{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZKJSF6L4EEVAJSHQSJBFWFRHQS","short_pith_number":"pith:ZKJSF6L4","schema_version":"1.0","canonical_sha256":"ca9322f97c212a04c8f092425b162784965f18f3c3030891859c7b227ee0def1","source":{"kind":"arxiv","id":"1403.7338","version":2},"attestation_state":"computed","paper":{"title":"Oseledec multiplicative ergodic theorem for laminations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG","math.GT"],"primary_cat":"math.DS","authors_text":"Viet-Anh Nguyen","submitted_at":"2014-03-28T10:51:38Z","abstract_excerpt":"Given a n-dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, we define the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. We also prove an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1403.7338","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-03-28T10:51:38Z","cross_cats_sorted":["math.CV","math.DG","math.GT"],"title_canon_sha256":"f2069da8f2c2958604ee4d3df5626156e1aede33318e46f6e7fe34ffdd13a257","abstract_canon_sha256":"367b61b55d0ea1a7f8d9cc943b6aaf377b161453de4907409be6d81cd7282364"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:33.885803Z","signature_b64":"fHYhgXZ/cmrT34LmXK59VtaIcXaslWQU6G12Ov8bg8Xtj0/nOAxJ+Qxl8y3CQuLSnHHr9Hr7ZQU5lzciyTPBCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca9322f97c212a04c8f092425b162784965f18f3c3030891859c7b227ee0def1","last_reissued_at":"2026-05-18T02:17:33.884990Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:33.884990Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Oseledec multiplicative ergodic theorem for laminations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.DG","math.GT"],"primary_cat":"math.DS","authors_text":"Viet-Anh Nguyen","submitted_at":"2014-03-28T10:51:38Z","abstract_excerpt":"Given a n-dimensional lamination endowed with a Riemannian metric, we introduce the notion of a multiplicative cocycle of rank d, where n and d are arbitrary positive integers. The holonomy cocycle of a foliation and its exterior powers as well as its tensor powers provide examples of multiplicative cocycles. Next, we define the Lyapunov exponents of such a cocycle with respect to a harmonic probability measure directed by the lamination. We also prove an Oseledec multiplicative ergodic theorem in this context. This theorem implies the existence of an Oseledec decomposition almost everywhere w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7338","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1403.7338","created_at":"2026-05-18T02:17:33.885126+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.7338v2","created_at":"2026-05-18T02:17:33.885126+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7338","created_at":"2026-05-18T02:17:33.885126+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZKJSF6L4EEVA","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZKJSF6L4EEVAJSHQ","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZKJSF6L4","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS","json":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS.json","graph_json":"https://pith.science/api/pith-number/ZKJSF6L4EEVAJSHQSJBFWFRHQS/graph.json","events_json":"https://pith.science/api/pith-number/ZKJSF6L4EEVAJSHQSJBFWFRHQS/events.json","paper":"https://pith.science/paper/ZKJSF6L4"},"agent_actions":{"view_html":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS","download_json":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS.json","view_paper":"https://pith.science/paper/ZKJSF6L4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.7338&json=true","fetch_graph":"https://pith.science/api/pith-number/ZKJSF6L4EEVAJSHQSJBFWFRHQS/graph.json","fetch_events":"https://pith.science/api/pith-number/ZKJSF6L4EEVAJSHQSJBFWFRHQS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS/action/storage_attestation","attest_author":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS/action/author_attestation","sign_citation":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS/action/citation_signature","submit_replication":"https://pith.science/pith/ZKJSF6L4EEVAJSHQSJBFWFRHQS/action/replication_record"}},"created_at":"2026-05-18T02:17:33.885126+00:00","updated_at":"2026-05-18T02:17:33.885126+00:00"}