{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ZHH43F5HC5ZXEAI3AX35ZXDNID","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":"df27f146bf80f83dc2182683c57a2367b95974e2a29b4c2d8d315958ca10f3b1","cross_cats_sorted":[],"license":"","primary_cat":"math.AC","submitted_at":"2007-02-24T05:51:56Z","title_canon_sha256":"3bf92aef0cfe0cd13bd79d97fc08c36b53067f0e295197ab22915843880ae1db"},"schema_version":"1.0","source":{"id":"math/0702728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0702728","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0702728v1","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0702728","created_at":"2026-05-18T04:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZHH43F5HC5ZX","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"ZHH43F5HC5ZXEAI3","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"ZHH43F5H","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:b24321fd84b05b7767de94706b7a013e308da307884174eba3e63c6ced0130f7","target":"graph","created_at":"2026-05-18T04:31:12Z","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 show that Stanley's conjecture holds for a polynomial ring over a field in four variables. In the case of polynomial ring in five variables, we prove that the monomial ideals with all associated primes of height two, are Stanley ideals.","authors_text":"Dorin Popescu, Imran Anwar","cross_cats":[],"headline":"","license":"","primary_cat":"math.AC","submitted_at":"2007-02-24T05:51:56Z","title":"Stanley Conjecture in small embedding dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0702728","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":"sha256:1f76888273bd58143bfa6dea2de1805e322d34cef379e7cb75d634d593a0ad72","target":"record","created_at":"2026-05-18T04:31:12Z","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":"df27f146bf80f83dc2182683c57a2367b95974e2a29b4c2d8d315958ca10f3b1","cross_cats_sorted":[],"license":"","primary_cat":"math.AC","submitted_at":"2007-02-24T05:51:56Z","title_canon_sha256":"3bf92aef0cfe0cd13bd79d97fc08c36b53067f0e295197ab22915843880ae1db"},"schema_version":"1.0","source":{"id":"math/0702728","kind":"arxiv","version":1}},"canonical_sha256":"c9cfcd97a7177372011b05f7dcdc6d40ce383e33355e3afafd651fd3a462dec9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9cfcd97a7177372011b05f7dcdc6d40ce383e33355e3afafd651fd3a462dec9","first_computed_at":"2026-05-18T04:31:12.504133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:12.504133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aJtXe+KVovrEfZzShW0V1K1ZLZdLrR9ck3OHOcUvKVVH494tJa69264qpvy2aotABwBlgYjPWeCP0McOtHZQCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:12.504771Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0702728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f76888273bd58143bfa6dea2de1805e322d34cef379e7cb75d634d593a0ad72","sha256:b24321fd84b05b7767de94706b7a013e308da307884174eba3e63c6ced0130f7"],"state_sha256":"810fddea3d42843aeb9865f158ea45c184c4fd376ee94f47fc4764fdb11c3d29"}