{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ENMC4HOJ6D4Q63QHTBLSXE6YLF","short_pith_number":"pith:ENMC4HOJ","schema_version":"1.0","canonical_sha256":"23582e1dc9f0f90f6e0798572b93d859654dc85b83266e5ba9f8a929186f3ec2","source":{"kind":"arxiv","id":"1506.05223","version":1},"attestation_state":"computed","paper":{"title":"A Characterization of class groups via sets of lengths {II}","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alfred Geroldinger, Qinghai Zhong","submitted_at":"2015-06-17T07:23:57Z","abstract_excerpt":"Let $H$ be a Krull monoid with finite class group $G$ and suppose that every class contains a prime divisor. If an element $a \\in H$ has a factorization $a=u_1 \\cdot \\ldots \\cdot u_k$ into irreducible elements $u_1, \\ldots, u_k \\in H$, then $k$ is called the length of the factorization and the set $\\mathsf L (a)$ of all possible factorization lengths is the set of lengths of $a$. It is classical that the system $\\mathcal L (H) = \\{ \\mathsf L (a) \\mid a \\in H \\}$ of all sets of lengths depends only on the class group $G$, and a standing conjecture states that conversely the system $\\mathcal L ("},"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":"1506.05223","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.NT","submitted_at":"2015-06-17T07:23:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"0ff6e9ea23e14d6f246eaed1de225c00057af14c31e061a644a86fa1834901fe","abstract_canon_sha256":"349d57dac1ec9d19b9b8f0ba2842b30a57bc74517d81322ef6a0145dd24e8362"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:22.408058Z","signature_b64":"8HTm9Pfj5Oxr2DVbJLqAPZctq8lTP8V0TCLJNNeNH9eaQNRPkqvpHXBw7XLOAcciToEhxE0e/71NAMpstbK8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23582e1dc9f0f90f6e0798572b93d859654dc85b83266e5ba9f8a929186f3ec2","last_reissued_at":"2026-05-17T23:41:22.407404Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:22.407404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Characterization of class groups via sets of lengths {II}","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Alfred Geroldinger, Qinghai Zhong","submitted_at":"2015-06-17T07:23:57Z","abstract_excerpt":"Let $H$ be a Krull monoid with finite class group $G$ and suppose that every class contains a prime divisor. If an element $a \\in H$ has a factorization $a=u_1 \\cdot \\ldots \\cdot u_k$ into irreducible elements $u_1, \\ldots, u_k \\in H$, then $k$ is called the length of the factorization and the set $\\mathsf L (a)$ of all possible factorization lengths is the set of lengths of $a$. It is classical that the system $\\mathcal L (H) = \\{ \\mathsf L (a) \\mid a \\in H \\}$ of all sets of lengths depends only on the class group $G$, and a standing conjecture states that conversely the system $\\mathcal L ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05223","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":"1506.05223","created_at":"2026-05-17T23:41:22.407506+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.05223v1","created_at":"2026-05-17T23:41:22.407506+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05223","created_at":"2026-05-17T23:41:22.407506+00:00"},{"alias_kind":"pith_short_12","alias_value":"ENMC4HOJ6D4Q","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"ENMC4HOJ6D4Q63QH","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"ENMC4HOJ","created_at":"2026-05-18T12:29:19.899920+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/ENMC4HOJ6D4Q63QHTBLSXE6YLF","json":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF.json","graph_json":"https://pith.science/api/pith-number/ENMC4HOJ6D4Q63QHTBLSXE6YLF/graph.json","events_json":"https://pith.science/api/pith-number/ENMC4HOJ6D4Q63QHTBLSXE6YLF/events.json","paper":"https://pith.science/paper/ENMC4HOJ"},"agent_actions":{"view_html":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF","download_json":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF.json","view_paper":"https://pith.science/paper/ENMC4HOJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.05223&json=true","fetch_graph":"https://pith.science/api/pith-number/ENMC4HOJ6D4Q63QHTBLSXE6YLF/graph.json","fetch_events":"https://pith.science/api/pith-number/ENMC4HOJ6D4Q63QHTBLSXE6YLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF/action/storage_attestation","attest_author":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF/action/author_attestation","sign_citation":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF/action/citation_signature","submit_replication":"https://pith.science/pith/ENMC4HOJ6D4Q63QHTBLSXE6YLF/action/replication_record"}},"created_at":"2026-05-17T23:41:22.407506+00:00","updated_at":"2026-05-17T23:41:22.407506+00:00"}