{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MIFJ2TISY37Z7I37ZZ7LZPNQ7P","short_pith_number":"pith:MIFJ2TIS","canonical_record":{"source":{"id":"1908.06088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-08-16T08:51:53Z","cross_cats_sorted":["cs.NA","math.DS","math.NA","physics.comp-ph"],"title_canon_sha256":"c4e0aea6eee313368dab1abe4d3ba3d7f0bf29b4e68afe8d60f2ae27a7b8cd0f","abstract_canon_sha256":"bfdf2e3f6a93f49ef6c8526fb2174304811b19e34fea7c9e5379641f3b93c12c"},"schema_version":"1.0"},"canonical_sha256":"620a9d4d12c6ff9fa37fce7ebcbdb0fbc2436040a687b73d88d3531f3c2a4b4b","source":{"kind":"arxiv","id":"1908.06088","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06088","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06088v1","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06088","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"MIFJ2TISY37Z","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_16","alias_value":"MIFJ2TISY37Z7I37","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_8","alias_value":"MIFJ2TIS","created_at":"2026-07-04T23:58:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MIFJ2TISY37Z7I37ZZ7LZPNQ7P","target":"record","payload":{"canonical_record":{"source":{"id":"1908.06088","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-08-16T08:51:53Z","cross_cats_sorted":["cs.NA","math.DS","math.NA","physics.comp-ph"],"title_canon_sha256":"c4e0aea6eee313368dab1abe4d3ba3d7f0bf29b4e68afe8d60f2ae27a7b8cd0f","abstract_canon_sha256":"bfdf2e3f6a93f49ef6c8526fb2174304811b19e34fea7c9e5379641f3b93c12c"},"schema_version":"1.0"},"canonical_sha256":"620a9d4d12c6ff9fa37fce7ebcbdb0fbc2436040a687b73d88d3531f3c2a4b4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:12.269805Z","signature_b64":"PSnYg0KvtlSfzU8JQTVWYc+dBBkCmqFCn77EQqbE8NNyp1oInIpXnEfHY9yFb8K44rZV6AQe0660XAOM+RVnDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"620a9d4d12c6ff9fa37fce7ebcbdb0fbc2436040a687b73d88d3531f3c2a4b4b","last_reissued_at":"2026-07-04T23:58:12.269392Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:12.269392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.06088","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":"2026-07-04T23:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i1508NKB0JWgaBqepuAMaysgrTB9V4iUDa/c5tZ6POgJCSuH6debMV2HS3dHdES7CntMx0FgrnKxJqer1mSzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:28:49.957837Z"},"content_sha256":"05c8ed1c95a7d4bc818453be7d0818960dd974593ca18120c2eb8e9e4dc0f74d","schema_version":"1.0","event_id":"sha256:05c8ed1c95a7d4bc818453be7d0818960dd974593ca18120c2eb8e9e4dc0f74d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MIFJ2TISY37Z7I37ZZ7LZPNQ7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Matrix Lie Maps and Neural Networks for Solving Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.DS","math.NA","physics.comp-ph"],"primary_cat":"cs.NE","authors_text":"Andrei Ivanov, Sergei Andrianov","submitted_at":"2019-08-16T08:51:53Z","abstract_excerpt":"The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It can be used for solving systems of differential equations more efficiently than traditional step-by-step numerical methods. Implementation of the Lie map as a polynomial neural network provides a tool for both simulation and data-driven identification of dynamical systems. If the differential equation is provided, training a neural network is unnecessary. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06088/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":"2026-07-04T23:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bX4I+h4iUATEHl5meUJYzEBHHxC8SscjzK5NlIZuB8LPmk3SLz0ko4ys4BsymvEUTApnbEc6G1MdXYlBIAn4AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:28:49.958444Z"},"content_sha256":"e5846954b52196883937b6e282463245dadbf11d6cfb2413591f4890695ac54a","schema_version":"1.0","event_id":"sha256:e5846954b52196883937b6e282463245dadbf11d6cfb2413591f4890695ac54a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/bundle.json","state_url":"https://pith.science/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/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":"2026-08-16T17:28:49Z","links":{"resolver":"https://pith.science/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P","bundle":"https://pith.science/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/bundle.json","state":"https://pith.science/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIFJ2TISY37Z7I37ZZ7LZPNQ7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MIFJ2TISY37Z7I37ZZ7LZPNQ7P","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":"bfdf2e3f6a93f49ef6c8526fb2174304811b19e34fea7c9e5379641f3b93c12c","cross_cats_sorted":["cs.NA","math.DS","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-08-16T08:51:53Z","title_canon_sha256":"c4e0aea6eee313368dab1abe4d3ba3d7f0bf29b4e68afe8d60f2ae27a7b8cd0f"},"schema_version":"1.0","source":{"id":"1908.06088","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06088","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06088v1","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06088","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"MIFJ2TISY37Z","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_16","alias_value":"MIFJ2TISY37Z7I37","created_at":"2026-07-04T23:58:12Z"},{"alias_kind":"pith_short_8","alias_value":"MIFJ2TIS","created_at":"2026-07-04T23:58:12Z"}],"graph_snapshots":[{"event_id":"sha256:e5846954b52196883937b6e282463245dadbf11d6cfb2413591f4890695ac54a","target":"graph","created_at":"2026-07-04T23:58:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.06088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It can be used for solving systems of differential equations more efficiently than traditional step-by-step numerical methods. Implementation of the Lie map as a polynomial neural network provides a tool for both simulation and data-driven identification of dynamical systems. If the differential equation is provided, training a neural network is unnecessary. Th","authors_text":"Andrei Ivanov, Sergei Andrianov","cross_cats":["cs.NA","math.DS","math.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-08-16T08:51:53Z","title":"Matrix Lie Maps and Neural Networks for Solving Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06088","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":"sha256:05c8ed1c95a7d4bc818453be7d0818960dd974593ca18120c2eb8e9e4dc0f74d","target":"record","created_at":"2026-07-04T23:58:12Z","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":"bfdf2e3f6a93f49ef6c8526fb2174304811b19e34fea7c9e5379641f3b93c12c","cross_cats_sorted":["cs.NA","math.DS","math.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2019-08-16T08:51:53Z","title_canon_sha256":"c4e0aea6eee313368dab1abe4d3ba3d7f0bf29b4e68afe8d60f2ae27a7b8cd0f"},"schema_version":"1.0","source":{"id":"1908.06088","kind":"arxiv","version":1}},"canonical_sha256":"620a9d4d12c6ff9fa37fce7ebcbdb0fbc2436040a687b73d88d3531f3c2a4b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"620a9d4d12c6ff9fa37fce7ebcbdb0fbc2436040a687b73d88d3531f3c2a4b4b","first_computed_at":"2026-07-04T23:58:12.269392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:12.269392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSnYg0KvtlSfzU8JQTVWYc+dBBkCmqFCn77EQqbE8NNyp1oInIpXnEfHY9yFb8K44rZV6AQe0660XAOM+RVnDA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:12.269805Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06088","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05c8ed1c95a7d4bc818453be7d0818960dd974593ca18120c2eb8e9e4dc0f74d","sha256:e5846954b52196883937b6e282463245dadbf11d6cfb2413591f4890695ac54a"],"state_sha256":"e31e2eb0b20d47a42f5c5517f47973dfe932ab1b778478ba7c1aa624cb49b0ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+4ob2LmXBGtro70SdOTKG7Rcpd3Kvrx97sFWZft4AuijH/LzVB21i9RlWsEqiv1hdvF4yIocPqp1jlSv4A7Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:28:49.962828Z","bundle_sha256":"8bf738280d75d1e64915056198f5ed937cd5925b5a8ed8d052ce77ffbc1c7ef0"}}