{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:FVDK2OZUYUSMOMJW24SWSL63ZL","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":"1c1c460bcaf4a33ff62c372560dbc67a4a669756584197d30e2773c415cccfa0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-13T14:38:41Z","title_canon_sha256":"413607982614c04cd729fd36a30c509ef340b2362cdec9172641b01e626eb7a7"},"schema_version":"1.0","source":{"id":"0803.1977","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.1977","created_at":"2026-05-18T00:37:23Z"},{"alias_kind":"arxiv_version","alias_value":"0803.1977v2","created_at":"2026-05-18T00:37:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.1977","created_at":"2026-05-18T00:37:23Z"},{"alias_kind":"pith_short_12","alias_value":"FVDK2OZUYUSM","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"FVDK2OZUYUSMOMJW","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"FVDK2OZU","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:79ef8edbb2f91b811e38fb38d9de44b513e06338d1144c0d5f35a417777417d7","target":"graph","created_at":"2026-05-18T00:37:23Z","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 short note, we describe some recent results on the pointwise existence of the Lyapunov exponent for certain quasi-periodic cocyles.","authors_text":"Alexander Fedotov (Department of Mathematical Physics), Fr\\'ed\\'eric Klopp (LAGA)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-13T14:38:41Z","title":"Pointwise existence of the Lyapunov exponent for a quasi-periodic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.1977","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:bdb03c813a495c9d680486fa7e70b6ca812a0dfa3ac741b6ad3a1c3b44b6f394","target":"record","created_at":"2026-05-18T00:37:23Z","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":"1c1c460bcaf4a33ff62c372560dbc67a4a669756584197d30e2773c415cccfa0","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-03-13T14:38:41Z","title_canon_sha256":"413607982614c04cd729fd36a30c509ef340b2362cdec9172641b01e626eb7a7"},"schema_version":"1.0","source":{"id":"0803.1977","kind":"arxiv","version":2}},"canonical_sha256":"2d46ad3b34c524c73136d725692fdbcac454d3b981878cd82e4583ee566454b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d46ad3b34c524c73136d725692fdbcac454d3b981878cd82e4583ee566454b7","first_computed_at":"2026-05-18T00:37:23.572050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:23.572050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0+JTcgg7dYygeW0Q8i13ZpHcQGghT6MA8/MyJipHDzGB+J9gBCySpGC3vEmwhGbc6GUKLkT+DeMfDgIC+/gAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:23.572629Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.1977","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdb03c813a495c9d680486fa7e70b6ca812a0dfa3ac741b6ad3a1c3b44b6f394","sha256:79ef8edbb2f91b811e38fb38d9de44b513e06338d1144c0d5f35a417777417d7"],"state_sha256":"dbf94088140301ef3dfb81842e2b817844cbe4fd44e2f26de1b630a53cce6fc8"}