{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:3IAWRLDTWGN54VHTCPPD25HU7H","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":"cca86e6749917f08a95eb8d60c326559e06f153630d49cef5d0979081a31ca75","cross_cats_sorted":[],"license":"","primary_cat":"cs.SC","submitted_at":"2006-10-24T08:24:08Z","title_canon_sha256":"4481c00fe7f3a62bf615f38d5d20b4909f22ee8cf4d719a7210290ce2fa61c3e"},"schema_version":"1.0","source":{"id":"cs/0610136","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0610136","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0610136v4","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0610136","created_at":"2026-05-18T04:08:43Z"},{"alias_kind":"pith_short_12","alias_value":"3IAWRLDTWGN5","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"3IAWRLDTWGN54VHT","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"3IAWRLDT","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:91de2f6130d088299182c4a59527bf5442bc6002ed8319995fe1fd3103ae267f","target":"graph","created_at":"2026-05-18T04:08:43Z","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":"This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise input-dependant bounds on these coefficients. Such bounds are e.g. useful to perform deterministic chinese remaindering of the characteristic or minimal polynomial of an integer matrix.","authors_text":"Jean-Guillaume Dumas (LJK)","cross_cats":[],"headline":"","license":"","primary_cat":"cs.SC","submitted_at":"2006-10-24T08:24:08Z","title":"Bounds on the coefficients of the characteristic and minimal polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0610136","kind":"arxiv","version":4},"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":"sha256:49337d24fe04ecdd40d5ff6dbe9e29d3d4cfd28b427531466d60d9ca907affe5","target":"record","created_at":"2026-05-18T04:08:43Z","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":"cca86e6749917f08a95eb8d60c326559e06f153630d49cef5d0979081a31ca75","cross_cats_sorted":[],"license":"","primary_cat":"cs.SC","submitted_at":"2006-10-24T08:24:08Z","title_canon_sha256":"4481c00fe7f3a62bf615f38d5d20b4909f22ee8cf4d719a7210290ce2fa61c3e"},"schema_version":"1.0","source":{"id":"cs/0610136","kind":"arxiv","version":4}},"canonical_sha256":"da0168ac73b19bde54f313de3d74f4f9c70865378edeb169d44fac61b539beb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da0168ac73b19bde54f313de3d74f4f9c70865378edeb169d44fac61b539beb3","first_computed_at":"2026-05-18T04:08:43.512691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:43.512691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pDN3B9VghGhkjqyhqf+tmxio1Njr/GdR8oc5C8CB9wfbIF7hppvYu9dKEvX3G4fOE3J4Z8evgk1fPlPFN71nDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:43.513249Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0610136","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49337d24fe04ecdd40d5ff6dbe9e29d3d4cfd28b427531466d60d9ca907affe5","sha256:91de2f6130d088299182c4a59527bf5442bc6002ed8319995fe1fd3103ae267f"],"state_sha256":"1dad73a3730bdf2966a8e5f1f0ea5292aeaac370976a57220fd53ed2e0f6e4ba"}