{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2IAJ4YLZ27K7KKR5UJFKE4ARQC","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":"4b844a2b459ba36fee5ba8cc610d7a27d999e194bc81266e06100201ab7d9e9b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-29T18:29:28Z","title_canon_sha256":"5930a047b22615791b6a4410982faf6c171ac16ca120ada8734ee616d9d57e69"},"schema_version":"1.0","source":{"id":"1604.08929","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.08929","created_at":"2026-05-18T01:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"1604.08929v2","created_at":"2026-05-18T01:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.08929","created_at":"2026-05-18T01:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"2IAJ4YLZ27K7","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2IAJ4YLZ27K7KKR5","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2IAJ4YLZ","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:b1f9e777b3f877bb56a7c66ca892854bb2d12e7ebf7a57c4e008a166aa26ff55","target":"graph","created_at":"2026-05-18T01:09:45Z","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 present procedures to calculate the set of Arf numerical semigroups with given genus, given conductor and given genus and conductor. We characterize the Kunz coordinates of an Arf numerical semigroup. We also describe Arf numerical semigroups with fixed Frobenius number and multiplicity up to six.","authors_text":"B. A. Heredia, H. \\.I. Karaka\\c{s}, J. C. Rosales, P. A. Garc\\'ia-S\\'anchez","cross_cats":["math.AG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-29T18:29:28Z","title":"Parametrizing Arf numerical semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.08929","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:aaafa4a98110f34fd29f67825a0aba9d5c7718ab308774c32766b208eb15121e","target":"record","created_at":"2026-05-18T01:09:45Z","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":"4b844a2b459ba36fee5ba8cc610d7a27d999e194bc81266e06100201ab7d9e9b","cross_cats_sorted":["math.AG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2016-04-29T18:29:28Z","title_canon_sha256":"5930a047b22615791b6a4410982faf6c171ac16ca120ada8734ee616d9d57e69"},"schema_version":"1.0","source":{"id":"1604.08929","kind":"arxiv","version":2}},"canonical_sha256":"d2009e6179d7d5f52a3da24aa2701180b1732c7bdee71a91d6568a24ddfa6adb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2009e6179d7d5f52a3da24aa2701180b1732c7bdee71a91d6568a24ddfa6adb","first_computed_at":"2026-05-18T01:09:45.335668Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:45.335668Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HnJqwfw4AVt2lMAP6Ejvc7NTQHBheKEpTYANjqU6MBetcr4KeVxffb+4/7gM9fyLHIWzUDq1swT6fDpvsWsBCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:45.336403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.08929","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaafa4a98110f34fd29f67825a0aba9d5c7718ab308774c32766b208eb15121e","sha256:b1f9e777b3f877bb56a7c66ca892854bb2d12e7ebf7a57c4e008a166aa26ff55"],"state_sha256":"ce9efcd2a83f5c9610dd0b2e232a66239701d68e25848fe943ee3bf7c3cc358e"}