{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:EWB4TVP3M4PR2B6AYTD5V4L2AO","short_pith_number":"pith:EWB4TVP3","canonical_record":{"source":{"id":"2312.11093","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-18T10:46:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"65a31eaccce86e90d305986997201290c6fea3fc0894577f130019e04b2e4ad1","abstract_canon_sha256":"439a2e399b04d30857be1320f81262542ccb2a965e93ddcf872a258e93f11d30"},"schema_version":"1.0"},"canonical_sha256":"2583c9d5fb671f1d07c0c4c7daf17a038f8fb2fb8ffbe52063734c49be10ce69","source":{"kind":"arxiv","id":"2312.11093","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11093","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11093v2","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11093","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"EWB4TVP3M4PR","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"EWB4TVP3M4PR2B6A","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"EWB4TVP3","created_at":"2026-07-05T08:17:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:EWB4TVP3M4PR2B6AYTD5V4L2AO","target":"record","payload":{"canonical_record":{"source":{"id":"2312.11093","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-18T10:46:16Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"65a31eaccce86e90d305986997201290c6fea3fc0894577f130019e04b2e4ad1","abstract_canon_sha256":"439a2e399b04d30857be1320f81262542ccb2a965e93ddcf872a258e93f11d30"},"schema_version":"1.0"},"canonical_sha256":"2583c9d5fb671f1d07c0c4c7daf17a038f8fb2fb8ffbe52063734c49be10ce69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:17:12.246066Z","signature_b64":"3ZXyqoLBoJJEa0wvQKtmy3BQdlAgB1NhhXawjN0/vTjncsu3RnfzzNADIgxaah7ID4fG57SDdAn8Mq7SwpbRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2583c9d5fb671f1d07c0c4c7daf17a038f8fb2fb8ffbe52063734c49be10ce69","last_reissued_at":"2026-07-05T08:17:12.245692Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:17:12.245692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.11093","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":"2026-07-05T08:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TEw45Ppm1xkBZZQGVXVZI8DkizMpfmxla4qjGAaSihxIGe0iVtJdNqI22brMKPwa1SFU/9cJ11c7fUVkfD1NCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:34:40.886383Z"},"content_sha256":"2a8a04f6e9ad2b4d2aba4d52d92af97e7070858ffa62dc18d7831a873a8c696b","schema_version":"1.0","event_id":"sha256:2a8a04f6e9ad2b4d2aba4d52d92af97e7070858ffa62dc18d7831a873a8c696b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:EWB4TVP3M4PR2B6AYTD5V4L2AO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Chensong Zhang, Minrui Lv, Yan Xie","submitted_at":"2023-12-18T10:46:16Z","abstract_excerpt":"This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the algorithm design process for a class of PDEs through training, which requires only training data of coefficient distributions. The proposed method is anchored by three core principles: (1) a multilevel hierarchy to promote rapid convergence, (2) adherence to linearity concerning the right-hand-side of equations, and (3) weights sharing across different levels "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11093","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/2312.11093/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":"2026-07-05T08:17:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LtQ/TogMV5cWy5J7ZGFfnc+g0hlbzFgI+Ej3YyxHw3d1e/jVTwT9ySNWI0eBLl96JkvB/z3dB48ysz2QMV+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T15:34:40.886710Z"},"content_sha256":"eef1059a6ce3ea9ebb7205a30b5d4018df58cdc4019d855681ea12411e33b54c","schema_version":"1.0","event_id":"sha256:eef1059a6ce3ea9ebb7205a30b5d4018df58cdc4019d855681ea12411e33b54c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/bundle.json","state_url":"https://pith.science/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/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":"2026-08-14T15:34:40Z","links":{"resolver":"https://pith.science/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO","bundle":"https://pith.science/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/bundle.json","state":"https://pith.science/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EWB4TVP3M4PR2B6AYTD5V4L2AO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:EWB4TVP3M4PR2B6AYTD5V4L2AO","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":"439a2e399b04d30857be1320f81262542ccb2a965e93ddcf872a258e93f11d30","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-18T10:46:16Z","title_canon_sha256":"65a31eaccce86e90d305986997201290c6fea3fc0894577f130019e04b2e4ad1"},"schema_version":"1.0","source":{"id":"2312.11093","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.11093","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"2312.11093v2","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.11093","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"EWB4TVP3M4PR","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_16","alias_value":"EWB4TVP3M4PR2B6A","created_at":"2026-07-05T08:17:12Z"},{"alias_kind":"pith_short_8","alias_value":"EWB4TVP3","created_at":"2026-07-05T08:17:12Z"}],"graph_snapshots":[{"event_id":"sha256:eef1059a6ce3ea9ebb7205a30b5d4018df58cdc4019d855681ea12411e33b54c","target":"graph","created_at":"2026-07-05T08:17:12Z","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/2312.11093/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the algorithm design process for a class of PDEs through training, which requires only training data of coefficient distributions. The proposed method is anchored by three core principles: (1) a multilevel hierarchy to promote rapid convergence, (2) adherence to linearity concerning the right-hand-side of equations, and (3) weights sharing across different levels ","authors_text":"Chensong Zhang, Minrui Lv, Yan Xie","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-18T10:46:16Z","title":"MGCNN: a learnable multigrid solver for sparse linear systems from PDEs on structured grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11093","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":"sha256:2a8a04f6e9ad2b4d2aba4d52d92af97e7070858ffa62dc18d7831a873a8c696b","target":"record","created_at":"2026-07-05T08:17:12Z","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":"439a2e399b04d30857be1320f81262542ccb2a965e93ddcf872a258e93f11d30","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2023-12-18T10:46:16Z","title_canon_sha256":"65a31eaccce86e90d305986997201290c6fea3fc0894577f130019e04b2e4ad1"},"schema_version":"1.0","source":{"id":"2312.11093","kind":"arxiv","version":2}},"canonical_sha256":"2583c9d5fb671f1d07c0c4c7daf17a038f8fb2fb8ffbe52063734c49be10ce69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2583c9d5fb671f1d07c0c4c7daf17a038f8fb2fb8ffbe52063734c49be10ce69","first_computed_at":"2026-07-05T08:17:12.245692Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:17:12.245692Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ZXyqoLBoJJEa0wvQKtmy3BQdlAgB1NhhXawjN0/vTjncsu3RnfzzNADIgxaah7ID4fG57SDdAn8Mq7SwpbRAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:17:12.246066Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.11093","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a8a04f6e9ad2b4d2aba4d52d92af97e7070858ffa62dc18d7831a873a8c696b","sha256:eef1059a6ce3ea9ebb7205a30b5d4018df58cdc4019d855681ea12411e33b54c"],"state_sha256":"c1065107a9567c636fb88ca4bd086dce2d4951e84b91ff04d2f7f0359dc938b9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2M597NmmkYjyGqRVUL5BQMNUgaBh/kp+IUKvTLKJw6ugqoRccZPAC2Ed8+qEExV54oCI9Uxbmqkm+jSYIOHcDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T15:34:40.888910Z","bundle_sha256":"e284ddd2671898baa7e691a030e59ec6667a2b4b37e64cc98d9942ea6413283b"}}