{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MPXAOEIHQTGHIN2U3OG7KPGUFN","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":"60d9e8cf8d41de313e25b85e061437003961bfad89d1a80c560770b9bb6546f8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-02T08:13:08Z","title_canon_sha256":"6309c42e35b4570b5322b70fc8502562d38da3d28f66e0fc0d3300164514c76f"},"schema_version":"1.0","source":{"id":"1907.01222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.01222","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"arxiv_version","alias_value":"1907.01222v1","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.01222","created_at":"2026-05-17T23:41:40Z"},{"alias_kind":"pith_short_12","alias_value":"MPXAOEIHQTGH","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"MPXAOEIHQTGHIN2U","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"MPXAOEIH","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:3373cdfd254a5651fcca13a73a9d7f2a38de1729c945fe27bc04ff6f5a39127b","target":"graph","created_at":"2026-05-17T23:41:40Z","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":"A simple way of computing the Ap\\'ery set of a numerical semigroup (or monoid) with respect to a generator, using Groebner bases, is presented, together with a generalization for affine semigroups. This computation allows us to calculate the type set and, henceforth, to check the Gorenstein condition which characterizes the symmetric numerical subgroups.","authors_text":"Guadalupe M\\'arquez-Campos, Ignacio Ojeda, Jos\\'e M. Tornero","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-02T08:13:08Z","title":"On the computation of the Ap\\'ery set of numerical monoids and affine semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.01222","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:ed8a87b6684b3438547e00a1c025fd7a57c9fad4a479544bb86a10600c8ebb21","target":"record","created_at":"2026-05-17T23:41:40Z","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":"60d9e8cf8d41de313e25b85e061437003961bfad89d1a80c560770b9bb6546f8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-07-02T08:13:08Z","title_canon_sha256":"6309c42e35b4570b5322b70fc8502562d38da3d28f66e0fc0d3300164514c76f"},"schema_version":"1.0","source":{"id":"1907.01222","kind":"arxiv","version":1}},"canonical_sha256":"63ee07110784cc743754db8df53cd42b7bcf64a5687079014ea37b8353164da3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63ee07110784cc743754db8df53cd42b7bcf64a5687079014ea37b8353164da3","first_computed_at":"2026-05-17T23:41:40.926841Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:40.926841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tEsoLD+yjmRR+48R3e6VO6Olh5hJ2h51gZAjUaoq8DKj7wxxS2umuMPqALt5nC3tmh7TdORoCyoRJAf+Sp+2BA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:40.927328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.01222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed8a87b6684b3438547e00a1c025fd7a57c9fad4a479544bb86a10600c8ebb21","sha256:3373cdfd254a5651fcca13a73a9d7f2a38de1729c945fe27bc04ff6f5a39127b"],"state_sha256":"fe8a145d820909546fd0c26f03f4bf795985a391bb5dd8ab0428a8b310edab93"}