{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:6CY6B57FQLMTJXZNITZAKREJ6K","short_pith_number":"pith:6CY6B57F","canonical_record":{"source":{"id":"2301.07293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-01-18T03:53:56Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"e4a51618589dbfd561ab4f21d96d7eb7982ed2436dae8c023a1e4089a7c193f9","abstract_canon_sha256":"ddefb49929e3fda5a0818cd595c3b83634b1029f5f7690b3855f238ba9e52056"},"schema_version":"1.0"},"canonical_sha256":"f0b1e0f7e582d934df2d44f2054489f2bf3ef8c7665123e7a3b95824ebb94c1f","source":{"kind":"arxiv","id":"2301.07293","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.07293","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"arxiv_version","alias_value":"2301.07293v1","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.07293","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_12","alias_value":"6CY6B57FQLMT","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_16","alias_value":"6CY6B57FQLMTJXZN","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_8","alias_value":"6CY6B57F","created_at":"2026-07-05T05:34:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:6CY6B57FQLMTJXZNITZAKREJ6K","target":"record","payload":{"canonical_record":{"source":{"id":"2301.07293","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-01-18T03:53:56Z","cross_cats_sorted":["physics.flu-dyn"],"title_canon_sha256":"e4a51618589dbfd561ab4f21d96d7eb7982ed2436dae8c023a1e4089a7c193f9","abstract_canon_sha256":"ddefb49929e3fda5a0818cd595c3b83634b1029f5f7690b3855f238ba9e52056"},"schema_version":"1.0"},"canonical_sha256":"f0b1e0f7e582d934df2d44f2054489f2bf3ef8c7665123e7a3b95824ebb94c1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:34:07.281694Z","signature_b64":"ExqDBfTqk7uDk00H/R0bACmkqHQxkDRln4WhC1STGWrygFDeqGiFU55yefpqyBvDARNjlA7O20ejnS2ReSElCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0b1e0f7e582d934df2d44f2054489f2bf3ef8c7665123e7a3b95824ebb94c1f","last_reissued_at":"2026-07-05T05:34:07.281248Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:34:07.281248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.07293","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":"2026-07-05T05:34:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9GWwrKbhZZaEyf3Dcf3+VD451w7Z7F/3KI2UcD/+onCXW8rX/Iv09l0dK836bSzwkT3jNmvBuVprm9KiCjrPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T21:07:34.889405Z"},"content_sha256":"ff029b92d6291ebacccab24354a2087724fb91d35a4614bce612872ba2a36d04","schema_version":"1.0","event_id":"sha256:ff029b92d6291ebacccab24354a2087724fb91d35a4614bce612872ba2a36d04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:6CY6B57FQLMTJXZNITZAKREJ6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turbulence Model Development based on a Novel Method Combining Gene Expression Programming with an Artificial Neural Network","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"physics.comp-ph","authors_text":"Fabian Waschkowski, Haochen Li, Richard D. Sandberg, Yaomin Zhao","submitted_at":"2023-01-18T03:53:56Z","abstract_excerpt":"Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network (ANN), we propose a novel method for symbolic regression called the gene expression programming neural network (GEPNN). In this method, candidate expressions generated by evolutionary algorithms are transformed between the GEP and ANN structures during training iterations, and efficient and robust convergence to accurate models is achieved by combining the G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07293","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/2301.07293/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":"2026-07-05T05:34:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/mFZh/PKYl8tHpI5clsC5/NtY9b9/Zuv3ZAm3fDVab75yHfaIN/hmlldQmmxQ2hyf0hD6eWyzwSG8b6C3mTzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T21:07:34.890508Z"},"content_sha256":"fb012c287357b5ffefa4b6f8b0e35147b04dea9d301985c8422f11e2e881e8db","schema_version":"1.0","event_id":"sha256:fb012c287357b5ffefa4b6f8b0e35147b04dea9d301985c8422f11e2e881e8db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6CY6B57FQLMTJXZNITZAKREJ6K/bundle.json","state_url":"https://pith.science/pith/6CY6B57FQLMTJXZNITZAKREJ6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6CY6B57FQLMTJXZNITZAKREJ6K/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":"2026-08-06T21:07:34Z","links":{"resolver":"https://pith.science/pith/6CY6B57FQLMTJXZNITZAKREJ6K","bundle":"https://pith.science/pith/6CY6B57FQLMTJXZNITZAKREJ6K/bundle.json","state":"https://pith.science/pith/6CY6B57FQLMTJXZNITZAKREJ6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6CY6B57FQLMTJXZNITZAKREJ6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:6CY6B57FQLMTJXZNITZAKREJ6K","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":"ddefb49929e3fda5a0818cd595c3b83634b1029f5f7690b3855f238ba9e52056","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-01-18T03:53:56Z","title_canon_sha256":"e4a51618589dbfd561ab4f21d96d7eb7982ed2436dae8c023a1e4089a7c193f9"},"schema_version":"1.0","source":{"id":"2301.07293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.07293","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"arxiv_version","alias_value":"2301.07293v1","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.07293","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_12","alias_value":"6CY6B57FQLMT","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_16","alias_value":"6CY6B57FQLMTJXZN","created_at":"2026-07-05T05:34:07Z"},{"alias_kind":"pith_short_8","alias_value":"6CY6B57F","created_at":"2026-07-05T05:34:07Z"}],"graph_snapshots":[{"event_id":"sha256:fb012c287357b5ffefa4b6f8b0e35147b04dea9d301985c8422f11e2e881e8db","target":"graph","created_at":"2026-07-05T05:34:07Z","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/2301.07293/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network (ANN), we propose a novel method for symbolic regression called the gene expression programming neural network (GEPNN). In this method, candidate expressions generated by evolutionary algorithms are transformed between the GEP and ANN structures during training iterations, and efficient and robust convergence to accurate models is achieved by combining the G","authors_text":"Fabian Waschkowski, Haochen Li, Richard D. Sandberg, Yaomin Zhao","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-01-18T03:53:56Z","title":"Turbulence Model Development based on a Novel Method Combining Gene Expression Programming with an Artificial Neural Network"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.07293","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:ff029b92d6291ebacccab24354a2087724fb91d35a4614bce612872ba2a36d04","target":"record","created_at":"2026-07-05T05:34:07Z","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":"ddefb49929e3fda5a0818cd595c3b83634b1029f5f7690b3855f238ba9e52056","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2023-01-18T03:53:56Z","title_canon_sha256":"e4a51618589dbfd561ab4f21d96d7eb7982ed2436dae8c023a1e4089a7c193f9"},"schema_version":"1.0","source":{"id":"2301.07293","kind":"arxiv","version":1}},"canonical_sha256":"f0b1e0f7e582d934df2d44f2054489f2bf3ef8c7665123e7a3b95824ebb94c1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0b1e0f7e582d934df2d44f2054489f2bf3ef8c7665123e7a3b95824ebb94c1f","first_computed_at":"2026-07-05T05:34:07.281248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:34:07.281248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ExqDBfTqk7uDk00H/R0bACmkqHQxkDRln4WhC1STGWrygFDeqGiFU55yefpqyBvDARNjlA7O20ejnS2ReSElCw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:34:07.281694Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.07293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff029b92d6291ebacccab24354a2087724fb91d35a4614bce612872ba2a36d04","sha256:fb012c287357b5ffefa4b6f8b0e35147b04dea9d301985c8422f11e2e881e8db"],"state_sha256":"c5f94a744eb60894662bb19f81224817e86d7d61ef2c84a69e5587afccc50883"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCVSLGmeVJKo3YLeuPoDd1jf9ofk8x7p7/OvePUEN6fPlz3cpnOkNqCZCkJkHv4Hut3uYdhhchOYEsWoMnaNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T21:07:34.897788Z","bundle_sha256":"22c5c94fc8a24ab9e7796b79ca274ea93b877e57d2e7a60c22e971e988c72c49"}}