{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TD6SLFZL4DDB3NOZCGZRWYKKXE","short_pith_number":"pith:TD6SLFZL","canonical_record":{"source":{"id":"2409.01222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-09-02T12:57:16Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"fa3c11b77d495acebf242200043751c91f642dcd7aedd952e4886ae59eff5c0d","abstract_canon_sha256":"619594a27a55d2cf8562ff21deb7ea7f9bde94419e34f454a91998064c38dd9c"},"schema_version":"1.0"},"canonical_sha256":"98fd25972be0c61db5d911b31b614ab9168d1532388cab49d65e8ec1399a5e10","source":{"kind":"arxiv","id":"2409.01222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01222","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01222v1","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01222","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"TD6SLFZL4DDB","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_16","alias_value":"TD6SLFZL4DDB3NOZ","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_8","alias_value":"TD6SLFZL","created_at":"2026-07-05T09:02:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TD6SLFZL4DDB3NOZCGZRWYKKXE","target":"record","payload":{"canonical_record":{"source":{"id":"2409.01222","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-09-02T12:57:16Z","cross_cats_sorted":["cs.SY"],"title_canon_sha256":"fa3c11b77d495acebf242200043751c91f642dcd7aedd952e4886ae59eff5c0d","abstract_canon_sha256":"619594a27a55d2cf8562ff21deb7ea7f9bde94419e34f454a91998064c38dd9c"},"schema_version":"1.0"},"canonical_sha256":"98fd25972be0c61db5d911b31b614ab9168d1532388cab49d65e8ec1399a5e10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:02:26.209525Z","signature_b64":"BkeOvcQTcNEOXL7S3ls7Sb6pLbq3j3nfUn+df7R3UKXoTRYOKTBXTdl/V2EFOXYw/spMtVb3XaEb5m6ZrnNFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"98fd25972be0c61db5d911b31b614ab9168d1532388cab49d65e8ec1399a5e10","last_reissued_at":"2026-07-05T09:02:26.209043Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:02:26.209043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.01222","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":"2026-07-05T09:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9J3QDwvfHJog5/CNFju3M0VAF3V6L7YViHQGHMxCd2+K6UUa1px4U064m0rlOyYoZ55YMBVeapPOrF+ZWYdHDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:19:43.979859Z"},"content_sha256":"4161f799417ff2c4f95812da384eaedf3d4e3a8231884b224cd2dd4adee23135","schema_version":"1.0","event_id":"sha256:4161f799417ff2c4f95812da384eaedf3d4e3a8231884b224cd2dd4adee23135"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TD6SLFZL4DDB3NOZCGZRWYKKXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear PDE Constrained Optimal Dispatch of Gas and Power: A Global Linearization Approach","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.SY"],"primary_cat":"eess.SY","authors_text":"Ruizhi Yu, Shuai Lu, Suhan Zhang, Wei Gu, Yijun Xu, Yuan Li, Zhikai Huang","submitted_at":"2024-09-02T12:57:16Z","abstract_excerpt":"The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear partial differential equations (PDE), making the dispatch problem of the EG-IES a complicated optimization model constrained by nonlinear PDE. To address it, we propose a globally linearized gas network model based on the Koopman operator theory, avoiding the commonly used local linearization and spatial discretization. Particularly, we propose a data-driven Ko"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01222","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/2409.01222/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":"2026-07-05T09:02:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+u2/pmIdH4pNYPJQRyGgP8YWxdWEb3+ibT/CbIquPnjrec7sljfD3XLg898Te5Q3rXn7vJ6o3cQHhfwBjRIDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T00:19:43.980309Z"},"content_sha256":"bd45c1c127c9ce24766e88c12c295eadbc1e649ebed237a00dd1be2ef40d5d49","schema_version":"1.0","event_id":"sha256:bd45c1c127c9ce24766e88c12c295eadbc1e649ebed237a00dd1be2ef40d5d49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/bundle.json","state_url":"https://pith.science/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/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":"2026-08-06T00:19:43Z","links":{"resolver":"https://pith.science/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE","bundle":"https://pith.science/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/bundle.json","state":"https://pith.science/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TD6SLFZL4DDB3NOZCGZRWYKKXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TD6SLFZL4DDB3NOZCGZRWYKKXE","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":"619594a27a55d2cf8562ff21deb7ea7f9bde94419e34f454a91998064c38dd9c","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-09-02T12:57:16Z","title_canon_sha256":"fa3c11b77d495acebf242200043751c91f642dcd7aedd952e4886ae59eff5c0d"},"schema_version":"1.0","source":{"id":"2409.01222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.01222","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"arxiv_version","alias_value":"2409.01222v1","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.01222","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_12","alias_value":"TD6SLFZL4DDB","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_16","alias_value":"TD6SLFZL4DDB3NOZ","created_at":"2026-07-05T09:02:26Z"},{"alias_kind":"pith_short_8","alias_value":"TD6SLFZL","created_at":"2026-07-05T09:02:26Z"}],"graph_snapshots":[{"event_id":"sha256:bd45c1c127c9ce24766e88c12c295eadbc1e649ebed237a00dd1be2ef40d5d49","target":"graph","created_at":"2026-07-05T09:02:26Z","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/2409.01222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear partial differential equations (PDE), making the dispatch problem of the EG-IES a complicated optimization model constrained by nonlinear PDE. To address it, we propose a globally linearized gas network model based on the Koopman operator theory, avoiding the commonly used local linearization and spatial discretization. Particularly, we propose a data-driven Ko","authors_text":"Ruizhi Yu, Shuai Lu, Suhan Zhang, Wei Gu, Yijun Xu, Yuan Li, Zhikai Huang","cross_cats":["cs.SY"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-09-02T12:57:16Z","title":"Nonlinear PDE Constrained Optimal Dispatch of Gas and Power: A Global Linearization Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.01222","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":"sha256:4161f799417ff2c4f95812da384eaedf3d4e3a8231884b224cd2dd4adee23135","target":"record","created_at":"2026-07-05T09:02:26Z","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":"619594a27a55d2cf8562ff21deb7ea7f9bde94419e34f454a91998064c38dd9c","cross_cats_sorted":["cs.SY"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"eess.SY","submitted_at":"2024-09-02T12:57:16Z","title_canon_sha256":"fa3c11b77d495acebf242200043751c91f642dcd7aedd952e4886ae59eff5c0d"},"schema_version":"1.0","source":{"id":"2409.01222","kind":"arxiv","version":1}},"canonical_sha256":"98fd25972be0c61db5d911b31b614ab9168d1532388cab49d65e8ec1399a5e10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98fd25972be0c61db5d911b31b614ab9168d1532388cab49d65e8ec1399a5e10","first_computed_at":"2026-07-05T09:02:26.209043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:02:26.209043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BkeOvcQTcNEOXL7S3ls7Sb6pLbq3j3nfUn+df7R3UKXoTRYOKTBXTdl/V2EFOXYw/spMtVb3XaEb5m6ZrnNFCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:02:26.209525Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.01222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4161f799417ff2c4f95812da384eaedf3d4e3a8231884b224cd2dd4adee23135","sha256:bd45c1c127c9ce24766e88c12c295eadbc1e649ebed237a00dd1be2ef40d5d49"],"state_sha256":"1ab1afe6c1a42f689240ba19acd5b9bc4d01e6681c030c659df653df06d7f45e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYGtzqVGvpKeXGjnqht5DVqcsFqk2+GgYFHEiPbt+6cWtdTyN5iAMbU/+prw9U1KZeBhpcPoTs7hS3PSOtGyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T00:19:43.983274Z","bundle_sha256":"82c4e7156f4e308a30b96ab7edcf025e64930b8f24d534dddb2b947e51c86bfc"}}