{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:5HF6TZ64GDLKZZEGI677LATVPQ","short_pith_number":"pith:5HF6TZ64","canonical_record":{"source":{"id":"1712.03132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-08T15:41:42Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"05e2428b6e3f3c75e0714a797fff079e2b83d986ba7077ef6f3873082a923ba8","abstract_canon_sha256":"e276608a8dcdb8e2ffad26523fbd2f9b422812592e9b81fbc1725ec764c45ddd"},"schema_version":"1.0"},"canonical_sha256":"e9cbe9e7dc30d6ace48647bff582757c309d0657e10cb6018ebc0603550c625c","source":{"kind":"arxiv","id":"1712.03132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03132","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03132v1","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03132","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"5HF6TZ64GDLK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HF6TZ64GDLKZZEG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HF6TZ64","created_at":"2026-05-18T12:31:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:5HF6TZ64GDLKZZEGI677LATVPQ","target":"record","payload":{"canonical_record":{"source":{"id":"1712.03132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-08T15:41:42Z","cross_cats_sorted":["cs.AI","math.OC"],"title_canon_sha256":"05e2428b6e3f3c75e0714a797fff079e2b83d986ba7077ef6f3873082a923ba8","abstract_canon_sha256":"e276608a8dcdb8e2ffad26523fbd2f9b422812592e9b81fbc1725ec764c45ddd"},"schema_version":"1.0"},"canonical_sha256":"e9cbe9e7dc30d6ace48647bff582757c309d0657e10cb6018ebc0603550c625c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:28.241536Z","signature_b64":"XK0XsFbd74zxOIBWA2ld77xTXCwZqBo40cZQLt5vbhO/v/UTCMoJk62fvswbD8OWmoU/iHeFN6MSNxH1YfrPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e9cbe9e7dc30d6ace48647bff582757c309d0657e10cb6018ebc0603550c625c","last_reissued_at":"2026-05-18T00:28:28.241053Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:28.241053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.03132","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":"2026-05-18T00:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TkrZWz3wUVkyOAyP/UT0RC0pAqtPNryy68gfErEKW76IKMYk5uXBFrCg2jRrUqgaGDtUyT6diR/EjRX9rsn3AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:37:05.750811Z"},"content_sha256":"d249b55b8ea563d768ec4665a8fa6ab2457fa5e9045a1e3607d38f19c77e9fd0","schema_version":"1.0","event_id":"sha256:d249b55b8ea563d768ec4665a8fa6ab2457fa5e9045a1e3607d38f19c77e9fd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:5HF6TZ64GDLKZZEGI677LATVPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","math.OC"],"primary_cat":"cs.LG","authors_text":"Charles A. Johnson, Enoch Yeung","submitted_at":"2017-12-08T15:41:42Z","abstract_excerpt":"An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning methods have enabled data-driven discovery of Koopman operators, for both continuous and discrete-time systems. Since Koopman operators are often infinite-dimensional, they are approximated in practice using finite-dimensional systems. The fidelity and convergence of a given finite-dimensional Koopman approximation is a subject of ongoing research. In this p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03132","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":"2026-05-18T00:28:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7deto5lMjifxcFFxWxEWH8KvZwhaIJKlBetAqhtDoAEXM5f7PNYKc3EpBUOFlyRabfIZALMj1p+UpP/FNA1yBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T18:37:05.751147Z"},"content_sha256":"112511b1c386337493a5404363f8dae91829ad2bf8b4caaf660c721bd84ec33f","schema_version":"1.0","event_id":"sha256:112511b1c386337493a5404363f8dae91829ad2bf8b4caaf660c721bd84ec33f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5HF6TZ64GDLKZZEGI677LATVPQ/bundle.json","state_url":"https://pith.science/pith/5HF6TZ64GDLKZZEGI677LATVPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5HF6TZ64GDLKZZEGI677LATVPQ/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":"2026-07-01T18:37:05Z","links":{"resolver":"https://pith.science/pith/5HF6TZ64GDLKZZEGI677LATVPQ","bundle":"https://pith.science/pith/5HF6TZ64GDLKZZEGI677LATVPQ/bundle.json","state":"https://pith.science/pith/5HF6TZ64GDLKZZEGI677LATVPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5HF6TZ64GDLKZZEGI677LATVPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:5HF6TZ64GDLKZZEGI677LATVPQ","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":"e276608a8dcdb8e2ffad26523fbd2f9b422812592e9b81fbc1725ec764c45ddd","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-08T15:41:42Z","title_canon_sha256":"05e2428b6e3f3c75e0714a797fff079e2b83d986ba7077ef6f3873082a923ba8"},"schema_version":"1.0","source":{"id":"1712.03132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.03132","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"arxiv_version","alias_value":"1712.03132v1","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03132","created_at":"2026-05-18T00:28:28Z"},{"alias_kind":"pith_short_12","alias_value":"5HF6TZ64GDLK","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_16","alias_value":"5HF6TZ64GDLKZZEG","created_at":"2026-05-18T12:31:00Z"},{"alias_kind":"pith_short_8","alias_value":"5HF6TZ64","created_at":"2026-05-18T12:31:00Z"}],"graph_snapshots":[{"event_id":"sha256:112511b1c386337493a5404363f8dae91829ad2bf8b4caaf660c721bd84ec33f","target":"graph","created_at":"2026-05-18T00:28:28Z","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":"An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models. Advances in extended dynamic mode decomposition approaches and machine learning methods have enabled data-driven discovery of Koopman operators, for both continuous and discrete-time systems. Since Koopman operators are often infinite-dimensional, they are approximated in practice using finite-dimensional systems. The fidelity and convergence of a given finite-dimensional Koopman approximation is a subject of ongoing research. In this p","authors_text":"Charles A. Johnson, Enoch Yeung","cross_cats":["cs.AI","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-08T15:41:42Z","title":"A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03132","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:d249b55b8ea563d768ec4665a8fa6ab2457fa5e9045a1e3607d38f19c77e9fd0","target":"record","created_at":"2026-05-18T00:28:28Z","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":"e276608a8dcdb8e2ffad26523fbd2f9b422812592e9b81fbc1725ec764c45ddd","cross_cats_sorted":["cs.AI","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2017-12-08T15:41:42Z","title_canon_sha256":"05e2428b6e3f3c75e0714a797fff079e2b83d986ba7077ef6f3873082a923ba8"},"schema_version":"1.0","source":{"id":"1712.03132","kind":"arxiv","version":1}},"canonical_sha256":"e9cbe9e7dc30d6ace48647bff582757c309d0657e10cb6018ebc0603550c625c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e9cbe9e7dc30d6ace48647bff582757c309d0657e10cb6018ebc0603550c625c","first_computed_at":"2026-05-18T00:28:28.241053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:28.241053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XK0XsFbd74zxOIBWA2ld77xTXCwZqBo40cZQLt5vbhO/v/UTCMoJk62fvswbD8OWmoU/iHeFN6MSNxH1YfrPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:28.241536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.03132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d249b55b8ea563d768ec4665a8fa6ab2457fa5e9045a1e3607d38f19c77e9fd0","sha256:112511b1c386337493a5404363f8dae91829ad2bf8b4caaf660c721bd84ec33f"],"state_sha256":"6749f5e05ec1eb591ba711587d2638dd20ba04be7a56b9df1bcf29166dd66988"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8y0YCZigOtHbF2KgjTPG7GIdv6SpRrN/dEmYVA/5yl+Esa0L2O5oeg8BWJI1hMpHMkEByHQfgpJ9kIx0NwH5Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T18:37:05.753083Z","bundle_sha256":"6b35f46e20825bb2336e07666a0901f919c018cb3da7f8aa146f69f99ff9bdad"}}