{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UPSJM6H3X2Z6RU5E2IGL65SWE5","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":"0c14425b99077803c2f82ff03dd07cacb646c284aadf4ded51f818f41442d476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-07T14:25:20Z","title_canon_sha256":"1171c4f69cb6a978115d40196b01882235e7ddbfeda8a278a27a45b3828c63a8"},"schema_version":"1.0","source":{"id":"1105.1448","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1448","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1448v2","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1448","created_at":"2026-05-18T02:53:05Z"},{"alias_kind":"pith_short_12","alias_value":"UPSJM6H3X2Z6","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UPSJM6H3X2Z6RU5E","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UPSJM6H3","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:eb1ed64a29adf1e3a09d79de5ce78f6cda99fcbcb05e52cabbfcd2bc0ef5c628","target":"graph","created_at":"2026-05-18T02:53:05Z","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 consider the question of when a semigroup is the semigroup of a valuation dominating a two dimensional noetherian local domain, giving some surprising examples. We give a necessary and sufficient condition for the pair of a semigroup S and a field extension L/k to be the semigroup and residue field of a valaution dominating a regular local ring R of dimension two with residue field k, generalizing the theorem of Spivakovsky for the case when there is no residue field extension.","authors_text":"Pham An Vinh, Steven Dale Cutkosky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-07T14:25:20Z","title":"Valuation Semigroups of Two Dimensional Local Rings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1448","kind":"arxiv","version":2},"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":"sha256:6d6a02fb3f20884d03b531bd444d1785d78ce3d84e6de2c98880120a89ab7150","target":"record","created_at":"2026-05-18T02:53:05Z","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":"0c14425b99077803c2f82ff03dd07cacb646c284aadf4ded51f818f41442d476","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-05-07T14:25:20Z","title_canon_sha256":"1171c4f69cb6a978115d40196b01882235e7ddbfeda8a278a27a45b3828c63a8"},"schema_version":"1.0","source":{"id":"1105.1448","kind":"arxiv","version":2}},"canonical_sha256":"a3e49678fbbeb3e8d3a4d20cbf76562759860fbc305b21ed59188c5f59adc74a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3e49678fbbeb3e8d3a4d20cbf76562759860fbc305b21ed59188c5f59adc74a","first_computed_at":"2026-05-18T02:53:05.075283Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:05.075283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lOfRRnpQmEawI/mtrHl5vo3YTiWBH5dYUFOiRyg9ty33HLABLtCE3VX8MgtrPj1MPj9l70G9EACGQURzfMSoDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:05.075937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1448","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d6a02fb3f20884d03b531bd444d1785d78ce3d84e6de2c98880120a89ab7150","sha256:eb1ed64a29adf1e3a09d79de5ce78f6cda99fcbcb05e52cabbfcd2bc0ef5c628"],"state_sha256":"e96363226d27ae9b078aa0a6d9862683bef09e1ef81df689a47aa9383416a393"}