{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:BVB2GRFF7R47FV4N5ANPTZQM4B","short_pith_number":"pith:BVB2GRFF","canonical_record":{"source":{"id":"2503.04056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-03-06T03:16:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4e7c70bb08fdc101f0061e2eeabe0bb019b42e3467908eed10a42b33a28e81c0","abstract_canon_sha256":"e1a2d83a263980f73dcebb2b6a4b28d0a96843c3f03c88a63b926d1a59e1c185"},"schema_version":"1.0"},"canonical_sha256":"0d43a344a5fc79f2d78de81af9e60ce0504ca14ad121dddf11e9d111ff85a2f5","source":{"kind":"arxiv","id":"2503.04056","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04056","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04056v1","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04056","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"BVB2GRFF7R47","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_16","alias_value":"BVB2GRFF7R47FV4N","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_8","alias_value":"BVB2GRFF","created_at":"2026-07-05T10:25:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:BVB2GRFF7R47FV4N5ANPTZQM4B","target":"record","payload":{"canonical_record":{"source":{"id":"2503.04056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-03-06T03:16:54Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4e7c70bb08fdc101f0061e2eeabe0bb019b42e3467908eed10a42b33a28e81c0","abstract_canon_sha256":"e1a2d83a263980f73dcebb2b6a4b28d0a96843c3f03c88a63b926d1a59e1c185"},"schema_version":"1.0"},"canonical_sha256":"0d43a344a5fc79f2d78de81af9e60ce0504ca14ad121dddf11e9d111ff85a2f5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:25:27.640180Z","signature_b64":"LIphjYJ8eTSaf7xqbTl7ccJyKlLUKS7wlbzLHq5/+SAhkUKic2YWbwGDZwKP7Wmm6oiwPKVTvOtAvACAGo1lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d43a344a5fc79f2d78de81af9e60ce0504ca14ad121dddf11e9d111ff85a2f5","last_reissued_at":"2026-07-05T10:25:27.639586Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:25:27.639586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2503.04056","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":"2026-07-05T10:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DipxyIXBXzTDQRdVKyaQHfQmf/M6GRDSFZfIG5+VWK4c7+u6EeFOOvhDUkJ9+h7XwAl9wC9ECp4ZL/g7o7ySBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:20:41.925787Z"},"content_sha256":"f4d5a333f096fe9b3a30e8694867c6c9809c84cfa133a15a02a75b0e3d697f7d","schema_version":"1.0","event_id":"sha256:f4d5a333f096fe9b3a30e8694867c6c9809c84cfa133a15a02a75b0e3d697f7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:BVB2GRFF7R47FV4N5ANPTZQM4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient-enhanced PINN with residual unit for studying forward-inverse problems of variable coefficient equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.comp-ph","authors_text":"Hui-Juan Zhou, Yong Chen","submitted_at":"2025-03-06T03:16:54Z","abstract_excerpt":"Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena, are of considerable physical significance and research value. This study proposes a gradient-enhanced PINN with residual unit (R-gPINN) method to solve the data-driven solution and function discovery for variable coefficient PDEs. On the one hand, the proposed method incorporates residual units into the neural networks to mitigate gradient vanishing and net"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04056","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/2503.04056/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":"2026-07-05T10:25:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u9aiSpGmp+8N8T3+9kD8jUuBTlp2ZZ8XO50v2ihStGgj24GrGgQHbqfgrYm+uiFH1dpoKMm0OuyxF3/+FzwXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T20:20:41.926737Z"},"content_sha256":"ceed365c4b9099fede589844b1ad06521d7eed3f926537d5083107dc202a8be3","schema_version":"1.0","event_id":"sha256:ceed365c4b9099fede589844b1ad06521d7eed3f926537d5083107dc202a8be3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/bundle.json","state_url":"https://pith.science/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/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":"2026-08-04T20:20:41Z","links":{"resolver":"https://pith.science/pith/BVB2GRFF7R47FV4N5ANPTZQM4B","bundle":"https://pith.science/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/bundle.json","state":"https://pith.science/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BVB2GRFF7R47FV4N5ANPTZQM4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BVB2GRFF7R47FV4N5ANPTZQM4B","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":"e1a2d83a263980f73dcebb2b6a4b28d0a96843c3f03c88a63b926d1a59e1c185","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-03-06T03:16:54Z","title_canon_sha256":"4e7c70bb08fdc101f0061e2eeabe0bb019b42e3467908eed10a42b33a28e81c0"},"schema_version":"1.0","source":{"id":"2503.04056","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.04056","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"2503.04056v1","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.04056","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"BVB2GRFF7R47","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_16","alias_value":"BVB2GRFF7R47FV4N","created_at":"2026-07-05T10:25:27Z"},{"alias_kind":"pith_short_8","alias_value":"BVB2GRFF","created_at":"2026-07-05T10:25:27Z"}],"graph_snapshots":[{"event_id":"sha256:ceed365c4b9099fede589844b1ad06521d7eed3f926537d5083107dc202a8be3","target":"graph","created_at":"2026-07-05T10:25:27Z","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/2503.04056/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena, are of considerable physical significance and research value. This study proposes a gradient-enhanced PINN with residual unit (R-gPINN) method to solve the data-driven solution and function discovery for variable coefficient PDEs. On the one hand, the proposed method incorporates residual units into the neural networks to mitigate gradient vanishing and net","authors_text":"Hui-Juan Zhou, Yong Chen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-03-06T03:16:54Z","title":"Gradient-enhanced PINN with residual unit for studying forward-inverse problems of variable coefficient equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.04056","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:f4d5a333f096fe9b3a30e8694867c6c9809c84cfa133a15a02a75b0e3d697f7d","target":"record","created_at":"2026-07-05T10:25:27Z","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":"e1a2d83a263980f73dcebb2b6a4b28d0a96843c3f03c88a63b926d1a59e1c185","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2025-03-06T03:16:54Z","title_canon_sha256":"4e7c70bb08fdc101f0061e2eeabe0bb019b42e3467908eed10a42b33a28e81c0"},"schema_version":"1.0","source":{"id":"2503.04056","kind":"arxiv","version":1}},"canonical_sha256":"0d43a344a5fc79f2d78de81af9e60ce0504ca14ad121dddf11e9d111ff85a2f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d43a344a5fc79f2d78de81af9e60ce0504ca14ad121dddf11e9d111ff85a2f5","first_computed_at":"2026-07-05T10:25:27.639586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:25:27.639586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LIphjYJ8eTSaf7xqbTl7ccJyKlLUKS7wlbzLHq5/+SAhkUKic2YWbwGDZwKP7Wmm6oiwPKVTvOtAvACAGo1lDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:25:27.640180Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.04056","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d5a333f096fe9b3a30e8694867c6c9809c84cfa133a15a02a75b0e3d697f7d","sha256:ceed365c4b9099fede589844b1ad06521d7eed3f926537d5083107dc202a8be3"],"state_sha256":"48fdac4651a5cf71d02525bc0f09a0f3948e4838ae1fb943b309afd2063283fa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItkeHRYSuCiS2lfMltXqHmZpqmbU0pcGcf6+2lXcH/40UVZgKc8kUCTyCGjZYBHO3k8i0zMGwnUiwbbv2Wo6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T20:20:41.933094Z","bundle_sha256":"c3f5b37c127e1c88d53995d615892b0f11cb5b80694bd837224497000da7a15a"}}