{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:7LCLK7QNM35KEJKZYIC3WYZ5LK","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":"78278e517c93f514d5b2ed9ff4b623930a298a8da9f57beb96fcc46f6e337e55","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-24T21:59:39Z","title_canon_sha256":"da03adf21f7a1817fc0ff3c7f327ef153af3c3a5c80972bf7c4983e9936c1c92"},"schema_version":"1.0","source":{"id":"2504.17957","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.17957","created_at":"2026-07-05T11:56:03Z"},{"alias_kind":"arxiv_version","alias_value":"2504.17957v4","created_at":"2026-07-05T11:56:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.17957","created_at":"2026-07-05T11:56:03Z"},{"alias_kind":"pith_short_12","alias_value":"7LCLK7QNM35K","created_at":"2026-07-05T11:56:03Z"},{"alias_kind":"pith_short_16","alias_value":"7LCLK7QNM35KEJKZ","created_at":"2026-07-05T11:56:03Z"},{"alias_kind":"pith_short_8","alias_value":"7LCLK7QN","created_at":"2026-07-05T11:56:03Z"}],"graph_snapshots":[{"event_id":"sha256:be7bd979ad505363edcbed85c2ba4511d8836c67845b3338f7200c6bfff72980","target":"graph","created_at":"2026-07-05T11:56:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.17957/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $R$ be an order in a number field whose conductor ideal $P := (R:\\overline{R})$ is prime in the ring of integers $\\overline{R}$. In this paper, we explore the factorization properties of such orders. Most notably, we give a complete characterization of the elasticity of $R$ in terms of its class group. We conclude with an application to the computation of class groups of certain orders.","authors_text":"Grant Moles, Jared Kettinger","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-24T21:59:39Z","title":"Elasticity of Orders with Prime Conductor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17957","kind":"arxiv","version":4},"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":"sha256:6d229471e0a7d8f151d3961f89d507d3896139e80957aafcac1e968e8c18b3de","target":"record","created_at":"2026-07-05T11:56:03Z","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":"78278e517c93f514d5b2ed9ff4b623930a298a8da9f57beb96fcc46f6e337e55","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AC","submitted_at":"2025-04-24T21:59:39Z","title_canon_sha256":"da03adf21f7a1817fc0ff3c7f327ef153af3c3a5c80972bf7c4983e9936c1c92"},"schema_version":"1.0","source":{"id":"2504.17957","kind":"arxiv","version":4}},"canonical_sha256":"fac4b57e0d66faa22559c205bb633d5ab05c26ab8ab93abed7e0aa52609c02b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fac4b57e0d66faa22559c205bb633d5ab05c26ab8ab93abed7e0aa52609c02b9","first_computed_at":"2026-07-05T11:56:03.340677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:56:03.340677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1npNMhH9LI9Jd32w/6/WewPzzeJeM/BiDKKxBIuy/9cCkarFswUWHfMdzr0QfU+e+SWKx7981j+Z2wD6/P2gBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:56:03.341149Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.17957","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d229471e0a7d8f151d3961f89d507d3896139e80957aafcac1e968e8c18b3de","sha256:be7bd979ad505363edcbed85c2ba4511d8836c67845b3338f7200c6bfff72980"],"state_sha256":"8a70b5541e3fb77d115710084cab500e37bd54d07a5b5a18b7f9138b89790c67"}