{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2KPKWXERJ4CDLWMX4HEYBJEOZC","short_pith_number":"pith:2KPKWXER","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"},"canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","source":{"kind":"arxiv","id":"1807.09675","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09675","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09675v1","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09675","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"2KPKWXERJ4CD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2KPKWXERJ4CDLWMX","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2KPKWXER","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2KPKWXERJ4CDLWMX4HEYBJEOZC","target":"record","payload":{"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"},"canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","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"},"source_kind":"arxiv","source_id":"1807.09675","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0eyUw4VuRS+/Dt6kKNxiqYFWUnbow3j2qA6EPHjrSpMrJRH7XnnTiD2BPYKwQdTTSWnsd0kM+hESgA5QUPpEBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:31:34.747997Z"},"content_sha256":"be060bfa6d5002f9a8091061347ac961a8857fd671d47391b8f394ab398037f7","schema_version":"1.0","event_id":"sha256:be060bfa6d5002f9a8091061347ac961a8857fd671d47391b8f394ab398037f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2KPKWXERJ4CDLWMX4HEYBJEOZC","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:58:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sedoJDQF/OrDC7bvitXiCoJEb1a2UP9XWt2Ek+GC06fwskqbNZmcObapuev1AEuxGA/vS6htPWRdppTMRz0zBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:31:34.748360Z"},"content_sha256":"ca4fc8e4182d6c0834095a465db764ad964a587844edcf7b739e3d436a4afffe","schema_version":"1.0","event_id":"sha256:ca4fc8e4182d6c0834095a465db764ad964a587844edcf7b739e3d436a4afffe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/bundle.json","state_url":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T19:31:34Z","links":{"resolver":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC","bundle":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/bundle.json","state":"https://pith.science/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KPKWXERJ4CDLWMX4HEYBJEOZC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2KPKWXERJ4CDLWMX4HEYBJEOZC","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":"6538b83c5e0ff8b8dbde2e59d3b7deea062fd5d76d577a6cfcb49df462981333","cross_cats_sorted":["cs.CC","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-07-25T15:49:49Z","title_canon_sha256":"9071ec5f9081dd384fe6b0da0ef1527e33872f5b15cb106530304421d5297d11"},"schema_version":"1.0","source":{"id":"1807.09675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09675","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09675v1","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09675","created_at":"2026-05-17T23:58:24Z"},{"alias_kind":"pith_short_12","alias_value":"2KPKWXERJ4CD","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2KPKWXERJ4CDLWMX","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2KPKWXER","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:ca4fc8e4182d6c0834095a465db764ad964a587844edcf7b739e3d436a4afffe","target":"graph","created_at":"2026-05-17T23:58:24Z","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":"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}.","authors_text":"Javad Doliskani","cross_cats":["cs.CC","math.NT","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-07-25T15:49:49Z","title":"Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09675","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:be060bfa6d5002f9a8091061347ac961a8857fd671d47391b8f394ab398037f7","target":"record","created_at":"2026-05-17T23:58:24Z","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":"6538b83c5e0ff8b8dbde2e59d3b7deea062fd5d76d577a6cfcb49df462981333","cross_cats_sorted":["cs.CC","math.NT","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-07-25T15:49:49Z","title_canon_sha256":"9071ec5f9081dd384fe6b0da0ef1527e33872f5b15cb106530304421d5297d11"},"schema_version":"1.0","source":{"id":"1807.09675","kind":"arxiv","version":1}},"canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d29eab5c914f0435d997e1c980a48ec8b2b7fc7b48d2ef00ad638b26359f1b76","first_computed_at":"2026-05-17T23:58:24.880024Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:24.880024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XwKdv36c7ckbcTwNnaOK9/I2yc05FYY2jNPhJcpAjxEuTSyX4a4WmHIAYWrTgs2Wxus25AAHzi889BqNHXGXDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:24.880753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be060bfa6d5002f9a8091061347ac961a8857fd671d47391b8f394ab398037f7","sha256:ca4fc8e4182d6c0834095a465db764ad964a587844edcf7b739e3d436a4afffe"],"state_sha256":"c514328bda1dc77696f6db42100afd2da1f7354881769897b762c6b83d8008df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z68nYuecmFCSsRoYaWnroRBiFm/LXWPCb2I2cqJrDuYqqD5+5w8e4SE+BOeT8hQokcdzYHy0OqSiPCIJkDLaCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:31:34.750416Z","bundle_sha256":"4c39983d48bf45d71c24cad1a6325e85ef6298703e3ea3f1bf2e07d9a89a11f4"}}