{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:WKEAM3S3HU73JV457AI36343LX","short_pith_number":"pith:WKEAM3S3","canonical_record":{"source":{"id":"1902.04507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-12T17:19:44Z","cross_cats_sorted":[],"title_canon_sha256":"1269d9867d972f02ea0a3d69ebc0ec06210db70d28b82fe58912359414a7e472","abstract_canon_sha256":"9e64c3498732e0871d5d7d68e7fadf1b17e67633a0b32feb1ac3dc898298572d"},"schema_version":"1.0"},"canonical_sha256":"b288066e5b3d3fb4d79df811bf6f9b5ddf3f4375722d901859f3ecbbcd88ce5d","source":{"kind":"arxiv","id":"1902.04507","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04507","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04507v1","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04507","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"WKEAM3S3HU73","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WKEAM3S3HU73JV45","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WKEAM3S3","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:WKEAM3S3HU73JV457AI36343LX","target":"record","payload":{"canonical_record":{"source":{"id":"1902.04507","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-12T17:19:44Z","cross_cats_sorted":[],"title_canon_sha256":"1269d9867d972f02ea0a3d69ebc0ec06210db70d28b82fe58912359414a7e472","abstract_canon_sha256":"9e64c3498732e0871d5d7d68e7fadf1b17e67633a0b32feb1ac3dc898298572d"},"schema_version":"1.0"},"canonical_sha256":"b288066e5b3d3fb4d79df811bf6f9b5ddf3f4375722d901859f3ecbbcd88ce5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:12.096797Z","signature_b64":"m3HLSrpdydOOa4WV0q80VnlQ3e95k/icw4FbA8nn+QSTEflFCeBJ0y8ugnFJYPSsKxmO+IYu8R3GUNmMDkg/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b288066e5b3d3fb4d79df811bf6f9b5ddf3f4375722d901859f3ecbbcd88ce5d","last_reissued_at":"2026-05-17T23:54:12.096143Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:12.096143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.04507","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":"2026-05-17T23:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tpcXeGVR6ql7zW6w827tzY41nI2chBBJMo4/mZ9vDJtLZjDhtM3WY0gy7jcCUwxKH+HoqapSut4ma7FTMLZVCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:13:30.701960Z"},"content_sha256":"8dcf0a868f94606776063a2d55a3d46671d55d3de975cd86d055ec6a47510fb7","schema_version":"1.0","event_id":"sha256:8dcf0a868f94606776063a2d55a3d46671d55d3de975cd86d055ec6a47510fb7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:WKEAM3S3HU73JV457AI36343LX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-local Linearization of Nonlinear Differential Equations via Polyflows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"P. Tabuada, R. M. Jungers","submitted_at":"2019-02-12T17:19:44Z","abstract_excerpt":"Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of approximating nonlinear differential equations with linear ones is not new, we propose a new approximation scheme that captures both local as well as global properties. This is achieved via a hierarchy of approximations, where the Nth degree of the hierarchy is a linear differential equation obtained by globally approximating the Nth Lie derivatives of the trajec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04507","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":"2026-05-17T23:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/yt0osspeEEL3+BVr4d1bLtt9kuPjMrb8O/ZzLA0Abf7Y3UJceb2QxOCKyqmgWYWFAG14GEd2vBWUkuU6uJ5CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T13:13:30.702309Z"},"content_sha256":"e618a9cbdf1c2af22d47de4079099acec6f080e6c64beed92c7571f3a9c4bb94","schema_version":"1.0","event_id":"sha256:e618a9cbdf1c2af22d47de4079099acec6f080e6c64beed92c7571f3a9c4bb94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WKEAM3S3HU73JV457AI36343LX/bundle.json","state_url":"https://pith.science/pith/WKEAM3S3HU73JV457AI36343LX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WKEAM3S3HU73JV457AI36343LX/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":"2026-06-25T13:13:30Z","links":{"resolver":"https://pith.science/pith/WKEAM3S3HU73JV457AI36343LX","bundle":"https://pith.science/pith/WKEAM3S3HU73JV457AI36343LX/bundle.json","state":"https://pith.science/pith/WKEAM3S3HU73JV457AI36343LX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WKEAM3S3HU73JV457AI36343LX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:WKEAM3S3HU73JV457AI36343LX","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":"9e64c3498732e0871d5d7d68e7fadf1b17e67633a0b32feb1ac3dc898298572d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-12T17:19:44Z","title_canon_sha256":"1269d9867d972f02ea0a3d69ebc0ec06210db70d28b82fe58912359414a7e472"},"schema_version":"1.0","source":{"id":"1902.04507","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.04507","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1902.04507v1","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.04507","created_at":"2026-05-17T23:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"WKEAM3S3HU73","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"WKEAM3S3HU73JV45","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"WKEAM3S3","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:e618a9cbdf1c2af22d47de4079099acec6f080e6c64beed92c7571f3a9c4bb94","target":"graph","created_at":"2026-05-17T23:54:12Z","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":"Motivated by the mathematics literature on the algebraic properties of so-called polynomial vector flows, we propose a technique for approximating nonlinear differential equations by linear differential equations. Although the idea of approximating nonlinear differential equations with linear ones is not new, we propose a new approximation scheme that captures both local as well as global properties. This is achieved via a hierarchy of approximations, where the Nth degree of the hierarchy is a linear differential equation obtained by globally approximating the Nth Lie derivatives of the trajec","authors_text":"P. Tabuada, R. M. Jungers","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-12T17:19:44Z","title":"Non-local Linearization of Nonlinear Differential Equations via Polyflows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.04507","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":"sha256:8dcf0a868f94606776063a2d55a3d46671d55d3de975cd86d055ec6a47510fb7","target":"record","created_at":"2026-05-17T23:54:12Z","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":"9e64c3498732e0871d5d7d68e7fadf1b17e67633a0b32feb1ac3dc898298572d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-02-12T17:19:44Z","title_canon_sha256":"1269d9867d972f02ea0a3d69ebc0ec06210db70d28b82fe58912359414a7e472"},"schema_version":"1.0","source":{"id":"1902.04507","kind":"arxiv","version":1}},"canonical_sha256":"b288066e5b3d3fb4d79df811bf6f9b5ddf3f4375722d901859f3ecbbcd88ce5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b288066e5b3d3fb4d79df811bf6f9b5ddf3f4375722d901859f3ecbbcd88ce5d","first_computed_at":"2026-05-17T23:54:12.096143Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:12.096143Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m3HLSrpdydOOa4WV0q80VnlQ3e95k/icw4FbA8nn+QSTEflFCeBJ0y8ugnFJYPSsKxmO+IYu8R3GUNmMDkg/Bg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:12.096797Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.04507","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dcf0a868f94606776063a2d55a3d46671d55d3de975cd86d055ec6a47510fb7","sha256:e618a9cbdf1c2af22d47de4079099acec6f080e6c64beed92c7571f3a9c4bb94"],"state_sha256":"1ddd097888c75e11a85d84f59f25e2abe7585717ae4a8e7479b7ced83c0ed74b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y+0qHoo95p/JKi6ycZIWMkAzz+X+s1WD6T1o3Y2nPS9JgEvQCtea1xQtYVxKWbzvoVnDR0m/dK4h/1WhX4F6Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T13:13:30.704247Z","bundle_sha256":"0da50d1ed5aa2b8c8376dba4f67042375e8146d4bdf0e7b087ccb2e6b6aeae52"}}