{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DOPAEPEYKKJYWULJ6A7KIIR3MW","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":"f32bf078cde127925e062948721389ee763f880a2ef80aeaf3b50664fcbac5f7","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-07T12:11:39Z","title_canon_sha256":"8a288037d257cd4c0aac651b91034f61be1c94284417167f70c38f4b0447958a"},"schema_version":"1.0","source":{"id":"1411.1893","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.1893","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.1893v2","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.1893","created_at":"2026-05-18T01:08:26Z"},{"alias_kind":"pith_short_12","alias_value":"DOPAEPEYKKJY","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DOPAEPEYKKJYWULJ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DOPAEPEY","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:251d5e3821e7944e071bd700079970b4299e693f5be99bfec6efb78758e6f562","target":"graph","created_at":"2026-05-18T01:08:26Z","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":"This is the third part in a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. The current part focuses on applications of general theory, developed in the authors' paper \"Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. I. General theory,\" Trans. Amer. Math. Soc. 365 (2013), pp. 5329-5365, to positive continuous-time random dynamical systems on infinite dimensional ordered Banach spaces arising from random parabolic equations and random delay ","authors_text":"Janusz Mierczy\\'nski, Wenxian Shen","cross_cats":["math.AP","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-07T12:11:39Z","title":"Principal Lyapunov exponents and principal Floquet spaces of positive random dynamical systems. III. Parabolic equations and delay systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1893","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:a82b9f492eaeaed4eff588b1c7ff75db86479176b2023f4d654112bd505d0728","target":"record","created_at":"2026-05-18T01:08:26Z","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":"f32bf078cde127925e062948721389ee763f880a2ef80aeaf3b50664fcbac5f7","cross_cats_sorted":["math.AP","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-11-07T12:11:39Z","title_canon_sha256":"8a288037d257cd4c0aac651b91034f61be1c94284417167f70c38f4b0447958a"},"schema_version":"1.0","source":{"id":"1411.1893","kind":"arxiv","version":2}},"canonical_sha256":"1b9e023c9852938b5169f03ea4223b659685f218fb9099ccd658c3d09a02eb4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b9e023c9852938b5169f03ea4223b659685f218fb9099ccd658c3d09a02eb4b","first_computed_at":"2026-05-18T01:08:26.765263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:26.765263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l0SJdL8B5fAOSO8Gfk/coKpBHHFDKCOy1biq/f1M0z0fzf3Zkzi5VhNTrVBEzmPmAuqV5vreYRFRU6ZXZmSWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:26.765990Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.1893","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a82b9f492eaeaed4eff588b1c7ff75db86479176b2023f4d654112bd505d0728","sha256:251d5e3821e7944e071bd700079970b4299e693f5be99bfec6efb78758e6f562"],"state_sha256":"04552a20a7d92ac2d857dc274dcfdd0da5861d2bfca82ac57354ea48c4e7aabb"}