{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:6OHKTG4AOHHEJP2WW7NKXYTLJO","short_pith_number":"pith:6OHKTG4A","canonical_record":{"source":{"id":"1204.0871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-04T05:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"05ef83d3fe5b7faf847ccb097d407010c2df7b0b31469c8521cb665e542d2393","abstract_canon_sha256":"a9d89593c400039cfd6996ba2ca66b2b8d899ff179a4b8aca91f052c3a8f5990"},"schema_version":"1.0"},"canonical_sha256":"f38ea99b8071ce44bf56b7daabe26b4ba5181ab6807ae776db30d53e4ffa06da","source":{"kind":"arxiv","id":"1204.0871","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0871","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0871v1","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0871","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"6OHKTG4AOHHE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6OHKTG4AOHHEJP2W","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6OHKTG4A","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:6OHKTG4AOHHEJP2WW7NKXYTLJO","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0871","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-04T05:50:34Z","cross_cats_sorted":[],"title_canon_sha256":"05ef83d3fe5b7faf847ccb097d407010c2df7b0b31469c8521cb665e542d2393","abstract_canon_sha256":"a9d89593c400039cfd6996ba2ca66b2b8d899ff179a4b8aca91f052c3a8f5990"},"schema_version":"1.0"},"canonical_sha256":"f38ea99b8071ce44bf56b7daabe26b4ba5181ab6807ae776db30d53e4ffa06da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:57.269405Z","signature_b64":"cNmL/BTj4Giimh/yhWhJzpQFoJyxiBRKwg4RwNX0Y+aspGKrdAS9zivmXGDcHhDyoVeFcx57w0iw75O6rS18AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f38ea99b8071ce44bf56b7daabe26b4ba5181ab6807ae776db30d53e4ffa06da","last_reissued_at":"2026-05-18T01:57:57.268794Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:57.268794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0871","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":"2026-05-18T01:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i5CpkPuP5pNtZItBMmdD7sdyAIPcBu933PpZit4922nUkS1N+j3OxMQvuPgsL6DticEny+FYjRLNf2Towo2yDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:42:19.800934Z"},"content_sha256":"da3b4723c0e15a49ad251b59d90d669e1f8a6269bf75e59e6f2d5bca3f118f74","schema_version":"1.0","event_id":"sha256:da3b4723c0e15a49ad251b59d90d669e1f8a6269bf75e59e6f2d5bca3f118f74"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:6OHKTG4AOHHEJP2WW7NKXYTLJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Gary Froyland, Gary P. Morriss, Thomas M. Watson, Thorsten H\\\"uls","submitted_at":"2012-04-04T05:50:34Z","abstract_excerpt":"Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical systems. These vectors identify spatially varying directions of specific asymptotic growth rates and obey equivariance principles. In recent years new computational methods for approximating Oseledets vectors have been developed, motivated by increasing model complexity and greater demands for accuracy. In this numerical study we introduce two new approaches bas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0871","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":"2026-05-18T01:57:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9fkRAirOYXHLJ7FWfiDmvI3jh95BwWbDNBWGhhryamjxpgayRjlK8yP5ahgOCg+tWDw8acZgseVyHI9cj8ULCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T14:42:19.801291Z"},"content_sha256":"7b3e0922947b99714351353f33ecef6165211d03a66fb5c917f944e11179a5fe","schema_version":"1.0","event_id":"sha256:7b3e0922947b99714351353f33ecef6165211d03a66fb5c917f944e11179a5fe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/bundle.json","state_url":"https://pith.science/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/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":"2026-06-22T14:42:19Z","links":{"resolver":"https://pith.science/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO","bundle":"https://pith.science/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/bundle.json","state":"https://pith.science/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6OHKTG4AOHHEJP2WW7NKXYTLJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6OHKTG4AOHHEJP2WW7NKXYTLJO","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":"a9d89593c400039cfd6996ba2ca66b2b8d899ff179a4b8aca91f052c3a8f5990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-04T05:50:34Z","title_canon_sha256":"05ef83d3fe5b7faf847ccb097d407010c2df7b0b31469c8521cb665e542d2393"},"schema_version":"1.0","source":{"id":"1204.0871","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0871","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0871v1","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0871","created_at":"2026-05-18T01:57:57Z"},{"alias_kind":"pith_short_12","alias_value":"6OHKTG4AOHHE","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6OHKTG4AOHHEJP2W","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6OHKTG4A","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:7b3e0922947b99714351353f33ecef6165211d03a66fb5c917f944e11179a5fe","target":"graph","created_at":"2026-05-18T01:57:57Z","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":"Covariant vectors, Lyapunov vectors, or Oseledets vectors are increasingly being used for a variety of model analyses in areas such as partial differential equations, nonautonomous differentiable dynamical systems, and random dynamical systems. These vectors identify spatially varying directions of specific asymptotic growth rates and obey equivariance principles. In recent years new computational methods for approximating Oseledets vectors have been developed, motivated by increasing model complexity and greater demands for accuracy. In this numerical study we introduce two new approaches bas","authors_text":"Gary Froyland, Gary P. Morriss, Thomas M. Watson, Thorsten H\\\"uls","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-04T05:50:34Z","title":"Computing covariant vectors, Lyapunov vectors, Oseledets vectors, and dichotomy projectors: a comparative numerical study"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0871","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:da3b4723c0e15a49ad251b59d90d669e1f8a6269bf75e59e6f2d5bca3f118f74","target":"record","created_at":"2026-05-18T01:57:57Z","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":"a9d89593c400039cfd6996ba2ca66b2b8d899ff179a4b8aca91f052c3a8f5990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-04-04T05:50:34Z","title_canon_sha256":"05ef83d3fe5b7faf847ccb097d407010c2df7b0b31469c8521cb665e542d2393"},"schema_version":"1.0","source":{"id":"1204.0871","kind":"arxiv","version":1}},"canonical_sha256":"f38ea99b8071ce44bf56b7daabe26b4ba5181ab6807ae776db30d53e4ffa06da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f38ea99b8071ce44bf56b7daabe26b4ba5181ab6807ae776db30d53e4ffa06da","first_computed_at":"2026-05-18T01:57:57.268794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:57.268794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cNmL/BTj4Giimh/yhWhJzpQFoJyxiBRKwg4RwNX0Y+aspGKrdAS9zivmXGDcHhDyoVeFcx57w0iw75O6rS18AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:57.269405Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0871","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da3b4723c0e15a49ad251b59d90d669e1f8a6269bf75e59e6f2d5bca3f118f74","sha256:7b3e0922947b99714351353f33ecef6165211d03a66fb5c917f944e11179a5fe"],"state_sha256":"ef80b37d834dc6b658f44d5f3519dd128f82c73e36455269ad8595e6a80fdd61"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLBdJnp6Kxb7jcPCck0Xk/7od+W+PvYwP0JLbM+yt1SRMKHAOBjeXf4KKeVH+QuVnDWJKDOGeDZe83vS8beGCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T14:42:19.804458Z","bundle_sha256":"90fc317c561fd64217272fa31273d5f12afa7e6639419093942686f1ce3d31a8"}}