{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MRATNK7MRLNHVEG4UU6M4HR7QO","short_pith_number":"pith:MRATNK7M","schema_version":"1.0","canonical_sha256":"644136abec8ada7a90dca53cce1e3f8389732801f47b1d33e0e47128766ec94f","source":{"kind":"arxiv","id":"1810.01478","version":1},"attestation_state":"computed","paper":{"title":"Smallest Eigenvalue of Large Hankel Matrices at Critical Point: Comparing Conjecture With Parallelised Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.NA","authors_text":"Jakub Sikorowski, Mengkun Zhu, Yang Chen","submitted_at":"2018-09-24T06:49:38Z","abstract_excerpt":"We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\\it LDLT} decomposition and involves finding a $k \\times k$ sub-matrix of the inverse of the original $N \\times N$ Hankel matrix $H_N^{-1}$ . The computation involves extremely high precision arithmetic, message passing interface, and shared memory parallelisation. We demonstrate that this approach achieves good scalability on a high performance computing cluster (HPCC) which constitute a major improvement of the earlier approaches. We use this method"},"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":"1810.01478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-24T06:49:38Z","cross_cats_sorted":["math-ph","math.MP","math.RA"],"title_canon_sha256":"b644d9a38cfc718c50fb0b5c0e6bd72da2c81b8cee4daee522e705985f964fee","abstract_canon_sha256":"39ed2d723d547633fa4be467ebad862d86f50258f7eb35d4b3db1ae78dcbf201"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:12.076517Z","signature_b64":"HbxD/7iT5Vq2QN+YsKfPTYnCXKv7XgURX88VxKwUzYGp3Av2P6Gwrw5fuqEVQ65vMc0hH4rrEtMaIVegMgSnBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"644136abec8ada7a90dca53cce1e3f8389732801f47b1d33e0e47128766ec94f","last_reissued_at":"2026-05-18T00:04:12.075884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:12.075884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Smallest Eigenvalue of Large Hankel Matrices at Critical Point: Comparing Conjecture With Parallelised Computation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RA"],"primary_cat":"math.NA","authors_text":"Jakub Sikorowski, Mengkun Zhu, Yang Chen","submitted_at":"2018-09-24T06:49:38Z","abstract_excerpt":"We propose a novel parallel numerical algorithm for calculating the smallest eigenvalues of highly ill-conditioned matrices. It is based on the {\\it LDLT} decomposition and involves finding a $k \\times k$ sub-matrix of the inverse of the original $N \\times N$ Hankel matrix $H_N^{-1}$ . The computation involves extremely high precision arithmetic, message passing interface, and shared memory parallelisation. We demonstrate that this approach achieves good scalability on a high performance computing cluster (HPCC) which constitute a major improvement of the earlier approaches. We use this method"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01478","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":""},"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":"1810.01478","created_at":"2026-05-18T00:04:12.076000+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01478v1","created_at":"2026-05-18T00:04:12.076000+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01478","created_at":"2026-05-18T00:04:12.076000+00:00"},{"alias_kind":"pith_short_12","alias_value":"MRATNK7MRLNH","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MRATNK7MRLNHVEG4","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MRATNK7M","created_at":"2026-05-18T12:32:40.477152+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/MRATNK7MRLNHVEG4UU6M4HR7QO","json":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO.json","graph_json":"https://pith.science/api/pith-number/MRATNK7MRLNHVEG4UU6M4HR7QO/graph.json","events_json":"https://pith.science/api/pith-number/MRATNK7MRLNHVEG4UU6M4HR7QO/events.json","paper":"https://pith.science/paper/MRATNK7M"},"agent_actions":{"view_html":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO","download_json":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO.json","view_paper":"https://pith.science/paper/MRATNK7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01478&json=true","fetch_graph":"https://pith.science/api/pith-number/MRATNK7MRLNHVEG4UU6M4HR7QO/graph.json","fetch_events":"https://pith.science/api/pith-number/MRATNK7MRLNHVEG4UU6M4HR7QO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO/action/storage_attestation","attest_author":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO/action/author_attestation","sign_citation":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO/action/citation_signature","submit_replication":"https://pith.science/pith/MRATNK7MRLNHVEG4UU6M4HR7QO/action/replication_record"}},"created_at":"2026-05-18T00:04:12.076000+00:00","updated_at":"2026-05-18T00:04:12.076000+00:00"}