{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UCQYJH2UHMZOMFCUIPWPEVC7G4","short_pith_number":"pith:UCQYJH2U","canonical_record":{"source":{"id":"2410.06832","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-09T12:45:27Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b9262049c3aa816521e45eb6e0d8286004d8855e48b10a0b837675b6efc841bb","abstract_canon_sha256":"5aa0e888375cdbb709b608677402e60f3714cf0e35af0a92bcc01c0af5fb831e"},"schema_version":"1.0"},"canonical_sha256":"a0a1849f543b32e6145443ecf2545f37111fe38ec87369b61679bebdefcf6e02","source":{"kind":"arxiv","id":"2410.06832","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.06832","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"2410.06832v2","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.06832","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"UCQYJH2UHMZO","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_16","alias_value":"UCQYJH2UHMZOMFCU","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_8","alias_value":"UCQYJH2U","created_at":"2026-07-05T09:59:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UCQYJH2UHMZOMFCUIPWPEVC7G4","target":"record","payload":{"canonical_record":{"source":{"id":"2410.06832","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-09T12:45:27Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"b9262049c3aa816521e45eb6e0d8286004d8855e48b10a0b837675b6efc841bb","abstract_canon_sha256":"5aa0e888375cdbb709b608677402e60f3714cf0e35af0a92bcc01c0af5fb831e"},"schema_version":"1.0"},"canonical_sha256":"a0a1849f543b32e6145443ecf2545f37111fe38ec87369b61679bebdefcf6e02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:59:53.817585Z","signature_b64":"vqhC48a7D5lXq4fJ63gLpvBJeXeqBRVbRlLT381f9zCWcn0RggAunRFF0z6XbfcF64dwXFzj56TtSav8vPzjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0a1849f543b32e6145443ecf2545f37111fe38ec87369b61679bebdefcf6e02","last_reissued_at":"2026-07-05T09:59:53.817074Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:59:53.817074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.06832","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":"2026-07-05T09:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/o5mIPD6zKhJd41EuUXV/Ycgcv7gwycxaRjajIEEuOcGV1k4gtquN3h9JF4iUUabLn8Q3yU/3+ChIqks8ilWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:02:15.639512Z"},"content_sha256":"6e485e84579f33209da24d08667576eab825593b4ffa15072de756344f42154e","schema_version":"1.0","event_id":"sha256:6e485e84579f33209da24d08667576eab825593b4ffa15072de756344f42154e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UCQYJH2UHMZOMFCUIPWPEVC7G4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning a generalized multiscale prolongation operator","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Changqing Ye, Eric T. Chung, Shubin Fu, Yingjie Zhou, Yucheng Liu","submitted_at":"2024-10-09T12:45:27Z","abstract_excerpt":"In this research, we address Darcy flow problems with random permeability using iterative solvers, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for high contrast profiles. To circumvent the need for repeatedly solving spectral problems with varying coefficients, we harness deep learning techniques to expedite the construction of the generalized multiscale prolongation operator. Considering linear transformations on multiscale basis have no impact on the performance of the preconditioner, we devise a loss"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06832","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/2410.06832/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":"2026-07-05T09:59:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Vp/BrPcL46/e2YSJ32q6ubYTMrUw0bmTtDT8uBLs9yFlmWDjqmA+zeMjkBlaWrwrpton9shKPKIAP1rFRFHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T19:02:15.641458Z"},"content_sha256":"2d3043a163f35df7ba1d7d7822b20f9c8f01aa19e661b1dd876184831c4069e6","schema_version":"1.0","event_id":"sha256:2d3043a163f35df7ba1d7d7822b20f9c8f01aa19e661b1dd876184831c4069e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/bundle.json","state_url":"https://pith.science/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/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":"2026-08-14T19:02:15Z","links":{"resolver":"https://pith.science/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4","bundle":"https://pith.science/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/bundle.json","state":"https://pith.science/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCQYJH2UHMZOMFCUIPWPEVC7G4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UCQYJH2UHMZOMFCUIPWPEVC7G4","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":"5aa0e888375cdbb709b608677402e60f3714cf0e35af0a92bcc01c0af5fb831e","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-09T12:45:27Z","title_canon_sha256":"b9262049c3aa816521e45eb6e0d8286004d8855e48b10a0b837675b6efc841bb"},"schema_version":"1.0","source":{"id":"2410.06832","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.06832","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"arxiv_version","alias_value":"2410.06832v2","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.06832","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_12","alias_value":"UCQYJH2UHMZO","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_16","alias_value":"UCQYJH2UHMZOMFCU","created_at":"2026-07-05T09:59:53Z"},{"alias_kind":"pith_short_8","alias_value":"UCQYJH2U","created_at":"2026-07-05T09:59:53Z"}],"graph_snapshots":[{"event_id":"sha256:2d3043a163f35df7ba1d7d7822b20f9c8f01aa19e661b1dd876184831c4069e6","target":"graph","created_at":"2026-07-05T09:59:53Z","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/2410.06832/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this research, we address Darcy flow problems with random permeability using iterative solvers, enhanced by a two-grid preconditioner based on a generalized multiscale prolongation operator, which has been demonstrated to be stable for high contrast profiles. To circumvent the need for repeatedly solving spectral problems with varying coefficients, we harness deep learning techniques to expedite the construction of the generalized multiscale prolongation operator. Considering linear transformations on multiscale basis have no impact on the performance of the preconditioner, we devise a loss","authors_text":"Changqing Ye, Eric T. Chung, Shubin Fu, Yingjie Zhou, Yucheng Liu","cross_cats":["cs.NA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-09T12:45:27Z","title":"Learning a generalized multiscale prolongation operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06832","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":"sha256:6e485e84579f33209da24d08667576eab825593b4ffa15072de756344f42154e","target":"record","created_at":"2026-07-05T09:59:53Z","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":"5aa0e888375cdbb709b608677402e60f3714cf0e35af0a92bcc01c0af5fb831e","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2024-10-09T12:45:27Z","title_canon_sha256":"b9262049c3aa816521e45eb6e0d8286004d8855e48b10a0b837675b6efc841bb"},"schema_version":"1.0","source":{"id":"2410.06832","kind":"arxiv","version":2}},"canonical_sha256":"a0a1849f543b32e6145443ecf2545f37111fe38ec87369b61679bebdefcf6e02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0a1849f543b32e6145443ecf2545f37111fe38ec87369b61679bebdefcf6e02","first_computed_at":"2026-07-05T09:59:53.817074Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:59:53.817074Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vqhC48a7D5lXq4fJ63gLpvBJeXeqBRVbRlLT381f9zCWcn0RggAunRFF0z6XbfcF64dwXFzj56TtSav8vPzjDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:59:53.817585Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.06832","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6e485e84579f33209da24d08667576eab825593b4ffa15072de756344f42154e","sha256:2d3043a163f35df7ba1d7d7822b20f9c8f01aa19e661b1dd876184831c4069e6"],"state_sha256":"dbe2564cd0eefa05247d577f32cd25368fde7a991381c1a2ca22e2620546c86b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8nnoBcp/nlj2WsPkiMCuf3re+LIDoMvyMnv1jNgOllWVmDR7Lj7cYuY3BD0fkX9FHjDAuUyOIq2b7cbjLOGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T19:02:15.652126Z","bundle_sha256":"290a6203a32f0d0f860b13076c556795ed47e11e146c6c87e31b75b50700f64c"}}