{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IGLIB5C5UXK6LHJJVOELEZNA34","short_pith_number":"pith:IGLIB5C5","canonical_record":{"source":{"id":"1603.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-04T19:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"16a74ddde0ac45ac38ff58f8d1ed178bf6bc88d57f1923bf648bd2c1242685d0","abstract_canon_sha256":"4f89369dc325416ea695f1e1b03dc8029447c4e3cd10b74f76a3a8c1f26f1d7c"},"schema_version":"1.0"},"canonical_sha256":"419680f45da5d5e59d29ab88b265a0df303598d8ba71e434e4a3433eddc71bfa","source":{"kind":"arxiv","id":"1603.01582","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01582","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01582v1","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01582","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"IGLIB5C5UXK6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGLIB5C5UXK6LHJJ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGLIB5C5","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IGLIB5C5UXK6LHJJVOELEZNA34","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-04T19:28:44Z","cross_cats_sorted":[],"title_canon_sha256":"16a74ddde0ac45ac38ff58f8d1ed178bf6bc88d57f1923bf648bd2c1242685d0","abstract_canon_sha256":"4f89369dc325416ea695f1e1b03dc8029447c4e3cd10b74f76a3a8c1f26f1d7c"},"schema_version":"1.0"},"canonical_sha256":"419680f45da5d5e59d29ab88b265a0df303598d8ba71e434e4a3433eddc71bfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:35.691798Z","signature_b64":"gcF6Rmz863KMpt5gL1cT9NMyPrVFm/YKjcCvU97b/s+g6n02WfrPrtgUKIy17zVuMZjyUEPVR0XGKkRmUyZLCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"419680f45da5d5e59d29ab88b265a0df303598d8ba71e434e4a3433eddc71bfa","last_reissued_at":"2026-05-18T01:19:35.691342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:35.691342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01582","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":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OltLY0dV5Ro1xg8+xzx8CgyH5KZJRVqZsKmka8KL+EXYjvmZQ6wjFXPAXGXzvW2NSz1Tw8qX/AMPuMmHwX0VDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:09:55.101748Z"},"content_sha256":"b6afbae18275513cdf7332bc6abaabee9a7b728b3d93b2aa8b0674cbd8746bd5","schema_version":"1.0","event_id":"sha256:b6afbae18275513cdf7332bc6abaabee9a7b728b3d93b2aa8b0674cbd8746bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IGLIB5C5UXK6LHJJVOELEZNA34","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kening Lu, Peidong Liu, Zeng Lian","submitted_at":"2016-03-04T19:28:44Z","abstract_excerpt":"In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01582","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":"2026-05-18T01:19:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D8xsa47M9c39c/oY1ucSXVli9Hj62fehmuefjnHMQX1MtUzQAEUlpC10cfJNAJaZ8JJg9QUowOr6Y+5JPh4eDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:09:55.102093Z"},"content_sha256":"c3412052f0f88651bcd46aa7b703bed55b2906e68bc5b2f481510da2a682a277","schema_version":"1.0","event_id":"sha256:c3412052f0f88651bcd46aa7b703bed55b2906e68bc5b2f481510da2a682a277"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IGLIB5C5UXK6LHJJVOELEZNA34/bundle.json","state_url":"https://pith.science/pith/IGLIB5C5UXK6LHJJVOELEZNA34/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IGLIB5C5UXK6LHJJVOELEZNA34/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":"2026-06-02T13:09:55Z","links":{"resolver":"https://pith.science/pith/IGLIB5C5UXK6LHJJVOELEZNA34","bundle":"https://pith.science/pith/IGLIB5C5UXK6LHJJVOELEZNA34/bundle.json","state":"https://pith.science/pith/IGLIB5C5UXK6LHJJVOELEZNA34/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IGLIB5C5UXK6LHJJVOELEZNA34/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IGLIB5C5UXK6LHJJVOELEZNA34","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":"4f89369dc325416ea695f1e1b03dc8029447c4e3cd10b74f76a3a8c1f26f1d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-04T19:28:44Z","title_canon_sha256":"16a74ddde0ac45ac38ff58f8d1ed178bf6bc88d57f1923bf648bd2c1242685d0"},"schema_version":"1.0","source":{"id":"1603.01582","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01582","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01582v1","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01582","created_at":"2026-05-18T01:19:35Z"},{"alias_kind":"pith_short_12","alias_value":"IGLIB5C5UXK6","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IGLIB5C5UXK6LHJJ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IGLIB5C5","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:c3412052f0f88651bcd46aa7b703bed55b2906e68bc5b2f481510da2a682a277","target":"graph","created_at":"2026-05-18T01:19:35Z","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":"In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.","authors_text":"Kening Lu, Peidong Liu, Zeng Lian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-04T19:28:44Z","title":"Existence of SRB Measures for A Class of Partially Hyperbolic Attractors in Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01582","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:b6afbae18275513cdf7332bc6abaabee9a7b728b3d93b2aa8b0674cbd8746bd5","target":"record","created_at":"2026-05-18T01:19:35Z","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":"4f89369dc325416ea695f1e1b03dc8029447c4e3cd10b74f76a3a8c1f26f1d7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-03-04T19:28:44Z","title_canon_sha256":"16a74ddde0ac45ac38ff58f8d1ed178bf6bc88d57f1923bf648bd2c1242685d0"},"schema_version":"1.0","source":{"id":"1603.01582","kind":"arxiv","version":1}},"canonical_sha256":"419680f45da5d5e59d29ab88b265a0df303598d8ba71e434e4a3433eddc71bfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"419680f45da5d5e59d29ab88b265a0df303598d8ba71e434e4a3433eddc71bfa","first_computed_at":"2026-05-18T01:19:35.691342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:35.691342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gcF6Rmz863KMpt5gL1cT9NMyPrVFm/YKjcCvU97b/s+g6n02WfrPrtgUKIy17zVuMZjyUEPVR0XGKkRmUyZLCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:35.691798Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01582","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b6afbae18275513cdf7332bc6abaabee9a7b728b3d93b2aa8b0674cbd8746bd5","sha256:c3412052f0f88651bcd46aa7b703bed55b2906e68bc5b2f481510da2a682a277"],"state_sha256":"9bba32fbf41ca8b8a5d348db144d77976fe2fc836fa836c866bb9d4fd5aef48a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"An+UFo522vANQ0OzkcDg+6Nqgf0L8qgVmKoq308cuQ1t/n/sUTapPvNmp6RRpYlrGlWOZNdNkFNclK3fYTftAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:09:55.104005Z","bundle_sha256":"dadbd35201cf917af1a4d4acab96250e663cb422eb7b41ab4489f5d9fb17c3ba"}}