{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:N3CCWO5Y3C7TDDFMYQRU44JZXW","short_pith_number":"pith:N3CCWO5Y","canonical_record":{"source":{"id":"1905.07896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-20T06:20:08Z","cross_cats_sorted":[],"title_canon_sha256":"5de71ac15174d75fd22b1727d1ffb469e94f137d7ea5a9485e242d8ff7827981","abstract_canon_sha256":"e7fefe835a415d90edda61053724387d3825c6c88d3fe7b223813c8efceab628"},"schema_version":"1.0"},"canonical_sha256":"6ec42b3bb8d8bf318cacc4234e7139bda2ef8df523454f482d39db6397f6dee9","source":{"kind":"arxiv","id":"1905.07896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07896","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07896v1","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07896","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"N3CCWO5Y3C7T","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N3CCWO5Y3C7TDDFM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N3CCWO5Y","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:N3CCWO5Y3C7TDDFMYQRU44JZXW","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-20T06:20:08Z","cross_cats_sorted":[],"title_canon_sha256":"5de71ac15174d75fd22b1727d1ffb469e94f137d7ea5a9485e242d8ff7827981","abstract_canon_sha256":"e7fefe835a415d90edda61053724387d3825c6c88d3fe7b223813c8efceab628"},"schema_version":"1.0"},"canonical_sha256":"6ec42b3bb8d8bf318cacc4234e7139bda2ef8df523454f482d39db6397f6dee9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:48.204388Z","signature_b64":"MpHZJydt5Kywc5OvFypU/9HNRwVWkXTHz26pH/mBW1Us2T9JU7zeLTx66G0telCRniRkU/CSMH4gDnc31+E6DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ec42b3bb8d8bf318cacc4234e7139bda2ef8df523454f482d39db6397f6dee9","last_reissued_at":"2026-05-17T23:45:48.203795Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:48.203795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07896","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":"2026-05-17T23:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"arojJEF0m4vwubzqKmYpsxqpGBRLJW87z7BFnEMy368mzMd+Y+Bk6XhrcubhrnukWzile/GchE/5e3LnhjTOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:44.337368Z"},"content_sha256":"daac31dbb6683ebd33c475b7c21a8965c92f458a2a101248cfa0664043ed4fe0","schema_version":"1.0","event_id":"sha256:daac31dbb6683ebd33c475b7c21a8965c92f458a2a101248cfa0664043ed4fe0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:N3CCWO5Y3C7TDDFMYQRU44JZXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigidity of center Lyapunov exponents and $su$-integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Shaobo Gan, Yi Shi","submitted_at":"2019-05-20T06:20:08Z","abstract_excerpt":"Let $f$ be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism $A$ on $\\mathbb{T}^3$. We show that the stable and unstable bundles of $f$ are jointly integrable if and only if every periodic point of $f$ admits the same center Lyapunov exponent with $A$. In particular, $f$ is Anosov. Thus every conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on $\\mathbb{T}^3$, is ergodic. This proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on $\\mathbb{T}^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07896","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":"2026-05-17T23:45:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q86MPfDoSbbTAwPA1eLKSJv7RZMxCYS9viSoM2V9gxX6wwYyHoZ95xbR+Oyir5n4tMWm+FLsaNdppD/H1GU5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:30:44.337714Z"},"content_sha256":"4c0f08f2b63bdaab1048edaec73efcc038f8757b5f8c7dbddd63968c2898a6ef","schema_version":"1.0","event_id":"sha256:4c0f08f2b63bdaab1048edaec73efcc038f8757b5f8c7dbddd63968c2898a6ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/bundle.json","state_url":"https://pith.science/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/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":"2026-06-01T10:30:44Z","links":{"resolver":"https://pith.science/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW","bundle":"https://pith.science/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/bundle.json","state":"https://pith.science/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N3CCWO5Y3C7TDDFMYQRU44JZXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N3CCWO5Y3C7TDDFMYQRU44JZXW","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":"e7fefe835a415d90edda61053724387d3825c6c88d3fe7b223813c8efceab628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-20T06:20:08Z","title_canon_sha256":"5de71ac15174d75fd22b1727d1ffb469e94f137d7ea5a9485e242d8ff7827981"},"schema_version":"1.0","source":{"id":"1905.07896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07896","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07896v1","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07896","created_at":"2026-05-17T23:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"N3CCWO5Y3C7T","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N3CCWO5Y3C7TDDFM","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N3CCWO5Y","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:4c0f08f2b63bdaab1048edaec73efcc038f8757b5f8c7dbddd63968c2898a6ef","target":"graph","created_at":"2026-05-17T23:45:48Z","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":"Let $f$ be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism $A$ on $\\mathbb{T}^3$. We show that the stable and unstable bundles of $f$ are jointly integrable if and only if every periodic point of $f$ admits the same center Lyapunov exponent with $A$. In particular, $f$ is Anosov. Thus every conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on $\\mathbb{T}^3$, is ergodic. This proves the Ergodic Conjecture proposed by Hertz-Hertz-Ures on $\\mathbb{T}^3$.","authors_text":"Shaobo Gan, Yi Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-20T06:20:08Z","title":"Rigidity of center Lyapunov exponents and $su$-integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07896","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:daac31dbb6683ebd33c475b7c21a8965c92f458a2a101248cfa0664043ed4fe0","target":"record","created_at":"2026-05-17T23:45:48Z","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":"e7fefe835a415d90edda61053724387d3825c6c88d3fe7b223813c8efceab628","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-20T06:20:08Z","title_canon_sha256":"5de71ac15174d75fd22b1727d1ffb469e94f137d7ea5a9485e242d8ff7827981"},"schema_version":"1.0","source":{"id":"1905.07896","kind":"arxiv","version":1}},"canonical_sha256":"6ec42b3bb8d8bf318cacc4234e7139bda2ef8df523454f482d39db6397f6dee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ec42b3bb8d8bf318cacc4234e7139bda2ef8df523454f482d39db6397f6dee9","first_computed_at":"2026-05-17T23:45:48.203795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:48.203795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MpHZJydt5Kywc5OvFypU/9HNRwVWkXTHz26pH/mBW1Us2T9JU7zeLTx66G0telCRniRkU/CSMH4gDnc31+E6DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:48.204388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daac31dbb6683ebd33c475b7c21a8965c92f458a2a101248cfa0664043ed4fe0","sha256:4c0f08f2b63bdaab1048edaec73efcc038f8757b5f8c7dbddd63968c2898a6ef"],"state_sha256":"465cf0fc0307802b33b3a00ff625e7f14608ec7705abe4cc52e94474cb60c1fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R3O4t6SZQ11gUUsDFrqed4LU5hq0kcSGXFMIzhR0vuKrpA4IhN/GRNmjgkIJPcHlhDeDRdQhjt6CRhNlM2aTCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:30:44.339628Z","bundle_sha256":"0c429eb74ec4cb858b91287759db9ff5acab6367afda5e378c859cd72dfc7a7e"}}