{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:2KPKWXERJ4CDLWMX4HEYBJEOZC","short_pith_number":"pith:2KPKWXER","schema_version":"1.0","canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","source":{"kind":"arxiv","id":"1807.09675","version":1},"attestation_state":"computed","paper":{"title":"Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT","quant-ph"],"primary_cat":"cs.SC","authors_text":"Javad Doliskani","submitted_at":"2018-07-25T15:49:49Z","abstract_excerpt":"We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \\log^{2 + o(1)}q)$ bit operations. Only for a negligible subset of polynomials of degree $n$ our algorithm has a higher complexity of $O(n^{4 / 3 + o(1)} \\log^{2 + o(1)}q)$ bit operations. This breaks the classical $3/2$-exponent barrier for polynomial factorization over finite fields \\cite{guo2016alg}."},"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":"1807.09675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-07-25T15:49:49Z","cross_cats_sorted":["cs.CC","math.NT","quant-ph"],"title_canon_sha256":"9071ec5f9081dd384fe6b0da0ef1527e33872f5b15cb106530304421d5297d11","abstract_canon_sha256":"6538b83c5e0ff8b8dbde2e59d3b7deea062fd5d76d577a6cfcb49df462981333"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:24.880753Z","signature_b64":"XwKdv36c7ckbcTwNnaOK9/I2yc05FYY2jNPhJcpAjxEuTSyX4a4WmHIAYWrTgs2Wxus25AAHzi889BqNHXGXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","last_reissued_at":"2026-05-17T23:58:24.880024Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:24.880024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT","quant-ph"],"primary_cat":"cs.SC","authors_text":"Javad Doliskani","submitted_at":"2018-07-25T15:49:49Z","abstract_excerpt":"We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \\log^{2 + o(1)}q)$ bit operations. Only for a negligible subset of polynomials of degree $n$ our algorithm has a higher complexity of $O(n^{4 / 3 + o(1)} \\log^{2 + o(1)}q)$ bit operations. This breaks the classical $3/2$-exponent barrier for polynomial factorization over finite fields \\cite{guo2016alg}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09675","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.09675","created_at":"2026-05-17T23:58:24.880141+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.09675v1","created_at":"2026-05-17T23:58:24.880141+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09675","created_at":"2026-05-17T23:58:24.880141+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KPKWXERJ4CD","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KPKWXERJ4CDLWMX","created_at":"2026-05-18T12:32:02.567920+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KPKWXER","created_at":"2026-05-18T12:32:02.567920+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/2KPKWXERJ4CDLWMX4HEYBJEOZC","json":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC.json","graph_json":"https://pith.science/api/pith-number/2KPKWXERJ4CDLWMX4HEYBJEOZC/graph.json","events_json":"https://pith.science/api/pith-number/2KPKWXERJ4CDLWMX4HEYBJEOZC/events.json","paper":"https://pith.science/paper/2KPKWXER"},"agent_actions":{"view_html":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC","download_json":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC.json","view_paper":"https://pith.science/paper/2KPKWXER","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.09675&json=true","fetch_graph":"https://pith.science/api/pith-number/2KPKWXERJ4CDLWMX4HEYBJEOZC/graph.json","fetch_events":"https://pith.science/api/pith-number/2KPKWXERJ4CDLWMX4HEYBJEOZC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/action/storage_attestation","attest_author":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/action/author_attestation","sign_citation":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/action/citation_signature","submit_replication":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/action/replication_record"}},"created_at":"2026-05-17T23:58:24.880141+00:00","updated_at":"2026-05-17T23:58:24.880141+00:00"}