{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4J4PU7HGIDNSPQZUU2TMCA7CTK","short_pith_number":"pith:4J4PU7HG","schema_version":"1.0","canonical_sha256":"e278fa7ce640db27c334a6a6c103e29a9f980c3999bd35bd068469e1d7d10b1a","source":{"kind":"arxiv","id":"1811.01038","version":1},"attestation_state":"computed","paper":{"title":"Semidualizing modules of $2 \\times 2$ ladder determinantal rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Sandra Spiroff, Sean K. Sather-Wagstaff, Tony Se","submitted_at":"2018-11-02T18:43:48Z","abstract_excerpt":"We continue our study of ladder determinantal rings over a field $\\mathsf k$ from the perspective of semidualizing modules. In particular, given a ladder of variables $Y$, we show that the associated ladder determinantal ring $\\mathsf k[Y]/I_2(Y)$ admits exactly $2^n$ non-isomorphic semidualizing modules where $n$ is determined from the combinatorics of the ladder $Y$: the number $n$ is essentially the number of non-Gorenstein factors in a certain decomposition of $Y$. From this, for each $n$, we show explicitly how to find ladders $Y$ such that $\\mathsf k[Y]/I_2(Y)$ admits exactly $2^n$ non-i"},"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":"1811.01038","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-11-02T18:43:48Z","cross_cats_sorted":[],"title_canon_sha256":"75f3f746696685f55d77f261efeb719181e264e45002544a0cf628f5bf02f438","abstract_canon_sha256":"38918bd6180a886e5067e484a0381380a4fa25da825303f729cc55ff947df473"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:37.221983Z","signature_b64":"vDdgzLMXleevkXQ99/f4tYKYfhaTkiroo22L453NmFibYssT1ntCy+BKLreBiYkvC2+qrqogUvcDVS/vrtwQBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e278fa7ce640db27c334a6a6c103e29a9f980c3999bd35bd068469e1d7d10b1a","last_reissued_at":"2026-05-18T00:01:37.221419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:37.221419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Semidualizing modules of $2 \\times 2$ ladder determinantal rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Sandra Spiroff, Sean K. Sather-Wagstaff, Tony Se","submitted_at":"2018-11-02T18:43:48Z","abstract_excerpt":"We continue our study of ladder determinantal rings over a field $\\mathsf k$ from the perspective of semidualizing modules. In particular, given a ladder of variables $Y$, we show that the associated ladder determinantal ring $\\mathsf k[Y]/I_2(Y)$ admits exactly $2^n$ non-isomorphic semidualizing modules where $n$ is determined from the combinatorics of the ladder $Y$: the number $n$ is essentially the number of non-Gorenstein factors in a certain decomposition of $Y$. From this, for each $n$, we show explicitly how to find ladders $Y$ such that $\\mathsf k[Y]/I_2(Y)$ admits exactly $2^n$ non-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01038","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":"1811.01038","created_at":"2026-05-18T00:01:37.221515+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.01038v1","created_at":"2026-05-18T00:01:37.221515+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01038","created_at":"2026-05-18T00:01:37.221515+00:00"},{"alias_kind":"pith_short_12","alias_value":"4J4PU7HGIDNS","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4J4PU7HGIDNSPQZU","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4J4PU7HG","created_at":"2026-05-18T12:32:05.422762+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/4J4PU7HGIDNSPQZUU2TMCA7CTK","json":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK.json","graph_json":"https://pith.science/api/pith-number/4J4PU7HGIDNSPQZUU2TMCA7CTK/graph.json","events_json":"https://pith.science/api/pith-number/4J4PU7HGIDNSPQZUU2TMCA7CTK/events.json","paper":"https://pith.science/paper/4J4PU7HG"},"agent_actions":{"view_html":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK","download_json":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK.json","view_paper":"https://pith.science/paper/4J4PU7HG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.01038&json=true","fetch_graph":"https://pith.science/api/pith-number/4J4PU7HGIDNSPQZUU2TMCA7CTK/graph.json","fetch_events":"https://pith.science/api/pith-number/4J4PU7HGIDNSPQZUU2TMCA7CTK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK/action/storage_attestation","attest_author":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK/action/author_attestation","sign_citation":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK/action/citation_signature","submit_replication":"https://pith.science/pith/4J4PU7HGIDNSPQZUU2TMCA7CTK/action/replication_record"}},"created_at":"2026-05-18T00:01:37.221515+00:00","updated_at":"2026-05-18T00:01:37.221515+00:00"}