{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6IE2HEKCQWZPWDRCUJLVKYES2E","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":"ed35832cf7e570db8971f8635b0c6978ecf80d5c1b73d5795e7a1469970a0861","cross_cats_sorted":["cs.DM","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-18T16:25:38Z","title_canon_sha256":"18d5340e3a3e4f3f5d43acdad9ce252d7bbf9704838dc008dc4bd299f5e4bf9e"},"schema_version":"1.0","source":{"id":"1404.4834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.4834","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"arxiv_version","alias_value":"1404.4834v2","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4834","created_at":"2026-05-18T02:45:39Z"},{"alias_kind":"pith_short_12","alias_value":"6IE2HEKCQWZP","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6IE2HEKCQWZPWDRC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6IE2HEKC","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:ec5e088ebb05bebb6101c2073fdf79ff49a42147f63979770fccf7387cfb839a","target":"graph","created_at":"2026-05-18T02:45:39Z","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 paper was removed due to an error in the proof (Claim 4.12 as stated is not true). The authors would like to thank Ilya Volkovich for pointing out a counterexample to this paper's main result in positive characteristic: If $F$ is a field with prime characteristic $p$, then the polynomial $x_1^p + x_2^p + \\ldots + x^n^p$ has the following factor: $(x_1+x_2+ \\ldots + x_n)^{p-1}$, which has sparsity $n^p$.","authors_text":"Rafael Mendes de Oliveira, Zeev Dvir","cross_cats":["cs.DM","math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-18T16:25:38Z","title":"Factors of Sparse Polynomials are Sparse"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4834","kind":"arxiv","version":2},"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":"sha256:03dfd6f4b5e713bb51ab58452c95888919d6525894b784d588d40ca2fa2bcaf0","target":"record","created_at":"2026-05-18T02:45:39Z","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":"ed35832cf7e570db8971f8635b0c6978ecf80d5c1b73d5795e7a1469970a0861","cross_cats_sorted":["cs.DM","math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-04-18T16:25:38Z","title_canon_sha256":"18d5340e3a3e4f3f5d43acdad9ce252d7bbf9704838dc008dc4bd299f5e4bf9e"},"schema_version":"1.0","source":{"id":"1404.4834","kind":"arxiv","version":2}},"canonical_sha256":"f209a3914285b2fb0e22a257556092d10726af1b8dcbb9f521064dce3a5c39d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f209a3914285b2fb0e22a257556092d10726af1b8dcbb9f521064dce3a5c39d5","first_computed_at":"2026-05-18T02:45:39.827831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:39.827831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+nYgpXPudpZI3Al2MHpSLNaRWd4BLqepU+whc3GZvnO1JLsA2Eb/YwBuu3Z2H4wUY+oA34xvuGG2PMqjJHFPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:39.828299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.4834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03dfd6f4b5e713bb51ab58452c95888919d6525894b784d588d40ca2fa2bcaf0","sha256:ec5e088ebb05bebb6101c2073fdf79ff49a42147f63979770fccf7387cfb839a"],"state_sha256":"b6c72974aadaed672550a6cabdb62a2584316349241291d4b2628b92de55bece"}