{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3KMWANBXEFLSDNFCU6PZDQTMDE","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":"682e2438ed15bbdf0b2ff63dc946e293ffb3a9d6f74e035dd6a05d098e4d02da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-04T19:11:12Z","title_canon_sha256":"a405efa4340ed638ddc3db160b8e28b330b8b50e23ef7603990beb25b83f3b63"},"schema_version":"1.0","source":{"id":"1512.01513","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01513","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01513v2","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01513","created_at":"2026-05-18T01:11:17Z"},{"alias_kind":"pith_short_12","alias_value":"3KMWANBXEFLS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3KMWANBXEFLSDNFC","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3KMWANBX","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:f490fa44dbb328b6b176e6ba450c8b3a3dd46af0d3d5fe79302b77c4f9f9d70d","target":"graph","created_at":"2026-05-18T01:11:17Z","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":"This work introduces a new kind of semigroup of $\\N^p$ called proportionally modular affine semigroup. These semigroups are defined by modular Diophantine inequalities and they are a generalization of proportionally modular numerical semigroups. We prove they are finitely generated and we give an algorithm to compute their minimal generating sets. We also specialise on the case $p=2$. For this case, we provide a faster algorithm to compute their minimal system of generators and we prove they are Cohen-Macaulay and Buchsbaum. Besides, the Gorenstein property is charactized, and their (minimal) ","authors_text":"A. Vigneron-Tenorio, J. I. Garc\\'ia-Garc\\'ia, M. A. Moreno-Fr\\'ias","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-04T19:11:12Z","title":"Proportionally modular affine semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01513","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:a4290ed292e306f4ab45517a2d3f819b919dbac37cbb0e1dd1d1e0888d3c6b98","target":"record","created_at":"2026-05-18T01:11:17Z","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":"682e2438ed15bbdf0b2ff63dc946e293ffb3a9d6f74e035dd6a05d098e4d02da","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-04T19:11:12Z","title_canon_sha256":"a405efa4340ed638ddc3db160b8e28b330b8b50e23ef7603990beb25b83f3b63"},"schema_version":"1.0","source":{"id":"1512.01513","kind":"arxiv","version":2}},"canonical_sha256":"da99603437215721b4a2a79f91c26c191f7db54bc2f914ea78e00dd403b7d27c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da99603437215721b4a2a79f91c26c191f7db54bc2f914ea78e00dd403b7d27c","first_computed_at":"2026-05-18T01:11:17.885428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:11:17.885428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u6Sx9C365Oiikg0ViWQ0lMV/IeofZ4wTD3/nVaP00kJJLkeanLyJsWuTu2JSkxhGys1hMoxu0IjMyNdSyKTQCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:11:17.886100Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01513","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4290ed292e306f4ab45517a2d3f819b919dbac37cbb0e1dd1d1e0888d3c6b98","sha256:f490fa44dbb328b6b176e6ba450c8b3a3dd46af0d3d5fe79302b77c4f9f9d70d"],"state_sha256":"b39ba5020c94c7914ddd07d291e5d0adc6c5009b173074a042c65275ef686d1d"}