical_sha256":"6a4b195761d9915014478e9865524acce96d682da2a26245accb79413e93c4a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a4b195761d9915014478e9865524acce96d682da2a26245accb79413e93c4a1","first_computed_at":"2026-07-05T01:52:13.804135Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:52:13.804135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i3/HgUFuG6WefpjGvdHt/7X7+g6gqd7/G8WvMSFf/B59RP9/7embZYaYhetERHc02GC4IvM9/JY7tRIj6x42Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:52:13.804598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eefbb63f98db2b6f6e6777b5664a8bd303038aec43329781f521e2d16d6156d6","sha256:69b71c3066009856fc4f7d972dec6dec18fe622b15c0eefa16584d640f6acb99"],"state_sha256":"7c59fc3688178f557b43cabdc6a8b2db81fc033afb97a41b497fef70e4520b5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pY+MWPpDYJVbyyuwctsl1HqFX+An/ghFz23mZ4D+L8H1SnEOmthopOWfgEFd3qE0Dyt4YYXJEzV9Qp+YnbViDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T18:46:26.884933Z","bundle_sha256":"f41517f1a44977aace23d4ab1e675a020bb973380df09e21ffd9554aac399f2e"}}