{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:RYE666ZH2KNPYGOW3BJV6EKSMQ","short_pith_number":"pith:RYE666ZH","canonical_record":{"source":{"id":"2207.12800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-26T10:46:56Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"f5302a910ac58243d13afc8b63e1478b81d7de8b900db3bce2b2cfe318461c93","abstract_canon_sha256":"2f47399abdbacbbfadec63319373dec354f10eef768abcac6d972740ed2d1921"},"schema_version":"1.0"},"canonical_sha256":"8e09ef7b27d29afc19d6d8535f1152643b74b16b047a860e95f6fd340b85fa78","source":{"kind":"arxiv","id":"2207.12800","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.12800","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"2207.12800v2","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12800","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"RYE666ZH2KNP","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_16","alias_value":"RYE666ZH2KNPYGOW","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_8","alias_value":"RYE666ZH","created_at":"2026-07-05T05:38:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:RYE666ZH2KNPYGOW3BJV6EKSMQ","target":"record","payload":{"canonical_record":{"source":{"id":"2207.12800","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-26T10:46:56Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"f5302a910ac58243d13afc8b63e1478b81d7de8b900db3bce2b2cfe318461c93","abstract_canon_sha256":"2f47399abdbacbbfadec63319373dec354f10eef768abcac6d972740ed2d1921"},"schema_version":"1.0"},"canonical_sha256":"8e09ef7b27d29afc19d6d8535f1152643b74b16b047a860e95f6fd340b85fa78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:38:43.481957Z","signature_b64":"wkiCea/su2q9Hc/ZCARvj/dJNTU8BDwofaE6SWFsQBV4uZKBEjUaiTrngJNfK4i2eyVXxMYnqm99iuSN8XZCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e09ef7b27d29afc19d6d8535f1152643b74b16b047a860e95f6fd340b85fa78","last_reissued_at":"2026-07-05T05:38:43.481559Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:38:43.481559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.12800","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ry1VDT1Mr9uBCYxn6XgOedsMfNMnzh9Rf/ztc7QB/wn6isMwl1EIeLjUtEFxMfODZaGLTbQ8a/Yt6RhCJHO9DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:08:07.966816Z"},"content_sha256":"fd99ab0e57e3cf1e20ce949c46ba99e9b3514b9743f7a13678dedd25c6d595eb","schema_version":"1.0","event_id":"sha256:fd99ab0e57e3cf1e20ce949c46ba99e9b3514b9743f7a13678dedd25c6d595eb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:RYE666ZH2KNPYGOW3BJV6EKSMQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Byeonghyeon Lee, Eunbyung Park, Namgyu Kang, Seok-Bae Yun, Youngjoon Hong","submitted_at":"2022-07-26T10:46:56Z","abstract_excerpt":"With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12800","kind":"arxiv","version":2},"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/2207.12800/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":"2026-07-05T05:38:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H74rxh3yCXyCC9big+aLYsazAgUBpNlsuT+lfdMGTv5JS0OPrTbMgiYF0bxdNMP7YoYhWpPD0zO9Ipzc7KDpCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T19:08:07.967192Z"},"content_sha256":"ffb552b9260b077e7e45868db3ad96410e8dbdfac497d07304c202f66229dd7b","schema_version":"1.0","event_id":"sha256:ffb552b9260b077e7e45868db3ad96410e8dbdfac497d07304c202f66229dd7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/bundle.json","state_url":"https://pith.science/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/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":"2026-08-20T19:08:07Z","links":{"resolver":"https://pith.science/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ","bundle":"https://pith.science/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/bundle.json","state":"https://pith.science/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RYE666ZH2KNPYGOW3BJV6EKSMQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:RYE666ZH2KNPYGOW3BJV6EKSMQ","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":"2f47399abdbacbbfadec63319373dec354f10eef768abcac6d972740ed2d1921","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-26T10:46:56Z","title_canon_sha256":"f5302a910ac58243d13afc8b63e1478b81d7de8b900db3bce2b2cfe318461c93"},"schema_version":"1.0","source":{"id":"2207.12800","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.12800","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"2207.12800v2","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12800","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"RYE666ZH2KNP","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_16","alias_value":"RYE666ZH2KNPYGOW","created_at":"2026-07-05T05:38:43Z"},{"alias_kind":"pith_short_8","alias_value":"RYE666ZH","created_at":"2026-07-05T05:38:43Z"}],"graph_snapshots":[{"event_id":"sha256:ffb552b9260b077e7e45868db3ad96410e8dbdfac497d07304c202f66229dd7b","target":"graph","created_at":"2026-07-05T05:38:43Z","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/2207.12800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded in various forward and inverse PDE problems thanks to their excellent properties, such as flexibility, mesh-free solutions, and unsupervised training. However, their slower convergence speed and relatively inaccurate solutions often limit their broader applicability in many science and engineering domains. This paper proposes a new kind of data-driven PDEs so","authors_text":"Byeonghyeon Lee, Eunbyung Park, Namgyu Kang, Seok-Bae Yun, Youngjoon Hong","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-26T10:46:56Z","title":"PIXEL: Physics-Informed Cell Representations for Fast and Accurate PDE Solvers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12800","kind":"arxiv","version":2},"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:fd99ab0e57e3cf1e20ce949c46ba99e9b3514b9743f7a13678dedd25c6d595eb","target":"record","created_at":"2026-07-05T05:38:43Z","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":"2f47399abdbacbbfadec63319373dec354f10eef768abcac6d972740ed2d1921","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-07-26T10:46:56Z","title_canon_sha256":"f5302a910ac58243d13afc8b63e1478b81d7de8b900db3bce2b2cfe318461c93"},"schema_version":"1.0","source":{"id":"2207.12800","kind":"arxiv","version":2}},"canonical_sha256":"8e09ef7b27d29afc19d6d8535f1152643b74b16b047a860e95f6fd340b85fa78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e09ef7b27d29afc19d6d8535f1152643b74b16b047a860e95f6fd340b85fa78","first_computed_at":"2026-07-05T05:38:43.481559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:38:43.481559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkiCea/su2q9Hc/ZCARvj/dJNTU8BDwofaE6SWFsQBV4uZKBEjUaiTrngJNfK4i2eyVXxMYnqm99iuSN8XZCDw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:38:43.481957Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.12800","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd99ab0e57e3cf1e20ce949c46ba99e9b3514b9743f7a13678dedd25c6d595eb","sha256:ffb552b9260b077e7e45868db3ad96410e8dbdfac497d07304c202f66229dd7b"],"state_sha256":"cdae36930742153cae6de920303f9cfbeee048523b233a5ec1b0a1c7d4904f5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O04oxRLpGgN7b5gUwLgzrl1hXk0pbfJM+YqUhXyM52Vb0tPQSiD462obT1ZYFnu9gHl+iMS8zGvoW5ZZB0omBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T19:08:07.969544Z","bundle_sha256":"c23d47ddacdd579e816ca7b5a77b6cf661c70d9712bb708ff5780367f53e5885"}}