{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:FODWCJYV6WX2OX4KCQ6O6ETKRR","short_pith_number":"pith:FODWCJYV","canonical_record":{"source":{"id":"1702.02912","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-07T18:26:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"caaf6e7fd2d75c589c102e940ea180f887245498cf168fe4ea8375b2aaf7f1bf","abstract_canon_sha256":"e6bc080ae56a3a07c8df8cc3a1d13a14d52db2dc57f7a87cd86f813b43a7ed47"},"schema_version":"1.0"},"canonical_sha256":"2b87612715f5afa75f8a143cef126a8c787b362461ee02999964f89087dcbae1","source":{"kind":"arxiv","id":"1702.02912","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02912","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02912v3","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02912","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"FODWCJYV6WX2","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_16","alias_value":"FODWCJYV6WX2OX4K","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_8","alias_value":"FODWCJYV","created_at":"2026-07-05T00:22:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:FODWCJYV6WX2OX4KCQ6O6ETKRR","target":"record","payload":{"canonical_record":{"source":{"id":"1702.02912","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-07T18:26:28Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"caaf6e7fd2d75c589c102e940ea180f887245498cf168fe4ea8375b2aaf7f1bf","abstract_canon_sha256":"e6bc080ae56a3a07c8df8cc3a1d13a14d52db2dc57f7a87cd86f813b43a7ed47"},"schema_version":"1.0"},"canonical_sha256":"2b87612715f5afa75f8a143cef126a8c787b362461ee02999964f89087dcbae1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:21.524360Z","signature_b64":"5to+4EtujUdp7eyMzy4DqPtFcGhWrTmt9ZwdmjFbq6aBlzaygtDvB2j8MQOYAWT4Tlc0Mh6n14BrIyL6QhbICg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b87612715f5afa75f8a143cef126a8c787b362461ee02999964f89087dcbae1","last_reissued_at":"2026-07-05T00:22:21.523927Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:21.523927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.02912","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Os+Ko5iQf/dA21wj99ssJxe2lERC2Y1qRHs2feCyFfKH3wpGgxX30Q74emsVh5YV1xi6sQk+Q90h8DA9yfAKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:06:28.491918Z"},"content_sha256":"5b80cd0c32c604b8143e713fac740d2d87686c93577ed76089bbe1bb0f2e310c","schema_version":"1.0","event_id":"sha256:5b80cd0c32c604b8143e713fac740d2d87686c93577ed76089bbe1bb0f2e310c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:FODWCJYV6WX2OX4KCQ6O6ETKRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Randomized Dynamic Mode Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"J. Nathan Kutz, Lionel Mathelin, N. Benjamin Erichson, Steven L. Brunton","submitted_at":"2017-02-07T18:26:28Z","abstract_excerpt":"This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of `big data'. The idea is to derive a small matrix from the high-dimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02912","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1702.02912/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0pwhbvc4s/f2dNlshEMhAJd91AWl3wQ+qV75mi14Hel2dkFFQNWKMRZh9QesjtPDQNkxJfDP7uVydYhDX0DFBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T09:06:28.492469Z"},"content_sha256":"06dd12a793719144fa877275e7799f5f9aff94ce9c707d6bd2dde5ce75b48871","schema_version":"1.0","event_id":"sha256:06dd12a793719144fa877275e7799f5f9aff94ce9c707d6bd2dde5ce75b48871"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/bundle.json","state_url":"https://pith.science/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/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":"2026-08-16T09:06:28Z","links":{"resolver":"https://pith.science/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR","bundle":"https://pith.science/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/bundle.json","state":"https://pith.science/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FODWCJYV6WX2OX4KCQ6O6ETKRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FODWCJYV6WX2OX4KCQ6O6ETKRR","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":"e6bc080ae56a3a07c8df8cc3a1d13a14d52db2dc57f7a87cd86f813b43a7ed47","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-07T18:26:28Z","title_canon_sha256":"caaf6e7fd2d75c589c102e940ea180f887245498cf168fe4ea8375b2aaf7f1bf"},"schema_version":"1.0","source":{"id":"1702.02912","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.02912","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.02912v3","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02912","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"FODWCJYV6WX2","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_16","alias_value":"FODWCJYV6WX2OX4K","created_at":"2026-07-05T00:22:21Z"},{"alias_kind":"pith_short_8","alias_value":"FODWCJYV","created_at":"2026-07-05T00:22:21Z"}],"graph_snapshots":[{"event_id":"sha256:06dd12a793719144fa877275e7799f5f9aff94ce9c707d6bd2dde5ce75b48871","target":"graph","created_at":"2026-07-05T00:22:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1702.02912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of `big data'. The idea is to derive a small matrix from the high-dimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversa","authors_text":"J. Nathan Kutz, Lionel Mathelin, N. Benjamin Erichson, Steven L. Brunton","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-07T18:26:28Z","title":"Randomized Dynamic Mode Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02912","kind":"arxiv","version":3},"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":"sha256:5b80cd0c32c604b8143e713fac740d2d87686c93577ed76089bbe1bb0f2e310c","target":"record","created_at":"2026-07-05T00:22:21Z","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":"e6bc080ae56a3a07c8df8cc3a1d13a14d52db2dc57f7a87cd86f813b43a7ed47","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-02-07T18:26:28Z","title_canon_sha256":"caaf6e7fd2d75c589c102e940ea180f887245498cf168fe4ea8375b2aaf7f1bf"},"schema_version":"1.0","source":{"id":"1702.02912","kind":"arxiv","version":3}},"canonical_sha256":"2b87612715f5afa75f8a143cef126a8c787b362461ee02999964f89087dcbae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b87612715f5afa75f8a143cef126a8c787b362461ee02999964f89087dcbae1","first_computed_at":"2026-07-05T00:22:21.523927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:22:21.523927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5to+4EtujUdp7eyMzy4DqPtFcGhWrTmt9ZwdmjFbq6aBlzaygtDvB2j8MQOYAWT4Tlc0Mh6n14BrIyL6QhbICg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:22:21.524360Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.02912","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b80cd0c32c604b8143e713fac740d2d87686c93577ed76089bbe1bb0f2e310c","sha256:06dd12a793719144fa877275e7799f5f9aff94ce9c707d6bd2dde5ce75b48871"],"state_sha256":"7a4855f0fed193b4dc1d066046418889e4c6e1afcb981feda12ca43c11eada20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EqLTlzmM5aH4ck0m5hDmF3kE4kkW/4aR9GXa6cmP6MWj19iR4XfjpsoWPhoIVce46cQr29wAlXKRbRb2LEzzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T09:06:28.497707Z","bundle_sha256":"87a70061e6bb551512d5aadcea643ca76ddccafbbdd2fb039166b4e313b0a403"}}