{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3ZRLL7RWTGTU7CWE7W2XFASEDU","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":"85395fdd21c122d25f2b4372b809e6d30000e718c78a90206f0971d30e1aecce","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-16T20:10:30Z","title_canon_sha256":"d5c3d3b1238937d89a400653ba8ce6a663c9dbc08dd4c64b53807ad3348d066e"},"schema_version":"1.0","source":{"id":"1102.4771","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4771","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4771v1","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4771","created_at":"2026-05-18T04:28:07Z"},{"alias_kind":"pith_short_12","alias_value":"3ZRLL7RWTGTU","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"3ZRLL7RWTGTU7CWE","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"3ZRLL7RW","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:4c4f052540ac4e855331575912b2f0a3a62b1ae09bf326db7cefd72861738cba","target":"graph","created_at":"2026-05-18T04:28:07Z","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":"A method is described which allows to evaluate efficiently a polynomial in a (possibly trivial) extension of the finite field of its coefficients. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large with respect to the base field. Applications to the syndrome computation in the decoding of cyclic codes, Reed-Solomon codes in particular, are highlighted.","authors_text":"Davide Schipani, Joachim Rosenthal, Michele Elia","cross_cats":["math.IT","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-16T20:10:30Z","title":"Efficient evaluation of polynomials over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4771","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":"sha256:00b9b3a3467f661ccfc5bb56df2ce5719cc25cec9f546903f4ff10c16c171233","target":"record","created_at":"2026-05-18T04:28:07Z","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":"85395fdd21c122d25f2b4372b809e6d30000e718c78a90206f0971d30e1aecce","cross_cats_sorted":["math.IT","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-16T20:10:30Z","title_canon_sha256":"d5c3d3b1238937d89a400653ba8ce6a663c9dbc08dd4c64b53807ad3348d066e"},"schema_version":"1.0","source":{"id":"1102.4771","kind":"arxiv","version":1}},"canonical_sha256":"de62b5fe3699a74f8ac4fdb57282441d2c4cf8f95fa6858874ebcbeb08bc3e11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de62b5fe3699a74f8ac4fdb57282441d2c4cf8f95fa6858874ebcbeb08bc3e11","first_computed_at":"2026-05-18T04:28:07.391877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:07.391877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YvEF+7XhnwwwfrfELVcv5nDWZ+4/cztwgO8y6UePWNeymYPKbN7nPbi+7XQ08EKg56DhhTpD+48iIWAr7ZcWAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:07.392515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4771","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00b9b3a3467f661ccfc5bb56df2ce5719cc25cec9f546903f4ff10c16c171233","sha256:4c4f052540ac4e855331575912b2f0a3a62b1ae09bf326db7cefd72861738cba"],"state_sha256":"7e7f028c0385449f2cf36d7140d2c6de38e36f8ecc56045204deb9c3eff51113"}