{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RQXKNFTG7PMYOX5M3QCEYMGNGE","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":"1a0420b5b456930339943ba65459f3a582c295ad8e8a590d39e5c02e6a0820a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-11-28T12:22:56Z","title_canon_sha256":"4983861389c7d4c9da320f07e4b76670ce8c5bac583b40535babece13ddf6093"},"schema_version":"1.0","source":{"id":"1312.0858","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0858","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0858v1","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0858","created_at":"2026-05-18T03:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"RQXKNFTG7PMY","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RQXKNFTG7PMYOX5M","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RQXKNFTG","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c06a9960ec289fd01c3e14e35ead41328349529213028a048bfeedabcf069f01","target":"graph","created_at":"2026-05-18T03:05:36Z","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 $K$ be a field and $S=K[x_1,\\ldots, x_n]$. Let $I$ be a monomial ideal of $S$ and $u_1,\\ldots, u_r$ be monomials in $S$ which form a filter-regular sequence on $S/I$. We show that $S/I$ is pretty clean if and only if $S/(I,u_1,\\ldots, u_r)$ is pretty clean.","authors_text":"Ali Soleyman Jahan, Kamran Divaani-Aazar, Somayeh Bandari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-11-28T12:22:56Z","title":"Pretty cleanness and filter-regular sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0858","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":"sha256:8ccb0a323d3882596a527e64c341f964e0e7b970d4bb0ed1f3473519f0e0013b","target":"record","created_at":"2026-05-18T03:05:36Z","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":"1a0420b5b456930339943ba65459f3a582c295ad8e8a590d39e5c02e6a0820a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-11-28T12:22:56Z","title_canon_sha256":"4983861389c7d4c9da320f07e4b76670ce8c5bac583b40535babece13ddf6093"},"schema_version":"1.0","source":{"id":"1312.0858","kind":"arxiv","version":1}},"canonical_sha256":"8c2ea69666fbd9875facdc044c30cd312b1b8dc3ec4da3667941a5cefe79d4fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c2ea69666fbd9875facdc044c30cd312b1b8dc3ec4da3667941a5cefe79d4fb","first_computed_at":"2026-05-18T03:05:36.541217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:36.541217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3F026Qjq3oTV5LRTypJ92gko7fLp+XTfvAaV30YQULrgSdXh46xxrq5swKyXnG4ssKq/w/EftKMrUVdzLYU8Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:36.541653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0858","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ccb0a323d3882596a527e64c341f964e0e7b970d4bb0ed1f3473519f0e0013b","sha256:c06a9960ec289fd01c3e14e35ead41328349529213028a048bfeedabcf069f01"],"state_sha256":"cfc60650c73de3b4342a9c3c576cb6e7011dc59dbd054621c45756da46272f7a"}