{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:X5WSZGW7YA6VEJX6OW6QCJAFE2","short_pith_number":"pith:X5WSZGW7","canonical_record":{"source":{"id":"2306.06333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-10T02:20:28Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"5d4569035211e66ddcbbe4a9ed1fd82d6317465d563e9c7886167da7b3fd549e","abstract_canon_sha256":"8bb9a00f91b6fc23e82ed5c84555952230a99ca120cf72c9db3860b85aefbc31"},"schema_version":"1.0"},"canonical_sha256":"bf6d2c9adfc03d5226fe75bd01240526a16efe889a129782ed2b7fbbf3b1ec92","source":{"kind":"arxiv","id":"2306.06333","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.06333","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"2306.06333v3","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.06333","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"X5WSZGW7YA6V","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_16","alias_value":"X5WSZGW7YA6VEJX6","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_8","alias_value":"X5WSZGW7","created_at":"2026-07-05T10:34:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:X5WSZGW7YA6VEJX6OW6QCJAFE2","target":"record","payload":{"canonical_record":{"source":{"id":"2306.06333","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-10T02:20:28Z","cross_cats_sorted":["cs.NA","physics.comp-ph"],"title_canon_sha256":"5d4569035211e66ddcbbe4a9ed1fd82d6317465d563e9c7886167da7b3fd549e","abstract_canon_sha256":"8bb9a00f91b6fc23e82ed5c84555952230a99ca120cf72c9db3860b85aefbc31"},"schema_version":"1.0"},"canonical_sha256":"bf6d2c9adfc03d5226fe75bd01240526a16efe889a129782ed2b7fbbf3b1ec92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:34:36.687186Z","signature_b64":"hpRujCdRzgQvTTkxekZa6prBXGQsFRJVnagyJU1BBOJggmYAuEX9RdBryLYmUX12nvS17O++QuEldqpqkUupBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf6d2c9adfc03d5226fe75bd01240526a16efe889a129782ed2b7fbbf3b1ec92","last_reissued_at":"2026-07-05T10:34:36.686640Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:34:36.686640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2306.06333","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pUQb3UQ2XE1eN71Ak8RJN2/dbzF4djL8/Iq8Sj75lBDZafqS6GMbNS0lczvraJCM/2PTVcY+OI0YMpqBowomBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:49:59.036686Z"},"content_sha256":"4213154e8c12ae1b23ed317af3f54b1a61f151441400a69ff584f070d0316b8a","schema_version":"1.0","event_id":"sha256:4213154e8c12ae1b23ed317af3f54b1a61f151441400a69ff584f070d0316b8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:X5WSZGW7YA6VEJX6OW6QCJAFE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A hybrid neural-network and MAC scheme for Stokes interface problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Che-Chia Chang, Chen-Yang Dai, Ming-Chih Lai, Te-Sheng Lin, Wei-Fan Hu","submitted_at":"2023-06-10T02:20:28Z","abstract_excerpt":"In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As known, the solution variables (the pressure and velocity) exhibit non-smooth behaviors across the interface so extra discretization efforts must be paid near the interface in order to have small order of local truncation errors in finite difference schemes. The present hybrid approach avoids such additional difficulty. It combines the expressive power of neural networks with the convergence of finite difference sche"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.06333","kind":"arxiv","version":3},"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/2306.06333/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":"2026-07-05T10:34:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TPXbRyzJAycqUygz046+3qmpGS4kwvoKTuuiMR/dx1x3p43AQ6r4i7ab8TUhSIadw1SKcU9HfTIaiy31UtstAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T07:49:59.037096Z"},"content_sha256":"d3ffe16169806d452a1da513c3b3f23638970932dc10c59e35b65aa50450a552","schema_version":"1.0","event_id":"sha256:d3ffe16169806d452a1da513c3b3f23638970932dc10c59e35b65aa50450a552"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/bundle.json","state_url":"https://pith.science/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/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":"2026-07-07T07:49:59Z","links":{"resolver":"https://pith.science/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2","bundle":"https://pith.science/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/bundle.json","state":"https://pith.science/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5WSZGW7YA6VEJX6OW6QCJAFE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:X5WSZGW7YA6VEJX6OW6QCJAFE2","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":"8bb9a00f91b6fc23e82ed5c84555952230a99ca120cf72c9db3860b85aefbc31","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-10T02:20:28Z","title_canon_sha256":"5d4569035211e66ddcbbe4a9ed1fd82d6317465d563e9c7886167da7b3fd549e"},"schema_version":"1.0","source":{"id":"2306.06333","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.06333","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"arxiv_version","alias_value":"2306.06333v3","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.06333","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_12","alias_value":"X5WSZGW7YA6V","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_16","alias_value":"X5WSZGW7YA6VEJX6","created_at":"2026-07-05T10:34:36Z"},{"alias_kind":"pith_short_8","alias_value":"X5WSZGW7","created_at":"2026-07-05T10:34:36Z"}],"graph_snapshots":[{"event_id":"sha256:d3ffe16169806d452a1da513c3b3f23638970932dc10c59e35b65aa50450a552","target":"graph","created_at":"2026-07-05T10:34:36Z","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/2306.06333/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we present a hybrid neural-network and MAC (Marker-And-Cell) scheme for solving Stokes equations with singular forces on an embedded interface in regular domains. As known, the solution variables (the pressure and velocity) exhibit non-smooth behaviors across the interface so extra discretization efforts must be paid near the interface in order to have small order of local truncation errors in finite difference schemes. The present hybrid approach avoids such additional difficulty. It combines the expressive power of neural networks with the convergence of finite difference sche","authors_text":"Che-Chia Chang, Chen-Yang Dai, Ming-Chih Lai, Te-Sheng Lin, Wei-Fan Hu","cross_cats":["cs.NA","physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-10T02:20:28Z","title":"A hybrid neural-network and MAC scheme for Stokes interface problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.06333","kind":"arxiv","version":3},"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":"sha256:4213154e8c12ae1b23ed317af3f54b1a61f151441400a69ff584f070d0316b8a","target":"record","created_at":"2026-07-05T10:34:36Z","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":"8bb9a00f91b6fc23e82ed5c84555952230a99ca120cf72c9db3860b85aefbc31","cross_cats_sorted":["cs.NA","physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-06-10T02:20:28Z","title_canon_sha256":"5d4569035211e66ddcbbe4a9ed1fd82d6317465d563e9c7886167da7b3fd549e"},"schema_version":"1.0","source":{"id":"2306.06333","kind":"arxiv","version":3}},"canonical_sha256":"bf6d2c9adfc03d5226fe75bd01240526a16efe889a129782ed2b7fbbf3b1ec92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf6d2c9adfc03d5226fe75bd01240526a16efe889a129782ed2b7fbbf3b1ec92","first_computed_at":"2026-07-05T10:34:36.686640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:34:36.686640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hpRujCdRzgQvTTkxekZa6prBXGQsFRJVnagyJU1BBOJggmYAuEX9RdBryLYmUX12nvS17O++QuEldqpqkUupBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:34:36.687186Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.06333","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4213154e8c12ae1b23ed317af3f54b1a61f151441400a69ff584f070d0316b8a","sha256:d3ffe16169806d452a1da513c3b3f23638970932dc10c59e35b65aa50450a552"],"state_sha256":"94b130734e397f4994e592aeaaf240510f86bc63aadb0360e38cbc57605d5d3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M8AqphvT0AQBBaJx3y102scoKC9dQBqT9T1LTEOoXqdedbE+lUmeBctN+LxqWA+MPU0AJT3KPBBFaXoKeMkfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T07:49:59.039692Z","bundle_sha256":"bf7554337ef5334f20593ab2c4bcf77aec3263e637e1eda6064159e1a47847af"}}