{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:JJTZYP3Y7GVMSIDVDVE2XGIDUZ","short_pith_number":"pith:JJTZYP3Y","schema_version":"1.0","canonical_sha256":"4a679c3f78f9aac920751d49ab9903a64aa74cb07c6209c52bfd6c786c4e61c2","source":{"kind":"arxiv","id":"1204.1113","version":2},"attestation_state":"computed","paper":{"title":"Sub-Linear Root Detection, and New Hardness Results, for Sparse Polynomials Over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.NT","authors_text":"Jingguo Bi, J. Maurice Rojas, Qi Cheng","submitted_at":"2012-04-05T02:54:28Z","abstract_excerpt":"We present a deterministic 2^O(t)q^{(t-2)(t-1)+o(1)} algorithm to decide whether a univariate polynomial f, with exactly t monomial terms and degree <q, has a root in F_q. A corollary of our method --- the first with complexity sub-linear in q when t is fixed --- is that the nonzero roots in F_q can be partitioned into at most 2 \\sqrt{t-1} (q-1)^{(t-2)(t-1)} cosets of two subgroups S_1,S_2 of F^*_q, with S_1 in S_2. Another corollary is the first deterministic sub-linear algorithm for detecting common degree one factors of k-tuples of t-nomials in F_q[x] when k and t are fixed.\n  When t is not"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1204.1113","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-04-05T02:54:28Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"298b61269d2759b9176809b3d4d84e97ed1a0a61c35ea37ee2e8a7db475ab5fd","abstract_canon_sha256":"91e2bc68abf5cd2e1a5f48b42369219e52340f02529c58eaf367f14402f64c38"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:30.480043Z","signature_b64":"KIjXKtzJiEo+H/zGrsPUPQzMP3lH9m77refoXo/8MVIx3Y+Rye0cregB8QVYzOe3/cTo5sX4Xp+llaz8aAAqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a679c3f78f9aac920751d49ab9903a64aa74cb07c6209c52bfd6c786c4e61c2","last_reissued_at":"2026-05-18T03:14:30.479521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:30.479521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sub-Linear Root Detection, and New Hardness Results, for Sparse Polynomials Over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.NT","authors_text":"Jingguo Bi, J. Maurice Rojas, Qi Cheng","submitted_at":"2012-04-05T02:54:28Z","abstract_excerpt":"We present a deterministic 2^O(t)q^{(t-2)(t-1)+o(1)} algorithm to decide whether a univariate polynomial f, with exactly t monomial terms and degree <q, has a root in F_q. A corollary of our method --- the first with complexity sub-linear in q when t is fixed --- is that the nonzero roots in F_q can be partitioned into at most 2 \\sqrt{t-1} (q-1)^{(t-2)(t-1)} cosets of two subgroups S_1,S_2 of F^*_q, with S_1 in S_2. Another corollary is the first deterministic sub-linear algorithm for detecting common degree one factors of k-tuples of t-nomials in F_q[x] when k and t are fixed.\n  When t is not"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1113","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1204.1113","created_at":"2026-05-18T03:14:30.479611+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1113v2","created_at":"2026-05-18T03:14:30.479611+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1113","created_at":"2026-05-18T03:14:30.479611+00:00"},{"alias_kind":"pith_short_12","alias_value":"JJTZYP3Y7GVM","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_16","alias_value":"JJTZYP3Y7GVMSIDV","created_at":"2026-05-18T12:27:11.947152+00:00"},{"alias_kind":"pith_short_8","alias_value":"JJTZYP3Y","created_at":"2026-05-18T12:27:11.947152+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ","json":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ.json","graph_json":"https://pith.science/api/pith-number/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/graph.json","events_json":"https://pith.science/api/pith-number/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/events.json","paper":"https://pith.science/paper/JJTZYP3Y"},"agent_actions":{"view_html":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ","download_json":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ.json","view_paper":"https://pith.science/paper/JJTZYP3Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1113&json=true","fetch_graph":"https://pith.science/api/pith-number/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/graph.json","fetch_events":"https://pith.science/api/pith-number/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/action/storage_attestation","attest_author":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/action/author_attestation","sign_citation":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/action/citation_signature","submit_replication":"https://pith.science/pith/JJTZYP3Y7GVMSIDVDVE2XGIDUZ/action/replication_record"}},"created_at":"2026-05-18T03:14:30.479611+00:00","updated_at":"2026-05-18T03:14:30.479611+00:00"}