{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HFW77GODH2G5O2F4B5JQM4NEKH","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":"aa9fa11e5e71da0613137705ef7016414fa69b5851c03bd3cf82a08d17757390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-05-25T21:45:48Z","title_canon_sha256":"28b0f80378036c75e425a84b1aca2c867c49cd405ed9f191e4945243dff9182d"},"schema_version":"1.0","source":{"id":"1805.10373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.10373","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"arxiv_version","alias_value":"1805.10373v1","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10373","created_at":"2026-05-18T00:14:52Z"},{"alias_kind":"pith_short_12","alias_value":"HFW77GODH2G5","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HFW77GODH2G5O2F4","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HFW77GOD","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:43d9a31a18065e895de6c0a4ecd248c5090dedf4ab03216b7d95ff9bb2467f7e","target":"graph","created_at":"2026-05-18T00:14:52Z","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 characterize the submonoids $M$ of the additive monoid $\\Q_+$ of nonnegative rational numbers for which the irreducible and the prime elements in the monoid domain $F[X;M]$ coincide. We present a diagram of implications between some types of submonoids of $\\Q_+$, with a precise position of the monoids $M$ with this property.","authors_text":"Hamid Kulosman, Ryan Gipson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-05-25T21:45:48Z","title":"For which additive submonoids $M$ of nonnegative rationals is $F[X;M]$ AP?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10373","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":"sha256:3d5ef5274d79a906f3aedfe601b0a8d35bfad632cd64e561c4005892db0785fe","target":"record","created_at":"2026-05-18T00:14:52Z","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":"aa9fa11e5e71da0613137705ef7016414fa69b5851c03bd3cf82a08d17757390","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-05-25T21:45:48Z","title_canon_sha256":"28b0f80378036c75e425a84b1aca2c867c49cd405ed9f191e4945243dff9182d"},"schema_version":"1.0","source":{"id":"1805.10373","kind":"arxiv","version":1}},"canonical_sha256":"396dff99c33e8dd768bc0f530671a451eff15283ef0d1842cb7adcb02f071de6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"396dff99c33e8dd768bc0f530671a451eff15283ef0d1842cb7adcb02f071de6","first_computed_at":"2026-05-18T00:14:52.752908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:52.752908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PgAF591Q0JWlS36AJAiqOoBmA/zwi4SOQf3jUqh4l5kp/eWlSXR0rtmyi1LwK+nb3cg18nK1MTqEcw8F1Ar9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:52.753614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.10373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d5ef5274d79a906f3aedfe601b0a8d35bfad632cd64e561c4005892db0785fe","sha256:43d9a31a18065e895de6c0a4ecd248c5090dedf4ab03216b7d95ff9bb2467f7e"],"state_sha256":"c672be5555d73cb6c4c9137eb5d1495c5610e1fab411be1de72c94fa1c1d81a1"}