{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4B3SJVNG7MK5WLHBM32GWG2BLW","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":"64ce799ca63a5c79ef11326ab22810dc6a8cdab602063f29c83737e7ec715eb5","cross_cats_sorted":["cs.DM","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-05T15:44:27Z","title_canon_sha256":"d754d94ea6fa598431632218c84813f820505a99a03a4ea20cf626812f605ee5"},"schema_version":"1.0","source":{"id":"1211.0895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0895","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0895v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0895","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"4B3SJVNG7MK5","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4B3SJVNG7MK5WLHB","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4B3SJVNG","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:98a81383cd5188680d9e16303c80b370b07d496faaabdd7581a39f9a530e5f3f","target":"graph","created_at":"2026-05-18T03:41:31Z","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":"Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers belonging to the semigroup. In a first approach, only homogeneous patterns where analized. In this contribution we study conditions for an eventually non-homogeneous pattern to be admissible, and particularize this study to the case the independent term of the pattern is a multiple of the multiplicity of the semigroup. Moreover, for the so called strongly admis","authors_text":"Albert Vico-Oton, Maria Bras-Amor\\'os, Pedro A. Garc\\'ia-S\\'anchez","cross_cats":["cs.DM","math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-05T15:44:27Z","title":"Nonhomogeneous patterns on numerical semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0895","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:b2117d03810a377b2dba183dbc5d7fcc26bfbfd5b15f5382240b1733aa935f29","target":"record","created_at":"2026-05-18T03:41:31Z","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":"64ce799ca63a5c79ef11326ab22810dc6a8cdab602063f29c83737e7ec715eb5","cross_cats_sorted":["cs.DM","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-11-05T15:44:27Z","title_canon_sha256":"d754d94ea6fa598431632218c84813f820505a99a03a4ea20cf626812f605ee5"},"schema_version":"1.0","source":{"id":"1211.0895","kind":"arxiv","version":1}},"canonical_sha256":"e07724d5a6fb15db2ce166f46b1b415d80d178e11a381c4d3c7095573d7dcef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e07724d5a6fb15db2ce166f46b1b415d80d178e11a381c4d3c7095573d7dcef3","first_computed_at":"2026-05-18T03:41:31.310138Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:31.310138Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rhqepoj3HWciWxOtICdsblb2c0OUz87roYvFaGF9KHVaRLEa9ABVaS5/9idVerfIE+6CSI/orXOadlXIrhyJBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:31.310643Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2117d03810a377b2dba183dbc5d7fcc26bfbfd5b15f5382240b1733aa935f29","sha256:98a81383cd5188680d9e16303c80b370b07d496faaabdd7581a39f9a530e5f3f"],"state_sha256":"6f4ab4d8cb85788fe79ad060e02b710ee8b46be62e67bda3c59dcf0654c09a66"}