{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:GLXJ2V7R6XCWU4KNJ3ALMK4NUM","short_pith_number":"pith:GLXJ2V7R","canonical_record":{"source":{"id":"2210.14989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-10-26T19:18:28Z","cross_cats_sorted":[],"title_canon_sha256":"439c71e1ddf36c5ca6dcb2fc964a097db026a86b8f9b497fcdacf80d8969764c","abstract_canon_sha256":"71231940e0533720bf6ea65529a3cb56fe1fa6a8e0121ff31345f815ceea3e1a"},"schema_version":"1.0"},"canonical_sha256":"32ee9d57f1f5c56a714d4ec0b62b8da310c7a13ed70e2e751aa8be86b19268c9","source":{"kind":"arxiv","id":"2210.14989","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.14989","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"2210.14989v2","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.14989","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"GLXJ2V7R6XCW","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_16","alias_value":"GLXJ2V7R6XCWU4KN","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_8","alias_value":"GLXJ2V7R","created_at":"2026-07-05T07:20:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:GLXJ2V7R6XCWU4KNJ3ALMK4NUM","target":"record","payload":{"canonical_record":{"source":{"id":"2210.14989","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-10-26T19:18:28Z","cross_cats_sorted":[],"title_canon_sha256":"439c71e1ddf36c5ca6dcb2fc964a097db026a86b8f9b497fcdacf80d8969764c","abstract_canon_sha256":"71231940e0533720bf6ea65529a3cb56fe1fa6a8e0121ff31345f815ceea3e1a"},"schema_version":"1.0"},"canonical_sha256":"32ee9d57f1f5c56a714d4ec0b62b8da310c7a13ed70e2e751aa8be86b19268c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:20:48.755598Z","signature_b64":"PR/FQdn6Vr3eMG9LA+TGCPn2xpAodwv5od1Vm+c6iwzETibBYN7/aHMtQkQooWUuxeZ0LwOniLeJUU7Tnu8pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32ee9d57f1f5c56a714d4ec0b62b8da310c7a13ed70e2e751aa8be86b19268c9","last_reissued_at":"2026-07-05T07:20:48.755062Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:20:48.755062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2210.14989","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":"2026-07-05T07:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5zOxf1fcWOfJeFKFuCWcTMNQh7HPc2wFe1VtCK3SQ09K1zowqfiSop6e23FOJwym4nj4+dlankt3OsNYlO/jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:11:57.058548Z"},"content_sha256":"98ea370411a038e3ff1aff03e5899b334ec0b57d3e5498ae31761c1cf0c46c84","schema_version":"1.0","event_id":"sha256:98ea370411a038e3ff1aff03e5899b334ec0b57d3e5498ae31761c1cf0c46c84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:GLXJ2V7R6XCWU4KNJ3ALMK4NUM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariance principle and non-compact center foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Mauricio Poletti, Sylvain Crovisier","submitted_at":"2022-10-26T19:18:28Z","abstract_excerpt":"We prove a generalization of a so called \"invariance principle\" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is invariant by stable and unstable holonomies. This was known for systems admitting a foliation by compact center leaves, and we extend it to a larger class which contains discretized Anosov flows.\n  We use our result to classify measures of maximal entropy and study physical measures for perturbations of the time-one map of Anosov flows."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.14989","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/2210.14989/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":"2026-07-05T07:20:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QUK29hn308zar9vw7hNTOt0nzHjCFlr681gmCrjwhFWckdEkRXWDju7PTd98kiDEmXfYqHrvV6QMYJTnCuODDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T13:11:57.059509Z"},"content_sha256":"39db1fb6ab2faa10a1eb8b8f5f5d41e8c40f2885c40819851a7acebcad04ca7c","schema_version":"1.0","event_id":"sha256:39db1fb6ab2faa10a1eb8b8f5f5d41e8c40f2885c40819851a7acebcad04ca7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/bundle.json","state_url":"https://pith.science/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/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":"2026-08-08T13:11:57Z","links":{"resolver":"https://pith.science/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM","bundle":"https://pith.science/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/bundle.json","state":"https://pith.science/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GLXJ2V7R6XCWU4KNJ3ALMK4NUM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:GLXJ2V7R6XCWU4KNJ3ALMK4NUM","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":"71231940e0533720bf6ea65529a3cb56fe1fa6a8e0121ff31345f815ceea3e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-10-26T19:18:28Z","title_canon_sha256":"439c71e1ddf36c5ca6dcb2fc964a097db026a86b8f9b497fcdacf80d8969764c"},"schema_version":"1.0","source":{"id":"2210.14989","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2210.14989","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"arxiv_version","alias_value":"2210.14989v2","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.14989","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_12","alias_value":"GLXJ2V7R6XCW","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_16","alias_value":"GLXJ2V7R6XCWU4KN","created_at":"2026-07-05T07:20:48Z"},{"alias_kind":"pith_short_8","alias_value":"GLXJ2V7R","created_at":"2026-07-05T07:20:48Z"}],"graph_snapshots":[{"event_id":"sha256:39db1fb6ab2faa10a1eb8b8f5f5d41e8c40f2885c40819851a7acebcad04ca7c","target":"graph","created_at":"2026-07-05T07:20:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2210.14989/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a generalization of a so called \"invariance principle\" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is invariant by stable and unstable holonomies. This was known for systems admitting a foliation by compact center leaves, and we extend it to a larger class which contains discretized Anosov flows.\n  We use our result to classify measures of maximal entropy and study physical measures for perturbations of the time-one map of Anosov flows.","authors_text":"Mauricio Poletti, Sylvain Crovisier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-10-26T19:18:28Z","title":"Invariance principle and non-compact center foliations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.14989","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":"sha256:98ea370411a038e3ff1aff03e5899b334ec0b57d3e5498ae31761c1cf0c46c84","target":"record","created_at":"2026-07-05T07:20:48Z","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":"71231940e0533720bf6ea65529a3cb56fe1fa6a8e0121ff31345f815ceea3e1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2022-10-26T19:18:28Z","title_canon_sha256":"439c71e1ddf36c5ca6dcb2fc964a097db026a86b8f9b497fcdacf80d8969764c"},"schema_version":"1.0","source":{"id":"2210.14989","kind":"arxiv","version":2}},"canonical_sha256":"32ee9d57f1f5c56a714d4ec0b62b8da310c7a13ed70e2e751aa8be86b19268c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32ee9d57f1f5c56a714d4ec0b62b8da310c7a13ed70e2e751aa8be86b19268c9","first_computed_at":"2026-07-05T07:20:48.755062Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:20:48.755062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PR/FQdn6Vr3eMG9LA+TGCPn2xpAodwv5od1Vm+c6iwzETibBYN7/aHMtQkQooWUuxeZ0LwOniLeJUU7Tnu8pBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:20:48.755598Z","signed_message":"canonical_sha256_bytes"},"source_id":"2210.14989","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98ea370411a038e3ff1aff03e5899b334ec0b57d3e5498ae31761c1cf0c46c84","sha256:39db1fb6ab2faa10a1eb8b8f5f5d41e8c40f2885c40819851a7acebcad04ca7c"],"state_sha256":"711dd99d94e82d1c80345958b25b9fb30e5ecf4267f7a934fffe2abb3d85d7d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SkFXQLXUrpWNiL1hdESooZPmhfjvSCubxmQonYn15d/tzUcfHgI5aAEm2FY5iik7XP+4F8mt43sND39PazFrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T13:11:57.067843Z","bundle_sha256":"2bdbc7da6fcfcfa2113317974e12ff0faf5437a1d76f11ccea5de281df9c77e5"}}