{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HJTJ2KMNTBWAV62AS2PF2V42I5","short_pith_number":"pith:HJTJ2KMN","canonical_record":{"source":{"id":"2311.09524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-11-16T03:03:08Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"31c3f18a5cdea84ea02774031d2787bb03a80da0a65ed799866036c921f24f9b","abstract_canon_sha256":"af8e64cb4eafc33fe1096906fc961f8d9275b16465aff8e7a40a272c22f50776"},"schema_version":"1.0"},"canonical_sha256":"3a669d298d986c0afb40969e5d579a476dcb42f99f7ad9825a2356fcfe327bbf","source":{"kind":"arxiv","id":"2311.09524","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.09524","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"2311.09524v3","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.09524","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"HJTJ2KMNTBWA","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_16","alias_value":"HJTJ2KMNTBWAV62A","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_8","alias_value":"HJTJ2KMN","created_at":"2026-07-05T10:59:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HJTJ2KMNTBWAV62AS2PF2V42I5","target":"record","payload":{"canonical_record":{"source":{"id":"2311.09524","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-11-16T03:03:08Z","cross_cats_sorted":["nlin.CD"],"title_canon_sha256":"31c3f18a5cdea84ea02774031d2787bb03a80da0a65ed799866036c921f24f9b","abstract_canon_sha256":"af8e64cb4eafc33fe1096906fc961f8d9275b16465aff8e7a40a272c22f50776"},"schema_version":"1.0"},"canonical_sha256":"3a669d298d986c0afb40969e5d579a476dcb42f99f7ad9825a2356fcfe327bbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:59:56.699670Z","signature_b64":"D889YHRRyGbvrn23v5JislX52MDXyKNrE04V78Q05H/yK3esga4deIUVHP1Q7Z3bQeGA9mfS28Flg1vfrmnEBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a669d298d986c0afb40969e5d579a476dcb42f99f7ad9825a2356fcfe327bbf","last_reissued_at":"2026-07-05T10:59:56.699179Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:59:56.699179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.09524","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":"2026-07-05T10:59:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpyejCDruH9VGFd5owXo4cnvdrM+brmypKRUelR9M22oNAtqWCdW3dQYz2kmZUoPiRZVM6JXQov3dzZ2zz5oBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:47:36.569966Z"},"content_sha256":"935522e56a896a30698771b0ebc0092fa36dc84e8788615dbc727fd2ae1212e0","schema_version":"1.0","event_id":"sha256:935522e56a896a30698771b0ebc0092fa36dc84e8788615dbc727fd2ae1212e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HJTJ2KMNTBWAV62AS2PF2V42I5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mori-Zwanzig mode decomposition: Comparison with time-delay embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD"],"primary_cat":"physics.flu-dyn","authors_text":"Christoph Hader, Daniel Livescu, Hermann Fasel, Michael Woodward, Yen Ting Lin, Yifeng Tian","submitted_at":"2023-11-16T03:03:08Z","abstract_excerpt":"We introduce the Mori-Zwanzig Mode Decomposition (MZMD), a novel data-driven technique for efficient modal analysis of and reduced-order modeling of large-scale spatio-temporal dynamical systems. MZMD represents an extension of Dynamic Mode Decomposition (DMD) by providing an approximate closure term with MZ memory kernels accounting for how the unresolved modes of DMD interact with the resolved modes, thus addressing limitations when the state-space observables do not form a Koopman-invariant subspace. Leveraging the Mori-Zwanzig (MZ) formalism, MZMD identifies the modes and spectrum of the d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.09524","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/2311.09524/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":"2026-07-05T10:59:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7enrXqRn5SGClbH90X9Qi040yhvm6uVrAIxRVF15FRTfXSxiaqk34MrWA3hZZzstW4hcBFJ3cE3sTxgFlbFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T10:47:36.570352Z"},"content_sha256":"a8d98468612a6731b31ec9bfe948e16813d64ac3e5c3b5c0c3e51d260e690c9a","schema_version":"1.0","event_id":"sha256:a8d98468612a6731b31ec9bfe948e16813d64ac3e5c3b5c0c3e51d260e690c9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/bundle.json","state_url":"https://pith.science/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/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":"2026-07-07T10:47:36Z","links":{"resolver":"https://pith.science/pith/HJTJ2KMNTBWAV62AS2PF2V42I5","bundle":"https://pith.science/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/bundle.json","state":"https://pith.science/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJTJ2KMNTBWAV62AS2PF2V42I5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HJTJ2KMNTBWAV62AS2PF2V42I5","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":"af8e64cb4eafc33fe1096906fc961f8d9275b16465aff8e7a40a272c22f50776","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-11-16T03:03:08Z","title_canon_sha256":"31c3f18a5cdea84ea02774031d2787bb03a80da0a65ed799866036c921f24f9b"},"schema_version":"1.0","source":{"id":"2311.09524","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.09524","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"2311.09524v3","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.09524","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"HJTJ2KMNTBWA","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_16","alias_value":"HJTJ2KMNTBWAV62A","created_at":"2026-07-05T10:59:56Z"},{"alias_kind":"pith_short_8","alias_value":"HJTJ2KMN","created_at":"2026-07-05T10:59:56Z"}],"graph_snapshots":[{"event_id":"sha256:a8d98468612a6731b31ec9bfe948e16813d64ac3e5c3b5c0c3e51d260e690c9a","target":"graph","created_at":"2026-07-05T10:59:56Z","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/2311.09524/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the Mori-Zwanzig Mode Decomposition (MZMD), a novel data-driven technique for efficient modal analysis of and reduced-order modeling of large-scale spatio-temporal dynamical systems. MZMD represents an extension of Dynamic Mode Decomposition (DMD) by providing an approximate closure term with MZ memory kernels accounting for how the unresolved modes of DMD interact with the resolved modes, thus addressing limitations when the state-space observables do not form a Koopman-invariant subspace. Leveraging the Mori-Zwanzig (MZ) formalism, MZMD identifies the modes and spectrum of the d","authors_text":"Christoph Hader, Daniel Livescu, Hermann Fasel, Michael Woodward, Yen Ting Lin, Yifeng Tian","cross_cats":["nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-11-16T03:03:08Z","title":"Mori-Zwanzig mode decomposition: Comparison with time-delay embeddings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.09524","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":"sha256:935522e56a896a30698771b0ebc0092fa36dc84e8788615dbc727fd2ae1212e0","target":"record","created_at":"2026-07-05T10:59:56Z","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":"af8e64cb4eafc33fe1096906fc961f8d9275b16465aff8e7a40a272c22f50776","cross_cats_sorted":["nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2023-11-16T03:03:08Z","title_canon_sha256":"31c3f18a5cdea84ea02774031d2787bb03a80da0a65ed799866036c921f24f9b"},"schema_version":"1.0","source":{"id":"2311.09524","kind":"arxiv","version":3}},"canonical_sha256":"3a669d298d986c0afb40969e5d579a476dcb42f99f7ad9825a2356fcfe327bbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a669d298d986c0afb40969e5d579a476dcb42f99f7ad9825a2356fcfe327bbf","first_computed_at":"2026-07-05T10:59:56.699179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:59:56.699179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D889YHRRyGbvrn23v5JislX52MDXyKNrE04V78Q05H/yK3esga4deIUVHP1Q7Z3bQeGA9mfS28Flg1vfrmnEBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:59:56.699670Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.09524","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:935522e56a896a30698771b0ebc0092fa36dc84e8788615dbc727fd2ae1212e0","sha256:a8d98468612a6731b31ec9bfe948e16813d64ac3e5c3b5c0c3e51d260e690c9a"],"state_sha256":"0a17998a327c80297f5d00197c54ae71b327a0db2a3648041206f06a0e719651"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vlScvRyj1G/c/134uBghKMsFrS6d9qfaURyfCQXbHBrBmrwst5EF5jf5F/FuZYsnf+U2dgljrbOyEv+9PUCcBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T10:47:36.572275Z","bundle_sha256":"7b0e20470d948270e53df040bbd577ac21d6a7488a9eba7a85f7e506b904a1ee"}}