{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:G45JAKS4HP726TN5WNWB2IYSZB","short_pith_number":"pith:G45JAKS4","canonical_record":{"source":{"id":"2503.05598","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CE","submitted_at":"2025-03-07T17:25:25Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0497208a27ce35989d61f5ec2b7d7a5584d53d13c82881745a25a6372e6d3414","abstract_canon_sha256":"25dc3a8364ff86d3b57d0bee7f0b9fe76efefa2369a2e732c9ebf53c17c128a0"},"schema_version":"1.0"},"canonical_sha256":"373a902a5c3bffaf4dbdb36c1d2312c8750fe3a8a780a034d1aa2fe713c59e9a","source":{"kind":"arxiv","id":"2503.05598","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05598","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05598v2","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05598","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"G45JAKS4HP72","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"G45JAKS4HP726TN5","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"G45JAKS4","created_at":"2026-06-19T16:10:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:G45JAKS4HP726TN5WNWB2IYSZB","target":"record","payload":{"canonical_record":{"source":{"id":"2503.05598","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CE","submitted_at":"2025-03-07T17:25:25Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"0497208a27ce35989d61f5ec2b7d7a5584d53d13c82881745a25a6372e6d3414","abstract_canon_sha256":"25dc3a8364ff86d3b57d0bee7f0b9fe76efefa2369a2e732c9ebf53c17c128a0"},"schema_version":"1.0"},"canonical_sha256":"373a902a5c3bffaf4dbdb36c1d2312c8750fe3a8a780a034d1aa2fe713c59e9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:29.356575Z","signature_b64":"0HyjHZCBLkuihjLFCjp2yB8r2j5EwaLZkZ8iJDfRsM2u5Y0hVKhz58GPNjr1ADLT+3z9N56b83TrcvfAKbj1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"373a902a5c3bffaf4dbdb36c1d2312c8750fe3a8a780a034d1aa2fe713c59e9a","last_reissued_at":"2026-06-19T16:10:29.356145Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:29.356145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.05598","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":"2026-06-19T16:10:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YLGxX62fKpyk/NNuLoRNShODb0iSlqwUViG1ph6cB4LWRFOw2hY7N4HSg/FNLVgbm30QNqOXUtVKDRkA1W8EBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:43:43.450591Z"},"content_sha256":"d07aaed4916157aedd23b3a628c76a014afc733fe1a7579f11dbba65a83d3803","schema_version":"1.0","event_id":"sha256:d07aaed4916157aedd23b3a628c76a014afc733fe1a7579f11dbba65a83d3803"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:G45JAKS4HP726TN5WNWB2IYSZB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CE","authors_text":"Prashant K. Jha","submitted_at":"2025-03-07T17:25:25Z","abstract_excerpt":"This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key found"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05598","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/2503.05598/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":"2026-06-19T16:10:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3kOcvdU63Pi9D32Vgf0WIhaF3K3ctSYSZOvllj6DdBrYJWHiy4vPn6EYnXJ5Bd7lh4G1omdN12wsHfCNYAZcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:43:43.450980Z"},"content_sha256":"28c0e5733f6a6a94793111c38e17586df68ad4a6d09ee35f8531291f4d00b0a8","schema_version":"1.0","event_id":"sha256:28c0e5733f6a6a94793111c38e17586df68ad4a6d09ee35f8531291f4d00b0a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G45JAKS4HP726TN5WNWB2IYSZB/bundle.json","state_url":"https://pith.science/pith/G45JAKS4HP726TN5WNWB2IYSZB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G45JAKS4HP726TN5WNWB2IYSZB/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":"2026-06-23T19:43:43Z","links":{"resolver":"https://pith.science/pith/G45JAKS4HP726TN5WNWB2IYSZB","bundle":"https://pith.science/pith/G45JAKS4HP726TN5WNWB2IYSZB/bundle.json","state":"https://pith.science/pith/G45JAKS4HP726TN5WNWB2IYSZB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G45JAKS4HP726TN5WNWB2IYSZB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:G45JAKS4HP726TN5WNWB2IYSZB","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":"25dc3a8364ff86d3b57d0bee7f0b9fe76efefa2369a2e732c9ebf53c17c128a0","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CE","submitted_at":"2025-03-07T17:25:25Z","title_canon_sha256":"0497208a27ce35989d61f5ec2b7d7a5584d53d13c82881745a25a6372e6d3414"},"schema_version":"1.0","source":{"id":"2503.05598","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.05598","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"arxiv_version","alias_value":"2503.05598v2","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.05598","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_12","alias_value":"G45JAKS4HP72","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_16","alias_value":"G45JAKS4HP726TN5","created_at":"2026-06-19T16:10:29Z"},{"alias_kind":"pith_short_8","alias_value":"G45JAKS4","created_at":"2026-06-19T16:10:29Z"}],"graph_snapshots":[{"event_id":"sha256:28c0e5733f6a6a94793111c38e17586df68ad4a6d09ee35f8531291f4d00b0a8","target":"graph","created_at":"2026-06-19T16:10:29Z","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/2503.05598/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This review examines neural operator architectures for learning solution operators of parametric partial differential equations (PDEs), with an emphasis on conceptual clarity and practical implementation. The work analyzes key models, including DeepONet, PCANet, and the Fourier Neural Operator, highlighting their underlying representations, computational structures, and comparative performance. These architectures are demonstrated on three canonical PDE problems: the Poisson equation, a linear elasticity problem, and a hyperelasticity problem. To make the presentation self-contained, key found","authors_text":"Prashant K. Jha","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CE","submitted_at":"2025-03-07T17:25:25Z","title":"From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.05598","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:d07aaed4916157aedd23b3a628c76a014afc733fe1a7579f11dbba65a83d3803","target":"record","created_at":"2026-06-19T16:10:29Z","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":"25dc3a8364ff86d3b57d0bee7f0b9fe76efefa2369a2e732c9ebf53c17c128a0","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.CE","submitted_at":"2025-03-07T17:25:25Z","title_canon_sha256":"0497208a27ce35989d61f5ec2b7d7a5584d53d13c82881745a25a6372e6d3414"},"schema_version":"1.0","source":{"id":"2503.05598","kind":"arxiv","version":2}},"canonical_sha256":"373a902a5c3bffaf4dbdb36c1d2312c8750fe3a8a780a034d1aa2fe713c59e9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"373a902a5c3bffaf4dbdb36c1d2312c8750fe3a8a780a034d1aa2fe713c59e9a","first_computed_at":"2026-06-19T16:10:29.356145Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:29.356145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0HyjHZCBLkuihjLFCjp2yB8r2j5EwaLZkZ8iJDfRsM2u5Y0hVKhz58GPNjr1ADLT+3z9N56b83TrcvfAKbj1Bw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:29.356575Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.05598","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d07aaed4916157aedd23b3a628c76a014afc733fe1a7579f11dbba65a83d3803","sha256:28c0e5733f6a6a94793111c38e17586df68ad4a6d09ee35f8531291f4d00b0a8"],"state_sha256":"1028aa565f4b182a4daf4fb548f50b2b9f81a6b0c30fedc0f7c8b8f94c9ae8d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPaMEKLmGoX/ZGcP+B5N6bf8MdJikd/1vmOATAJbIhKKG0aU5W7+rvga65uzzc+z/dW5JSh3tBCwQnherVWxCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:43:43.453373Z","bundle_sha256":"ce0a0db8ca5edff0fae906b45292b0690d4b992324a33fb430e91b6722bb8d44"}}