{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UOO5BYNBO4L7V7MOE3GDC4GES6","short_pith_number":"pith:UOO5BYNB","canonical_record":{"source":{"id":"1311.6077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-24T04:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"38c68fdc00df89b8f787727afde78dacb117f8914503b1457a2453feac1ed235","abstract_canon_sha256":"acf727f3332c11c45d6234384835dae212f9dad72ad8f26de8f597e686dd814c"},"schema_version":"1.0"},"canonical_sha256":"a39dd0e1a17717fafd8e26cc3170c49795aeb27a511a9ca784b2f5667fa38bc8","source":{"kind":"arxiv","id":"1311.6077","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6077","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6077v1","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6077","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"UOO5BYNBO4L7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UOO5BYNBO4L7V7MO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UOO5BYNB","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UOO5BYNBO4L7V7MOE3GDC4GES6","target":"record","payload":{"canonical_record":{"source":{"id":"1311.6077","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-24T04:04:56Z","cross_cats_sorted":[],"title_canon_sha256":"38c68fdc00df89b8f787727afde78dacb117f8914503b1457a2453feac1ed235","abstract_canon_sha256":"acf727f3332c11c45d6234384835dae212f9dad72ad8f26de8f597e686dd814c"},"schema_version":"1.0"},"canonical_sha256":"a39dd0e1a17717fafd8e26cc3170c49795aeb27a511a9ca784b2f5667fa38bc8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:20.618276Z","signature_b64":"B/jF3Or5vVrPBMA4Mg29JjgDRW4TJIaoCxw1dY6YCWtPSGszo/GFs6ynkoOWOj5sSAM6GW5HbqjxxZLctgI6BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a39dd0e1a17717fafd8e26cc3170c49795aeb27a511a9ca784b2f5667fa38bc8","last_reissued_at":"2026-05-18T03:06:20.617589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:20.617589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.6077","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpQB3UBCpZkG5D6I3+8wXQXvlvh9Jhm3T0QprM6Qn773sAQtEqNFtE0jVrWIY4QsusqWnn2DsqDw+jVMRnLNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:03:20.423572Z"},"content_sha256":"dcc17d11c187b7b47a1c730c24dd166f0ebd5a54177df2f2a1946eefec33af36","schema_version":"1.0","event_id":"sha256:dcc17d11c187b7b47a1c730c24dd166f0ebd5a54177df2f2a1946eefec33af36"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UOO5BYNBO4L7V7MOE3GDC4GES6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Structured Matrix Methods for Real and Complex Polynomial Root-finding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ai-Long Zheng, Victor Y. Pan","submitted_at":"2013-11-24T04:04:56Z","abstract_excerpt":"We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular numerical approximation of the real roots of a polynomial. Our analysis and experiments show efficiency of the resulting algorithms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6077","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ll0vqo90XaOS8tphzORNiDj4e7eUoOP420dkUqKZE1tU/FH1bCRZCj98zWV9V8lJM69MylvzY25DsKc/WomDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:03:20.424354Z"},"content_sha256":"d9e859203691e869adbe29a3b5d03684d13f3077ea6fce5b326b219bff77017a","schema_version":"1.0","event_id":"sha256:d9e859203691e869adbe29a3b5d03684d13f3077ea6fce5b326b219bff77017a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/bundle.json","state_url":"https://pith.science/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/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":"2026-06-11T15:03:20Z","links":{"resolver":"https://pith.science/pith/UOO5BYNBO4L7V7MOE3GDC4GES6","bundle":"https://pith.science/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/bundle.json","state":"https://pith.science/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOO5BYNBO4L7V7MOE3GDC4GES6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UOO5BYNBO4L7V7MOE3GDC4GES6","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":"acf727f3332c11c45d6234384835dae212f9dad72ad8f26de8f597e686dd814c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-24T04:04:56Z","title_canon_sha256":"38c68fdc00df89b8f787727afde78dacb117f8914503b1457a2453feac1ed235"},"schema_version":"1.0","source":{"id":"1311.6077","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.6077","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"1311.6077v1","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.6077","created_at":"2026-05-18T03:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"UOO5BYNBO4L7","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UOO5BYNBO4L7V7MO","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UOO5BYNB","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:d9e859203691e869adbe29a3b5d03684d13f3077ea6fce5b326b219bff77017a","target":"graph","created_at":"2026-05-18T03:06:20Z","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":"We combine the known methods for univariate polynomial root-finding and for computations in the Frobenius matrix algebra with our novel techniques to advance numerical solution of a univariate polynomial equation, and in particular numerical approximation of the real roots of a polynomial. Our analysis and experiments show efficiency of the resulting algorithms.","authors_text":"Ai-Long Zheng, Victor Y. Pan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-24T04:04:56Z","title":"New Structured Matrix Methods for Real and Complex Polynomial Root-finding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.6077","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:dcc17d11c187b7b47a1c730c24dd166f0ebd5a54177df2f2a1946eefec33af36","target":"record","created_at":"2026-05-18T03:06:20Z","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":"acf727f3332c11c45d6234384835dae212f9dad72ad8f26de8f597e686dd814c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-11-24T04:04:56Z","title_canon_sha256":"38c68fdc00df89b8f787727afde78dacb117f8914503b1457a2453feac1ed235"},"schema_version":"1.0","source":{"id":"1311.6077","kind":"arxiv","version":1}},"canonical_sha256":"a39dd0e1a17717fafd8e26cc3170c49795aeb27a511a9ca784b2f5667fa38bc8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a39dd0e1a17717fafd8e26cc3170c49795aeb27a511a9ca784b2f5667fa38bc8","first_computed_at":"2026-05-18T03:06:20.617589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:20.617589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B/jF3Or5vVrPBMA4Mg29JjgDRW4TJIaoCxw1dY6YCWtPSGszo/GFs6ynkoOWOj5sSAM6GW5HbqjxxZLctgI6BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:20.618276Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.6077","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcc17d11c187b7b47a1c730c24dd166f0ebd5a54177df2f2a1946eefec33af36","sha256:d9e859203691e869adbe29a3b5d03684d13f3077ea6fce5b326b219bff77017a"],"state_sha256":"a6ad0ac2c84a55496c00038fb792265d562f23e0997a2b569562044284712681"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QRoo30wrDApVD0yC8RCirOC7DAJHU36EHt2ePMCkCbJZaEA7yqWX422EuFbi9fZJnODUeRTyDswDId9GfhNxCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:03:20.428474Z","bundle_sha256":"2fd345739022f58ca81f801b93a28c12f706eb18cd4898bc08dfdba6a38bd6d7"}}