{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QQPVP32KPESRQB2AGFS3IHS2DD","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":"749515cafe231bc30adbedde2198df92fef0d7c2f783d842266f3c164c9399d9","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-03-16T15:12:43Z","title_canon_sha256":"1c4c62adeee95a76e8471932475f40afa900e793e88d7b67052e264fec2b3ac8"},"schema_version":"1.0","source":{"id":"1503.04679","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.04679","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1503.04679v2","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.04679","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"QQPVP32KPESR","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QQPVP32KPESRQB2A","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QQPVP32K","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:1a2886e541f9253929a24987e9fca508bde86fcc7f39eb9221b9d405f718f896","target":"graph","created_at":"2026-05-17T23:50:34Z","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":"Let $H$ be a Krull monoid with class group $G$ such that every class contains a prime divisor. Then every nonunit $a \\in H$ can be written as a finite product of irreducible elements. If $a=u\\_1 \\cdot \\ldots \\cdot u\\_k$, with irreducibles $u\\_1, \\ldots u\\_k \\in H$, then $k$ is called the length of the factorization and the set $\\mathsf L (a)$ of all possible $k$ is called the set of lengths of $a$. It is well-known that the system $\\mathcal L (H) = \\{\\mathsf L (a) \\mid a \\in H \\}$ depends only on the class group $G$. In the present paper we study the inverse question asking whether or not the ","authors_text":"Alfred Geroldinger (IM), Wolfgang Schmid (LAGA)","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-03-16T15:12:43Z","title":"A characterization of class groups via sets of lengths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04679","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":"sha256:72bf77d07dbec7fade4d5ab0c6b3522b0f1f9b2748f6b6b2579758601951cb64","target":"record","created_at":"2026-05-17T23:50:34Z","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":"749515cafe231bc30adbedde2198df92fef0d7c2f783d842266f3c164c9399d9","cross_cats_sorted":["math.CO","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-03-16T15:12:43Z","title_canon_sha256":"1c4c62adeee95a76e8471932475f40afa900e793e88d7b67052e264fec2b3ac8"},"schema_version":"1.0","source":{"id":"1503.04679","kind":"arxiv","version":2}},"canonical_sha256":"841f57ef4a79251807403165b41e5a18ff4a647a9e7e90d5a1ad7c9f3f830adf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"841f57ef4a79251807403165b41e5a18ff4a647a9e7e90d5a1ad7c9f3f830adf","first_computed_at":"2026-05-17T23:50:34.576035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:34.576035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DyrN57LJl1fx9bXH8gp1PVr5SLfC1rz0VXpLVeZ+EQ+U5gka/PQmxKE4GodsDJaEF/ftW+zR6cQXY8V3i/FSCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:34.576691Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.04679","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72bf77d07dbec7fade4d5ab0c6b3522b0f1f9b2748f6b6b2579758601951cb64","sha256:1a2886e541f9253929a24987e9fca508bde86fcc7f39eb9221b9d405f718f896"],"state_sha256":"2de5c69fc9382d05c9c32f1f8216f64e810c437226ea67d9c3ed6557c8343e4c"}