{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7AGAYVQBEDLHMFBNFT3D5U4T43","short_pith_number":"pith:7AGAYVQB","canonical_record":{"source":{"id":"2411.00040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-29T14:45:07Z","cross_cats_sorted":["cs.AI","cs.LG","cs.NA"],"title_canon_sha256":"8e7b26e296fd2c63e16d04db4ee87040b38508861384e8fcf17c310762c11bf4","abstract_canon_sha256":"d5bcb1149d03166115aeef683d72158936eda677e7bf92804d933e523907ca07"},"schema_version":"1.0"},"canonical_sha256":"f80c0c560120d676142d2cf63ed393e6ea20081536edfbb42ddf6f1ad9157661","source":{"kind":"arxiv","id":"2411.00040","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.00040","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"2411.00040v1","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.00040","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"7AGAYVQBEDLH","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_16","alias_value":"7AGAYVQBEDLHMFBN","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_8","alias_value":"7AGAYVQB","created_at":"2026-07-05T09:29:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7AGAYVQBEDLHMFBNFT3D5U4T43","target":"record","payload":{"canonical_record":{"source":{"id":"2411.00040","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-29T14:45:07Z","cross_cats_sorted":["cs.AI","cs.LG","cs.NA"],"title_canon_sha256":"8e7b26e296fd2c63e16d04db4ee87040b38508861384e8fcf17c310762c11bf4","abstract_canon_sha256":"d5bcb1149d03166115aeef683d72158936eda677e7bf92804d933e523907ca07"},"schema_version":"1.0"},"canonical_sha256":"f80c0c560120d676142d2cf63ed393e6ea20081536edfbb42ddf6f1ad9157661","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:29:36.614521Z","signature_b64":"/5aMIchzxIfeSeQIYSLvJl6ao9Je28fvRH3BUac/tOdibAmmfvK4D9vHe126jly+54xbDxurZJ68ajPPqxxXAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f80c0c560120d676142d2cf63ed393e6ea20081536edfbb42ddf6f1ad9157661","last_reissued_at":"2026-07-05T09:29:36.614010Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:29:36.614010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.00040","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":"2026-07-05T09:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KxzAPGhPIkJmGoxOsv15PEJtoDSLUGzTwHuQBTpYBXVZal8dt/P8NTpYfptjbZfkORxMZecyg0Wh/hK1FlHGAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T06:43:12.571916Z"},"content_sha256":"2630dd8397e30f8e388c414c58ffa97939f58d423d4d60785b93b26b7a3d8744","schema_version":"1.0","event_id":"sha256:2630dd8397e30f8e388c414c58ffa97939f58d423d4d60785b93b26b7a3d8744"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7AGAYVQBEDLHMFBNFT3D5U4T43","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.LG","cs.NA"],"primary_cat":"math.NA","authors_text":"Hao Sun, Hao Zhou, Hongsheng Liu, Jian-Xun Wang, Ji-Rong_Wen, Pu Ren, Qi Wang, Ruizhi Chengze, Xin-Yang Liu, Yang Liu, Yi Zhang, Zhiwen Deng, Zidong Wang","submitted_at":"2024-10-29T14:45:07Z","abstract_excerpt":"When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently, machine learning has been increasingly utilized to solve PDE problems, but they often encounter challenges related to interpretability, generalizability, and strong dependency on rich labeled data. Hence, we introduce a new PDE-Preserved Coarse Correction Network (P$^2$C$^2$Net) to efficiently solve spatiotemporal PDE problems on coarse mesh grids in small d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00040","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/2411.00040/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":"2026-07-05T09:29:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NlNkTjcG0F5Rahnqx3QDCWedx3hR836CTsWwEZHWsRrXDC9DJWRxR/imvaJ8a3+QP8pguZURBoJ1uX2PhbCfDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-20T06:43:12.572302Z"},"content_sha256":"57847445a9375f87c9a3ebc7f9fe3c4cdc170c0f6f166163f94483fbe4380465","schema_version":"1.0","event_id":"sha256:57847445a9375f87c9a3ebc7f9fe3c4cdc170c0f6f166163f94483fbe4380465"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/bundle.json","state_url":"https://pith.science/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/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":"2026-07-20T06:43:12Z","links":{"resolver":"https://pith.science/pith/7AGAYVQBEDLHMFBNFT3D5U4T43","bundle":"https://pith.science/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/bundle.json","state":"https://pith.science/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7AGAYVQBEDLHMFBNFT3D5U4T43/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7AGAYVQBEDLHMFBNFT3D5U4T43","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":"d5bcb1149d03166115aeef683d72158936eda677e7bf92804d933e523907ca07","cross_cats_sorted":["cs.AI","cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-29T14:45:07Z","title_canon_sha256":"8e7b26e296fd2c63e16d04db4ee87040b38508861384e8fcf17c310762c11bf4"},"schema_version":"1.0","source":{"id":"2411.00040","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.00040","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"arxiv_version","alias_value":"2411.00040v1","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.00040","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_12","alias_value":"7AGAYVQBEDLH","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_16","alias_value":"7AGAYVQBEDLHMFBN","created_at":"2026-07-05T09:29:36Z"},{"alias_kind":"pith_short_8","alias_value":"7AGAYVQB","created_at":"2026-07-05T09:29:36Z"}],"graph_snapshots":[{"event_id":"sha256:57847445a9375f87c9a3ebc7f9fe3c4cdc170c0f6f166163f94483fbe4380465","target":"graph","created_at":"2026-07-05T09:29:36Z","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/2411.00040/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently, machine learning has been increasingly utilized to solve PDE problems, but they often encounter challenges related to interpretability, generalizability, and strong dependency on rich labeled data. Hence, we introduce a new PDE-Preserved Coarse Correction Network (P$^2$C$^2$Net) to efficiently solve spatiotemporal PDE problems on coarse mesh grids in small d","authors_text":"Hao Sun, Hao Zhou, Hongsheng Liu, Jian-Xun Wang, Ji-Rong_Wen, Pu Ren, Qi Wang, Ruizhi Chengze, Xin-Yang Liu, Yang Liu, Yi Zhang, Zhiwen Deng, Zidong Wang","cross_cats":["cs.AI","cs.LG","cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-29T14:45:07Z","title":"P$^2$C$^2$Net: PDE-Preserved Coarse Correction Network for efficient prediction of spatiotemporal dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.00040","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":"sha256:2630dd8397e30f8e388c414c58ffa97939f58d423d4d60785b93b26b7a3d8744","target":"record","created_at":"2026-07-05T09:29:36Z","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":"d5bcb1149d03166115aeef683d72158936eda677e7bf92804d933e523907ca07","cross_cats_sorted":["cs.AI","cs.LG","cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-10-29T14:45:07Z","title_canon_sha256":"8e7b26e296fd2c63e16d04db4ee87040b38508861384e8fcf17c310762c11bf4"},"schema_version":"1.0","source":{"id":"2411.00040","kind":"arxiv","version":1}},"canonical_sha256":"f80c0c560120d676142d2cf63ed393e6ea20081536edfbb42ddf6f1ad9157661","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f80c0c560120d676142d2cf63ed393e6ea20081536edfbb42ddf6f1ad9157661","first_computed_at":"2026-07-05T09:29:36.614010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:29:36.614010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/5aMIchzxIfeSeQIYSLvJl6ao9Je28fvRH3BUac/tOdibAmmfvK4D9vHe126jly+54xbDxurZJ68ajPPqxxXAg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:29:36.614521Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.00040","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2630dd8397e30f8e388c414c58ffa97939f58d423d4d60785b93b26b7a3d8744","sha256:57847445a9375f87c9a3ebc7f9fe3c4cdc170c0f6f166163f94483fbe4380465"],"state_sha256":"6e5542530fcaeadce7cc393323b7baaa9ecb7a29a0d1cf3924eff1add427660a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcPDfMr5hU3QJks1Z1Lo982Ryz8nlN+8mSxoaRvvra5IazmbTQPYVl040gF/YFpX8MVGSoqzBFJ4sT8xKyPxDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-20T06:43:12.575038Z","bundle_sha256":"adaaaec48f56d00e530a73146cbcf16450f6727514ef48c66d394b131cd4b3cb"}}