{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:24C7LPTUPX3Y65C3GVMWIZAWCA","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":"0ce0c7180e0801a35cf3f54505536f8a947364d509e5bb2d3f2faace5513bd8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-11T08:27:58Z","title_canon_sha256":"813c0e6a73805a6c4dec70b1e1d93810551c677a0a85d57e533d4043dbcb26dc"},"schema_version":"1.0","source":{"id":"1809.03736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03736","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03736v1","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03736","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"24C7LPTUPX3Y","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"24C7LPTUPX3Y65C3","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"24C7LPTU","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:3376e6d896077787dd71ca000d2a2de0b0c08504f375af649cdfdbabb2a5b42c","target":"graph","created_at":"2026-05-18T00:05:59Z","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"},"paper":{"abstract_excerpt":"In this paper we shed more light on determinants of interval matrices. Computing the exact bounds on a determinant of an interval matrix is an NP-hard problem. Therefore, attention is first paid to approximations. NP-hardness of both relative and absolute approximation is proved. Next, methods computing verified enclosures of interval determinants and their possible combination with preconditioning are discussed. A new method based on Cramer's rule was designed. It returns similar results to the state-of-the-art method, however, it is less consuming regarding computational time. As a byproduct","authors_text":"Jaroslav Hor\\'a\\v{c}ek, Josef Mat\\v{e}jka, Milan Hlad\\'ik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-11T08:27:58Z","title":"Determinants of Interval Matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03736","kind":"arxiv","version":1},"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":"sha256:83d5c31edcbf6360514961857218da46d008878eac556546caab2949b49736b0","target":"record","created_at":"2026-05-18T00:05:59Z","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":"0ce0c7180e0801a35cf3f54505536f8a947364d509e5bb2d3f2faace5513bd8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-09-11T08:27:58Z","title_canon_sha256":"813c0e6a73805a6c4dec70b1e1d93810551c677a0a85d57e533d4043dbcb26dc"},"schema_version":"1.0","source":{"id":"1809.03736","kind":"arxiv","version":1}},"canonical_sha256":"d705f5be747df78f745b3559646416100eb6f6151aacc76839f40896215c852a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d705f5be747df78f745b3559646416100eb6f6151aacc76839f40896215c852a","first_computed_at":"2026-05-18T00:05:59.971412Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:59.971412Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a0y2AqItRy4ynZPZRYJ9lhIqt7Fu8+fU5GJIxjABRSi0Et9pU7xBppri5jKakmVGN+Ki6P585yLDYN+AepygBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:59.971865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:83d5c31edcbf6360514961857218da46d008878eac556546caab2949b49736b0","sha256:3376e6d896077787dd71ca000d2a2de0b0c08504f375af649cdfdbabb2a5b42c"],"state_sha256":"f1d39190e0e97449a4449c66743435b4d574c0222706d6323b2d2add4f1b84f1"}