{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:AMCISQL2TDJBF35EG4DUWZHZ52","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":"8026277551623a4b2fa10a95fac760724fee7bb1fc8ae6372a13890345758a3b","cross_cats_sorted":["cs.CC","cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-07-04T09:02:37Z","title_canon_sha256":"73cd8bef5405bc4d2745bf5f0b90bf2ecc25a7afc2362363166a75e5035ca7f5"},"schema_version":"1.0","source":{"id":"1507.01083","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01083","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01083v1","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01083","created_at":"2026-05-18T01:37:18Z"},{"alias_kind":"pith_short_12","alias_value":"AMCISQL2TDJB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"AMCISQL2TDJBF35E","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"AMCISQL2","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:936dd22c97a59b60c26271934c6cf245f995565b56e7723c54dd5b730b29bf81","target":"graph","created_at":"2026-05-18T01:37:18Z","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":"Certificates to a linear algebra computation are additional data structures for each output, which can be used by a-possibly randomized- verification algorithm that proves the correctness of each output. Wiede-mann's algorithm projects the Krylov sequence obtained by repeatedly multiplying a vector by a matrix to obtain a linearly recurrent sequence. The minimal polynomial of this sequence divides the minimal polynomial of the matrix. For instance, if the $n\\times n$ input matrix is sparse with n 1+o(1) non-zero entries, the computation of the sequence is quadratic in the dimension of the matr","authors_text":"Emmanuel Thom\\'e (CARAMEL), Erich Kaltofen (NCSU), Jean-Guillaume Dumas","cross_cats":["cs.CC","cs.CR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-07-04T09:02:37Z","title":"Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01083","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:c0ab0e12a97bd7f420b35e7b39b5590cfedc29b9ee05a4ea4d4602c489b36f4a","target":"record","created_at":"2026-05-18T01:37:18Z","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":"8026277551623a4b2fa10a95fac760724fee7bb1fc8ae6372a13890345758a3b","cross_cats_sorted":["cs.CC","cs.CR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-07-04T09:02:37Z","title_canon_sha256":"73cd8bef5405bc4d2745bf5f0b90bf2ecc25a7afc2362363166a75e5035ca7f5"},"schema_version":"1.0","source":{"id":"1507.01083","kind":"arxiv","version":1}},"canonical_sha256":"030489417a98d212efa437074b64f9eea9157d243a05c12d31f887db4235138d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"030489417a98d212efa437074b64f9eea9157d243a05c12d31f887db4235138d","first_computed_at":"2026-05-18T01:37:18.226801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:18.226801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ilyvi2t3bWWQQvUTxtuPMQoKpGMLxyuJ4JX7S/AlQr6/Et/t90s6kln63MCON/ZIQ0uOmCGdW/dWC2Jm391oBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:18.227389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01083","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0ab0e12a97bd7f420b35e7b39b5590cfedc29b9ee05a4ea4d4602c489b36f4a","sha256:936dd22c97a59b60c26271934c6cf245f995565b56e7723c54dd5b730b29bf81"],"state_sha256":"af2065b011ef39ea870f80319acb54363fb43c4e01dc3a947401e2d4ffcf0db4"}