{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GPKPDC6EAOTLJXDO67UOWVNDJM","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":"f89760aac1633044c60ea98254e15e30cac9ec30073916e97ee035caf5106042","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-13T00:57:32Z","title_canon_sha256":"9473b78f38be72b792aa8345201d3ff2146d871c02b60e4316e6ad74326c25bc"},"schema_version":"1.0","source":{"id":"1110.2822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2822","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2822v1","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2822","created_at":"2026-05-18T04:11:06Z"},{"alias_kind":"pith_short_12","alias_value":"GPKPDC6EAOTL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GPKPDC6EAOTLJXDO","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GPKPDC6E","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:7e163839c14018c3459fd6c76d4b0e70949186fd4ed60a1c28c25a45b731d99d","target":"graph","created_at":"2026-05-18T04:11:06Z","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":"Let $A=\\pmb k[x_1,...,x_n]/{(x_1^d,...,x_n^d)}$, where $\\pmb k$ is an infinite field. If $\\pmb k$ has characteristic zero, then Stanley proved that $A$ has the Weak Lefschetz Property (WLP). Henceforth, $\\pmb k$ has positive characteristic $p$. If $n=3$, then Brenner and Kaid have identified all $d$, as a function of $p$, for which $A$ has the WLP. In the present paper, the analogous project is carried out for $4\\le n$. If $4\\le n$ and $p=2$, then $A$ has the WLP if and only if $d=1$. If $n=4$ and $p$ is odd, then we prove that $A$ has the WLP if and only if $d=kq+r$ for integers $k,q,d$ with ","authors_text":"Adela Vraciu, Andrew R. Kustin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-13T00:57:32Z","title":"The Weak Lefschetz Property for monomial complete intersections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2822","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":"sha256:7946e223cab473d044ccb951cc5c25b94591b5e580f788d68c6bd86d96e46b37","target":"record","created_at":"2026-05-18T04:11:06Z","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":"f89760aac1633044c60ea98254e15e30cac9ec30073916e97ee035caf5106042","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-10-13T00:57:32Z","title_canon_sha256":"9473b78f38be72b792aa8345201d3ff2146d871c02b60e4316e6ad74326c25bc"},"schema_version":"1.0","source":{"id":"1110.2822","kind":"arxiv","version":1}},"canonical_sha256":"33d4f18bc403a6b4dc6ef7e8eb55a34b3bb6c9fa55e6d7c621e27fb5657d7a90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33d4f18bc403a6b4dc6ef7e8eb55a34b3bb6c9fa55e6d7c621e27fb5657d7a90","first_computed_at":"2026-05-18T04:11:06.904164Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:06.904164Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iDjCmzcgO2wO/zS5tLek4zeYbspeV5V1lGe8uRKBLfui0yCwcvL0F/fqnK5sMcHqYNwlh0+vgf7pJzhY3ElLBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:06.904677Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7946e223cab473d044ccb951cc5c25b94591b5e580f788d68c6bd86d96e46b37","sha256:7e163839c14018c3459fd6c76d4b0e70949186fd4ed60a1c28c25a45b731d99d"],"state_sha256":"977d9443d0ac0adaf0c36a2f7e72f2c5e129cfc193751f6abc99a161f0210e2e"}