{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EN4KEJ6636UYSXNQGHUIZSMJLF","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":"2f60d544ada232deaefcf2c97a84726a8f7d911744bf01947b74e4eb48d3b35f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T10:48:37Z","title_canon_sha256":"a335dd85d6324804197f36ff614dadc15d0d9a357612bf2120ded632614a3bae"},"schema_version":"1.0","source":{"id":"1009.0385","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0385","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0385v3","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0385","created_at":"2026-05-18T04:18:44Z"},{"alias_kind":"pith_short_12","alias_value":"EN4KEJ6636UY","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EN4KEJ6636UYSXNQ","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EN4KEJ66","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:f43696946dadfc40a663ab5c401a34b5b2ddc8770f3501947860cd19131afa34","target":"graph","created_at":"2026-05-18T04:18:44Z","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":"In this work, we give a new method to compute the Hilbert basis of the semigroup of certain positive divisors supported on the exceptional divisor of a normal surface singularity. Our approach is purely combinatorial which permits to avoid the long calculation of the invariants of the ring as it is presented in the work of Altinok and Tosun.","authors_text":"Mesut Sahin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T10:48:37Z","title":"Hilbert basis of the Lipman semigroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0385","kind":"arxiv","version":3},"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":"sha256:6c88b4ebd01df9d39df5aedeb039d3390c5887682f3617ba21123de5005b0e13","target":"record","created_at":"2026-05-18T04:18:44Z","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":"2f60d544ada232deaefcf2c97a84726a8f7d911744bf01947b74e4eb48d3b35f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-02T10:48:37Z","title_canon_sha256":"a335dd85d6324804197f36ff614dadc15d0d9a357612bf2120ded632614a3bae"},"schema_version":"1.0","source":{"id":"1009.0385","kind":"arxiv","version":3}},"canonical_sha256":"2378a227dedfa9895db031e88cc9895972490a95e11e75d6869bc881e69d92b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2378a227dedfa9895db031e88cc9895972490a95e11e75d6869bc881e69d92b1","first_computed_at":"2026-05-18T04:18:44.998540Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:44.998540Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYr6nTLMFelBjvHABdV9B+VHyrN0ImT4hsQuC4Ssyrr9deErqjUXQX3emqIknAljj4kRZNlQLCqPPiv19l/4Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:44.999089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0385","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c88b4ebd01df9d39df5aedeb039d3390c5887682f3617ba21123de5005b0e13","sha256:f43696946dadfc40a663ab5c401a34b5b2ddc8770f3501947860cd19131afa34"],"state_sha256":"54cafbb999c388c1d9b0f874ce238fecd45d6fae6704e08dec4b40320ec91395"}