{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:CZ7P62CLQTW4AHLLL5CZ7RXRJW","short_pith_number":"pith:CZ7P62CL","canonical_record":{"source":{"id":"2206.12698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-25T17:07:15Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"34ff43901c3c673b38e5dfc6c8b2448cc9f44361c040aa7fdcb2982ef801696e","abstract_canon_sha256":"9928ce44db4c9f3ccd0aa9d6741b74635237b296fc224dadbfd2e475edec9fd3"},"schema_version":"1.0"},"canonical_sha256":"167eff684b84edc01d6b5f459fc6f14d8026d42271ddf0bc848410ef2f071a6b","source":{"kind":"arxiv","id":"2206.12698","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.12698","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"2206.12698v2","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.12698","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"CZ7P62CLQTW4","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_16","alias_value":"CZ7P62CLQTW4AHLL","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_8","alias_value":"CZ7P62CL","created_at":"2026-07-05T05:47:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:CZ7P62CLQTW4AHLLL5CZ7RXRJW","target":"record","payload":{"canonical_record":{"source":{"id":"2206.12698","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-25T17:07:15Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"34ff43901c3c673b38e5dfc6c8b2448cc9f44361c040aa7fdcb2982ef801696e","abstract_canon_sha256":"9928ce44db4c9f3ccd0aa9d6741b74635237b296fc224dadbfd2e475edec9fd3"},"schema_version":"1.0"},"canonical_sha256":"167eff684b84edc01d6b5f459fc6f14d8026d42271ddf0bc848410ef2f071a6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:47:45.295145Z","signature_b64":"1KqS+dmhgOCwvkBbVKNOODaxvX/VkjhBuzCuvPMyJ3LyXx8XvcR5dIEgy9TJDQhaxACB5YtZewL8/vLdKb7gAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"167eff684b84edc01d6b5f459fc6f14d8026d42271ddf0bc848410ef2f071a6b","last_reissued_at":"2026-07-05T05:47:45.294764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:47:45.294764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.12698","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":"2026-07-05T05:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"17aNq3adJlG7J+x9A8A+ncIMURvdhEvKVX03ponjmFF5Yg88EYFWjLcN99le++dQCt5ST4oBJdaGpwyypkNoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:17:20.433900Z"},"content_sha256":"ad3f87630945a5db99b8435aa933c60617cf4aa2969013614fc93cf47d6402e6","schema_version":"1.0","event_id":"sha256:ad3f87630945a5db99b8435aa933c60617cf4aa2969013614fc93cf47d6402e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:CZ7P62CLQTW4AHLLL5CZ7RXRJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"HaiFeng Wang, Hong Zhang, Kaijuna Bao, Songhe Song, Xu Qian, Ziyuan Liu","submitted_at":"2022-06-25T17:07:15Z","abstract_excerpt":"By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as differential equations, but faces concerns about their accuracy and reliability. To overcomes these limitations, combined with the structures of the spectral numerical method, a general neural architecture named spectral operator learning (SOL) is introduced, and one variant called the orthogonal polynomial neural operator (OPNO), developed for PDEs with Diri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.12698","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/2206.12698/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":"2026-07-05T05:47:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+m771j/vjNzqT3YIgb2RLkHlp3HTeHdjhi7q2o8dwVKFE+NnUsHdRGW6joFVRE5A5Jwho71v8fXnn+VWasYGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T23:17:20.434469Z"},"content_sha256":"d0e54567cf781be8e57942ab56563e99d2300d850a331e989bd585d89c0ed47e","schema_version":"1.0","event_id":"sha256:d0e54567cf781be8e57942ab56563e99d2300d850a331e989bd585d89c0ed47e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/bundle.json","state_url":"https://pith.science/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/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":"2026-08-03T23:17:20Z","links":{"resolver":"https://pith.science/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW","bundle":"https://pith.science/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/bundle.json","state":"https://pith.science/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CZ7P62CLQTW4AHLLL5CZ7RXRJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:CZ7P62CLQTW4AHLLL5CZ7RXRJW","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":"9928ce44db4c9f3ccd0aa9d6741b74635237b296fc224dadbfd2e475edec9fd3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-25T17:07:15Z","title_canon_sha256":"34ff43901c3c673b38e5dfc6c8b2448cc9f44361c040aa7fdcb2982ef801696e"},"schema_version":"1.0","source":{"id":"2206.12698","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.12698","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"arxiv_version","alias_value":"2206.12698v2","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.12698","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_12","alias_value":"CZ7P62CLQTW4","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_16","alias_value":"CZ7P62CLQTW4AHLL","created_at":"2026-07-05T05:47:45Z"},{"alias_kind":"pith_short_8","alias_value":"CZ7P62CL","created_at":"2026-07-05T05:47:45Z"}],"graph_snapshots":[{"event_id":"sha256:d0e54567cf781be8e57942ab56563e99d2300d850a331e989bd585d89c0ed47e","target":"graph","created_at":"2026-07-05T05:47:45Z","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/2206.12698/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as differential equations, but faces concerns about their accuracy and reliability. To overcomes these limitations, combined with the structures of the spectral numerical method, a general neural architecture named spectral operator learning (SOL) is introduced, and one variant called the orthogonal polynomial neural operator (OPNO), developed for PDEs with Diri","authors_text":"HaiFeng Wang, Hong Zhang, Kaijuna Bao, Songhe Song, Xu Qian, Ziyuan Liu","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-25T17:07:15Z","title":"Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.12698","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:ad3f87630945a5db99b8435aa933c60617cf4aa2969013614fc93cf47d6402e6","target":"record","created_at":"2026-07-05T05:47:45Z","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":"9928ce44db4c9f3ccd0aa9d6741b74635237b296fc224dadbfd2e475edec9fd3","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2022-06-25T17:07:15Z","title_canon_sha256":"34ff43901c3c673b38e5dfc6c8b2448cc9f44361c040aa7fdcb2982ef801696e"},"schema_version":"1.0","source":{"id":"2206.12698","kind":"arxiv","version":2}},"canonical_sha256":"167eff684b84edc01d6b5f459fc6f14d8026d42271ddf0bc848410ef2f071a6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"167eff684b84edc01d6b5f459fc6f14d8026d42271ddf0bc848410ef2f071a6b","first_computed_at":"2026-07-05T05:47:45.294764Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:47:45.294764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1KqS+dmhgOCwvkBbVKNOODaxvX/VkjhBuzCuvPMyJ3LyXx8XvcR5dIEgy9TJDQhaxACB5YtZewL8/vLdKb7gAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:47:45.295145Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.12698","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad3f87630945a5db99b8435aa933c60617cf4aa2969013614fc93cf47d6402e6","sha256:d0e54567cf781be8e57942ab56563e99d2300d850a331e989bd585d89c0ed47e"],"state_sha256":"260ee6d2956c2e54be0bbccd522bce0b4bbafe208dccaa4b4948dd93be5dd782"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vDJZyWvEqAP6ZF3aPpREYFuXDgTcnfnpDjnbTpR7HCwL3ptGRmh+oYkHFWUjfkEjm1C1k5aABbVeToIkpQPsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T23:17:20.441530Z","bundle_sha256":"476e12880311d46104b9ba76355e013eccc9663da67f3b046afc1270358139db"}}