{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3E6Y5T2YJNDYU7JRE2QTY3U6MW","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":"ab65e91d8950be2d9cd5977cb4f98990857fffd93ba30b224e07b41d29e95920","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2012-11-05T12:24:05Z","title_canon_sha256":"baa4c6622c34887840d57acc8c7df842fd1bae09dd8a7c27ddbdb00b23d87216"},"schema_version":"1.0","source":{"id":"1211.0842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0842","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0842v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0842","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"3E6Y5T2YJNDY","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3E6Y5T2YJNDYU7JR","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3E6Y5T2Y","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:2fa2309b06d23a3eca5c51bb8fcc810c4badd28f98168aabb1950954e2af99e7","target":"graph","created_at":"2026-05-18T03:41:31Z","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 $I\\supsetneq J$ be two square free monomial ideals of a polynomial algebra over a field generated in degree $\\geq 1$, resp. $\\geq 2$ . Almost always when $I$ contains precisely one variable, the other generators having degrees $\\geq 2$, if the Stanley depth of $I/J$ is $\\leq 2$ then the usual depth of $I/J$ is $\\leq 2$ too, that is the Stanley Conjecture holds in these cases.","authors_text":"Andrei Zarojanu, Dorin Popescu","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2012-11-05T12:24:05Z","title":"Depth of some square free monomial ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0842","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:f229530dd664b39ea8974d13e59cb14f64246756db7886962799fe87489922b9","target":"record","created_at":"2026-05-18T03:41:31Z","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":"ab65e91d8950be2d9cd5977cb4f98990857fffd93ba30b224e07b41d29e95920","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2012-11-05T12:24:05Z","title_canon_sha256":"baa4c6622c34887840d57acc8c7df842fd1bae09dd8a7c27ddbdb00b23d87216"},"schema_version":"1.0","source":{"id":"1211.0842","kind":"arxiv","version":1}},"canonical_sha256":"d93d8ecf584b478a7d3126a13c6e9e65b03fb66589487f6a51b23eccf374ef9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d93d8ecf584b478a7d3126a13c6e9e65b03fb66589487f6a51b23eccf374ef9b","first_computed_at":"2026-05-18T03:41:31.382756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:31.382756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBUGQK7QwzmfHkLVYkQ4iFLGwNu3hVz4OljtQJt563JOjZTR/54we9GqjmJmiuO1Gcqp9PQnO/UewCRVN8IeCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:31.383445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f229530dd664b39ea8974d13e59cb14f64246756db7886962799fe87489922b9","sha256:2fa2309b06d23a3eca5c51bb8fcc810c4badd28f98168aabb1950954e2af99e7"],"state_sha256":"88a6aab49532c86457cb5b398f668bbf5f4c324a4eee307dea6ffe4c4e14db0c"}