{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YZPG2B2DZ3YJXZ2HQZV6BPZDFQ","short_pith_number":"pith:YZPG2B2D","canonical_record":{"source":{"id":"1703.07324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T17:19:22Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"71ab339a7056365f9b2e13500c443c0ae69ad9ccd350767219fa43606e45d209","abstract_canon_sha256":"ce34d1c6fd2ec452b058fadc5cc03551fcab3b4e15812371ae7d98d741906a73"},"schema_version":"1.0"},"canonical_sha256":"c65e6d0743cef09be747866be0bf232c3d10fd8ba42cfeb31a9a1bc0c7a28fd1","source":{"kind":"arxiv","id":"1703.07324","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07324","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07324v1","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07324","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"YZPG2B2DZ3YJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZPG2B2DZ3YJXZ2H","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZPG2B2D","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YZPG2B2DZ3YJXZ2HQZV6BPZDFQ","target":"record","payload":{"canonical_record":{"source":{"id":"1703.07324","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T17:19:22Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"71ab339a7056365f9b2e13500c443c0ae69ad9ccd350767219fa43606e45d209","abstract_canon_sha256":"ce34d1c6fd2ec452b058fadc5cc03551fcab3b4e15812371ae7d98d741906a73"},"schema_version":"1.0"},"canonical_sha256":"c65e6d0743cef09be747866be0bf232c3d10fd8ba42cfeb31a9a1bc0c7a28fd1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:10.691249Z","signature_b64":"gOFUk89GvYYzfp/STdJhbyRf/G/2GDghTKerwz4z9K9r4O/moHbpPRyGsVE3w5KwCzh9IBBhPNqQAHIeqjY4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c65e6d0743cef09be747866be0bf232c3d10fd8ba42cfeb31a9a1bc0c7a28fd1","last_reissued_at":"2026-05-18T00:48:10.690632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:10.690632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.07324","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":"2026-05-18T00:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5amCULojuvnNPkFTuVkAt7+j/Ho9pkKlF70wBigo9A5ai+Tn841LD/grmPqezv76cLod8Iuyu6GS1JN8cpkBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:59:51.912107Z"},"content_sha256":"de6ed1a72aeb884eda3db6fd03d30ddb94c0f23ee1eb7c957dc9d7a9018d9f9c","schema_version":"1.0","event_id":"sha256:de6ed1a72aeb884eda3db6fd03d30ddb94c0f23ee1eb7c957dc9d7a9018d9f9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YZPG2B2DZ3YJXZ2HQZV6BPZDFQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Koopman Operator Family Spectrum for Nonautonomous Systems - Part 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.DS","authors_text":"(2) Faculty of Mechanical Engineering, Croatia, Igor Mezi\\'c (2) ((1) Faculty of Engineering University of Rijeka, Mathematics, Nelida \\v{C}rnjari\\'c-\\v{Z}ic (1), Santa Barbara), Senka Ma\\'ce\\v{s}i\\'c (1), University of California","submitted_at":"2017-03-21T17:19:22Z","abstract_excerpt":"For every non-autonomous system, there is the related family of Koopman operators $\\mathcal{K}^{(t,t_0)}$, parameterized by the time pair $(t,t_0)$. In this paper we are investigating the time dependency of the spectral properties of the Koopman operator family in the linear non-autonomous case and we propose an algorithm for computation of its spectrum from observed data only. To build this algorithm we use the concept of the fundamental matrix of linear non-autonomous systems and some specific aspects of Arnoldi-like methods. In particular, we use Arnoldi-like methods on local data stencils,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07324","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":"2026-05-18T00:48:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+r4R0emb31C1zqtqVRQKSJplSS579lJdKYhOfjuQSfsUqUR0o+fHjVa/2pQjJK9jkNqyD5j8WTNgsvTHfAb4Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T22:59:51.912837Z"},"content_sha256":"5bbd2287ece27309c78e67bdaa314b68ecb1bfecda5bea4843650dab1e02d588","schema_version":"1.0","event_id":"sha256:5bbd2287ece27309c78e67bdaa314b68ecb1bfecda5bea4843650dab1e02d588"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/bundle.json","state_url":"https://pith.science/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/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":"2026-05-29T22:59:51Z","links":{"resolver":"https://pith.science/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ","bundle":"https://pith.science/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/bundle.json","state":"https://pith.science/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YZPG2B2DZ3YJXZ2HQZV6BPZDFQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YZPG2B2DZ3YJXZ2HQZV6BPZDFQ","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":"ce34d1c6fd2ec452b058fadc5cc03551fcab3b4e15812371ae7d98d741906a73","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T17:19:22Z","title_canon_sha256":"71ab339a7056365f9b2e13500c443c0ae69ad9ccd350767219fa43606e45d209"},"schema_version":"1.0","source":{"id":"1703.07324","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07324","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07324v1","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07324","created_at":"2026-05-18T00:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"YZPG2B2DZ3YJ","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"YZPG2B2DZ3YJXZ2H","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"YZPG2B2D","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:5bbd2287ece27309c78e67bdaa314b68ecb1bfecda5bea4843650dab1e02d588","target":"graph","created_at":"2026-05-18T00:48:10Z","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":"For every non-autonomous system, there is the related family of Koopman operators $\\mathcal{K}^{(t,t_0)}$, parameterized by the time pair $(t,t_0)$. In this paper we are investigating the time dependency of the spectral properties of the Koopman operator family in the linear non-autonomous case and we propose an algorithm for computation of its spectrum from observed data only. To build this algorithm we use the concept of the fundamental matrix of linear non-autonomous systems and some specific aspects of Arnoldi-like methods. In particular, we use Arnoldi-like methods on local data stencils,","authors_text":"(2) Faculty of Mechanical Engineering, Croatia, Igor Mezi\\'c (2) ((1) Faculty of Engineering University of Rijeka, Mathematics, Nelida \\v{C}rnjari\\'c-\\v{Z}ic (1), Santa Barbara), Senka Ma\\'ce\\v{s}i\\'c (1), University of California","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T17:19:22Z","title":"Koopman Operator Family Spectrum for Nonautonomous Systems - Part 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07324","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:de6ed1a72aeb884eda3db6fd03d30ddb94c0f23ee1eb7c957dc9d7a9018d9f9c","target":"record","created_at":"2026-05-18T00:48:10Z","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":"ce34d1c6fd2ec452b058fadc5cc03551fcab3b4e15812371ae7d98d741906a73","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-03-21T17:19:22Z","title_canon_sha256":"71ab339a7056365f9b2e13500c443c0ae69ad9ccd350767219fa43606e45d209"},"schema_version":"1.0","source":{"id":"1703.07324","kind":"arxiv","version":1}},"canonical_sha256":"c65e6d0743cef09be747866be0bf232c3d10fd8ba42cfeb31a9a1bc0c7a28fd1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c65e6d0743cef09be747866be0bf232c3d10fd8ba42cfeb31a9a1bc0c7a28fd1","first_computed_at":"2026-05-18T00:48:10.690632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:10.690632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gOFUk89GvYYzfp/STdJhbyRf/G/2GDghTKerwz4z9K9r4O/moHbpPRyGsVE3w5KwCzh9IBBhPNqQAHIeqjY4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:10.691249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07324","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de6ed1a72aeb884eda3db6fd03d30ddb94c0f23ee1eb7c957dc9d7a9018d9f9c","sha256:5bbd2287ece27309c78e67bdaa314b68ecb1bfecda5bea4843650dab1e02d588"],"state_sha256":"767afa7cb84af8005981e9e24590e12a058d1c6291981ce3512a509b6c88f160"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WXOo87/LZg/dwuEI6PriK3Gp5QIZoJUK9WzoI0KA6xMuM3DwwkjUOl/4hmgXNz7od95Ty1+zUKKvVNWZGZFKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T22:59:51.916437Z","bundle_sha256":"dd78ef77951d81bcced15f29a44ae3d0102d6f6b2e1419fd039eac4a67e4b04b"}}