{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RW7XWFCJ5JBZPMTH43UV2JHMXQ","short_pith_number":"pith:RW7XWFCJ","canonical_record":{"source":{"id":"2411.01998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-04T11:35:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"616aa317563c79a954c9882bd11bd289a34cf4ccd4b6d5476fe89d303a591bd9","abstract_canon_sha256":"b4e453128a601e05d18ff36d3e2d3fe0dc0afbab4db7e7127dc541a8429f27bb"},"schema_version":"1.0"},"canonical_sha256":"8dbf7b1449ea4397b267e6e95d24ecbc09f1b08f2ac51233cb6025d896de460e","source":{"kind":"arxiv","id":"2411.01998","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.01998","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"2411.01998v1","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01998","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"RW7XWFCJ5JBZ","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"RW7XWFCJ5JBZPMTH","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"RW7XWFCJ","created_at":"2026-07-05T09:30:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RW7XWFCJ5JBZPMTH43UV2JHMXQ","target":"record","payload":{"canonical_record":{"source":{"id":"2411.01998","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-04T11:35:57Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"616aa317563c79a954c9882bd11bd289a34cf4ccd4b6d5476fe89d303a591bd9","abstract_canon_sha256":"b4e453128a601e05d18ff36d3e2d3fe0dc0afbab4db7e7127dc541a8429f27bb"},"schema_version":"1.0"},"canonical_sha256":"8dbf7b1449ea4397b267e6e95d24ecbc09f1b08f2ac51233cb6025d896de460e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:39.932271Z","signature_b64":"mP9iIhd+Vz9R7BcOJvRGtSbLbUOuFptD1sQlGapSGhHiSLqtVZQ7Sb+BtDT8xQ43Xja1m+toigHv5mDaQRTzBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dbf7b1449ea4397b267e6e95d24ecbc09f1b08f2ac51233cb6025d896de460e","last_reissued_at":"2026-07-05T09:30:39.931760Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:39.931760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.01998","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":"2026-07-05T09:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UGdyZt32xd8VlbqorVfRc6JF4mWlZxMvCWbP1D/LHLCpNe9qz4SWkaYRCF0E1ToOZFUb7egJVRJpOoKmNvOtAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:59:31.643212Z"},"content_sha256":"97976cc79be0877463481b010a9546a9be64016d6c01a448a7e5c25e76791076","schema_version":"1.0","event_id":"sha256:97976cc79be0877463481b010a9546a9be64016d6c01a448a7e5c25e76791076"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RW7XWFCJ5JBZPMTH43UV2JHMXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Adaptive neural network basis methods for partial differential equations with low-regular solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Haohao Wu, Jianguo Huang, Tao Zhou","submitted_at":"2024-11-04T11:35:57Z","abstract_excerpt":"This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining basis functions from a class of shallow neural networks and the resulting multi-scale analogues, a residual strategy in adaptive methods and the non-overlapping domain decomposition method. At the beginning, in view of the solution residual, we partition the total domain $\\Omega$ into $K+1$ non-overlapping subdomains, denoted respectively as $\\{\\Omega_k\\}_{k"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01998","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/2411.01998/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":"2026-07-05T09:30:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9oOdE8npGdDBpIxkkDy83OSKjXiIQfrS0/HE98Xyy5yXvMQglzqjEeXsaRn6hEFKnQzR58FE0wDlzPdJ7kwyDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T08:59:31.644016Z"},"content_sha256":"d46a794a00ad43c7f004e79df35004df04e01529245c3972ff402ecc4e51137f","schema_version":"1.0","event_id":"sha256:d46a794a00ad43c7f004e79df35004df04e01529245c3972ff402ecc4e51137f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/bundle.json","state_url":"https://pith.science/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/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":"2026-08-10T08:59:31Z","links":{"resolver":"https://pith.science/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ","bundle":"https://pith.science/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/bundle.json","state":"https://pith.science/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RW7XWFCJ5JBZPMTH43UV2JHMXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RW7XWFCJ5JBZPMTH43UV2JHMXQ","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":"b4e453128a601e05d18ff36d3e2d3fe0dc0afbab4db7e7127dc541a8429f27bb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-04T11:35:57Z","title_canon_sha256":"616aa317563c79a954c9882bd11bd289a34cf4ccd4b6d5476fe89d303a591bd9"},"schema_version":"1.0","source":{"id":"2411.01998","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.01998","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"arxiv_version","alias_value":"2411.01998v1","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.01998","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_12","alias_value":"RW7XWFCJ5JBZ","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"RW7XWFCJ5JBZPMTH","created_at":"2026-07-05T09:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"RW7XWFCJ","created_at":"2026-07-05T09:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:d46a794a00ad43c7f004e79df35004df04e01529245c3972ff402ecc4e51137f","target":"graph","created_at":"2026-07-05T09:30:39Z","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/2411.01998/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining basis functions from a class of shallow neural networks and the resulting multi-scale analogues, a residual strategy in adaptive methods and the non-overlapping domain decomposition method. At the beginning, in view of the solution residual, we partition the total domain $\\Omega$ into $K+1$ non-overlapping subdomains, denoted respectively as $\\{\\Omega_k\\}_{k","authors_text":"Haohao Wu, Jianguo Huang, Tao Zhou","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-04T11:35:57Z","title":"Adaptive neural network basis methods for partial differential equations with low-regular solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01998","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":"sha256:97976cc79be0877463481b010a9546a9be64016d6c01a448a7e5c25e76791076","target":"record","created_at":"2026-07-05T09:30:39Z","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":"b4e453128a601e05d18ff36d3e2d3fe0dc0afbab4db7e7127dc541a8429f27bb","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-04T11:35:57Z","title_canon_sha256":"616aa317563c79a954c9882bd11bd289a34cf4ccd4b6d5476fe89d303a591bd9"},"schema_version":"1.0","source":{"id":"2411.01998","kind":"arxiv","version":1}},"canonical_sha256":"8dbf7b1449ea4397b267e6e95d24ecbc09f1b08f2ac51233cb6025d896de460e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dbf7b1449ea4397b267e6e95d24ecbc09f1b08f2ac51233cb6025d896de460e","first_computed_at":"2026-07-05T09:30:39.931760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:39.931760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mP9iIhd+Vz9R7BcOJvRGtSbLbUOuFptD1sQlGapSGhHiSLqtVZQ7Sb+BtDT8xQ43Xja1m+toigHv5mDaQRTzBA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:39.932271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.01998","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97976cc79be0877463481b010a9546a9be64016d6c01a448a7e5c25e76791076","sha256:d46a794a00ad43c7f004e79df35004df04e01529245c3972ff402ecc4e51137f"],"state_sha256":"3f28433f319465c45e4b3a69f446256803853d195ae80b9c14652792db63b169"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TvlFlgDsV76ygy4gJlLnaRkfBliZlUSAphBubEl7BoVdzlc+h6ugyxYpUpqzW480ZGUsUgDYpfLPRPmyV+LkBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T08:59:31.648622Z","bundle_sha256":"9dc646ff04b80df4ae8623659ff0ecf2aa5d7bafdb32e5a0d615e3f18c6d9fcd"}}