{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:XFOMEUQET7U3YGQQS3SGGTFE46","short_pith_number":"pith:XFOMEUQE","schema_version":"1.0","canonical_sha256":"b95cc252049fe9bc1a1096e4634ca4e7b9a9a0497bf8e9e19399db42ea529218","source":{"kind":"arxiv","id":"1807.11885","version":1},"attestation_state":"computed","paper":{"title":"Inside factorial monoids and the cale monoid of a single Diophantine equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"David Llena, Pedro A. Garc\\'ia-S\\'anchez, Ulrich Krause","submitted_at":"2018-07-31T15:56:40Z","abstract_excerpt":"We give a structure theorem for inside factorial domains. As an example we study the monoid of nonnegative integer solutions of equations of the form $a_1x_1+\\cdots +a_{r-1}x_{r-1}=a_rx_r$, with $a_1,\\ldots,a_r$ positive integers. This set is isomorphic to a simplicial full affine semigroup, and thus it can be described in terms of its extremal rays and the Ap\\'ery sets with respect to the extremal rays."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.11885","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-07-31T15:56:40Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"38df0ce96714c2ff642c509babcd709abf37551a737c92c45cdceafc0c8460f8","abstract_canon_sha256":"aceabc934d986ced3891432045ee56fee86a7173f63164100b548a56afa1e4f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:20.856036Z","signature_b64":"sTKJZMQt4kZc/bjDp/S7iRAqd+7Al4fwEzppiE+THSgfi0jkahPw/C0Zlb1GEmGwlbPKWmFjqQ+xFaJBNSJGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b95cc252049fe9bc1a1096e4634ca4e7b9a9a0497bf8e9e19399db42ea529218","last_reissued_at":"2026-05-18T00:09:20.855308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:20.855308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Inside factorial monoids and the cale monoid of a single Diophantine equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AC","authors_text":"David Llena, Pedro A. Garc\\'ia-S\\'anchez, Ulrich Krause","submitted_at":"2018-07-31T15:56:40Z","abstract_excerpt":"We give a structure theorem for inside factorial domains. As an example we study the monoid of nonnegative integer solutions of equations of the form $a_1x_1+\\cdots +a_{r-1}x_{r-1}=a_rx_r$, with $a_1,\\ldots,a_r$ positive integers. This set is isomorphic to a simplicial full affine semigroup, and thus it can be described in terms of its extremal rays and the Ap\\'ery sets with respect to the extremal rays."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11885","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.11885","created_at":"2026-05-18T00:09:20.855440+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.11885v1","created_at":"2026-05-18T00:09:20.855440+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11885","created_at":"2026-05-18T00:09:20.855440+00:00"},{"alias_kind":"pith_short_12","alias_value":"XFOMEUQET7U3","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"XFOMEUQET7U3YGQQ","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"XFOMEUQE","created_at":"2026-05-18T12:33:01.666342+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46","json":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46.json","graph_json":"https://pith.science/api/pith-number/XFOMEUQET7U3YGQQS3SGGTFE46/graph.json","events_json":"https://pith.science/api/pith-number/XFOMEUQET7U3YGQQS3SGGTFE46/events.json","paper":"https://pith.science/paper/XFOMEUQE"},"agent_actions":{"view_html":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46","download_json":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46.json","view_paper":"https://pith.science/paper/XFOMEUQE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.11885&json=true","fetch_graph":"https://pith.science/api/pith-number/XFOMEUQET7U3YGQQS3SGGTFE46/graph.json","fetch_events":"https://pith.science/api/pith-number/XFOMEUQET7U3YGQQS3SGGTFE46/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46/action/storage_attestation","attest_author":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46/action/author_attestation","sign_citation":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46/action/citation_signature","submit_replication":"https://pith.science/pith/XFOMEUQET7U3YGQQS3SGGTFE46/action/replication_record"}},"created_at":"2026-05-18T00:09:20.855440+00:00","updated_at":"2026-05-18T00:09:20.855440+00:00"}