{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:KWG3VENMC436JVEULYRPSW35SR","short_pith_number":"pith:KWG3VENM","schema_version":"1.0","canonical_sha256":"558dba91ac1737e4d4945e22f95b7d94694c1be4756ada217368ed419e2f64cb","source":{"kind":"arxiv","id":"2603.10277","version":3},"attestation_state":"computed","paper":{"title":"Estimating condition number with Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Erin Carson, Xinye Chen","submitted_at":"2026-03-10T23:38:48Z","abstract_excerpt":"In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs). For efficient deployment of GNNs, we introduce a graph feature construction with $\\mathrm{O}(\\mathrm{nnz} + n)$ complexity, where $\\mathrm{nnz}$ is the number of non-zero elements in the matrix and $n$ denotes the matrix dimension. We propose two schemes for estimating the matrix condition number using GNNs; One follows by decomposing the condition number and predicts the relatively more computationally intensive part $\\|\\mathbf{A}^{-1}\\|$, without explicitly formi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2603.10277","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-03-10T23:38:48Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"0d1493176696133d377eb2c7c8e107aa9134d36cfa17e3aae507ca83fce38b4b","abstract_canon_sha256":"173e2332e8f8352f9559374575ea53602fb44df588cb6ed982b90ff942f1594e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-25T01:18:37.254248Z","signature_b64":"l5A6MLTeUyqCg4yUBrhgz3V17Kp20j0HlFzo5sJNGnfKhMNHCGyzUy7MGwHxw8YRVZBvK+AaEOnrzxvLlVtaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"558dba91ac1737e4d4945e22f95b7d94694c1be4756ada217368ed419e2f64cb","last_reissued_at":"2026-06-25T01:18:37.253900Z","signature_status":"signed_v1","first_computed_at":"2026-06-25T01:18:37.253900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating condition number with Graph Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.LG","authors_text":"Erin Carson, Xinye Chen","submitted_at":"2026-03-10T23:38:48Z","abstract_excerpt":"In this paper, we propose a fast method for estimating the condition number of sparse matrices using graph neural networks (GNNs). For efficient deployment of GNNs, we introduce a graph feature construction with $\\mathrm{O}(\\mathrm{nnz} + n)$ complexity, where $\\mathrm{nnz}$ is the number of non-zero elements in the matrix and $n$ denotes the matrix dimension. We propose two schemes for estimating the matrix condition number using GNNs; One follows by decomposing the condition number and predicts the relatively more computationally intensive part $\\|\\mathbf{A}^{-1}\\|$, without explicitly formi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.10277","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/2603.10277/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.10277","created_at":"2026-06-25T01:18:37.253958+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.10277v3","created_at":"2026-06-25T01:18:37.253958+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.10277","created_at":"2026-06-25T01:18:37.253958+00:00"},{"alias_kind":"pith_short_12","alias_value":"KWG3VENMC436","created_at":"2026-06-25T01:18:37.253958+00:00"},{"alias_kind":"pith_short_16","alias_value":"KWG3VENMC436JVEU","created_at":"2026-06-25T01:18:37.253958+00:00"},{"alias_kind":"pith_short_8","alias_value":"KWG3VENM","created_at":"2026-06-25T01:18:37.253958+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR","json":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR.json","graph_json":"https://pith.science/api/pith-number/KWG3VENMC436JVEULYRPSW35SR/graph.json","events_json":"https://pith.science/api/pith-number/KWG3VENMC436JVEULYRPSW35SR/events.json","paper":"https://pith.science/paper/KWG3VENM"},"agent_actions":{"view_html":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR","download_json":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR.json","view_paper":"https://pith.science/paper/KWG3VENM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.10277&json=true","fetch_graph":"https://pith.science/api/pith-number/KWG3VENMC436JVEULYRPSW35SR/graph.json","fetch_events":"https://pith.science/api/pith-number/KWG3VENMC436JVEULYRPSW35SR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR/action/storage_attestation","attest_author":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR/action/author_attestation","sign_citation":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR/action/citation_signature","submit_replication":"https://pith.science/pith/KWG3VENMC436JVEULYRPSW35SR/action/replication_record"}},"created_at":"2026-06-25T01:18:37.253958+00:00","updated_at":"2026-06-25T01:18:37.253958+00:00"}