{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:QT5OX7BEOQGQ45YGDK27AHKVTB","short_pith_number":"pith:QT5OX7BE","schema_version":"1.0","canonical_sha256":"84faebfc24740d0e77061ab5f01d55985527078b6deccd8333296075fc30d0f1","source":{"kind":"arxiv","id":"1212.5754","version":1},"attestation_state":"computed","paper":{"title":"Universal deformation rings of string modules over a certain symmetric special biserial algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2012-12-23T02:36:35Z","abstract_excerpt":"Let $\\k$ be an algebraically closed field, let $\\A$ be a finite dimensional $\\k$-algebra and let $V$ be a $\\A$-module with stable endomorphism ring isomorphic to $\\k$. If $\\A$ is self-injective then $V$ has a universal deformation ring $R(\\A,V)$, which is a complete local commutative Noetherian $\\k$-algebra with residue field $\\k$. Moreover, if $\\Lambda$ is also a Frobenius $\\k$-algebra then $R(\\A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $\\Ar$-modules whose stable endomorphism ring isomorphic to $\\k$, where $\\Ar$ is a symmetric spe"},"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":"1212.5754","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2012-12-23T02:36:35Z","cross_cats_sorted":[],"title_canon_sha256":"13802c0990cd0080be1cbfb2f5f509e9263001c03c1d7383308529db4955332d","abstract_canon_sha256":"eb24e27646cdac8b8694ec5d0560fe6eb71d6210cb9c0e7c788e06ba2169ab5f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:51.498552Z","signature_b64":"vAT5Iefa56T9eATcGoxxixCAPFT9cCcArb2SOUWh4WimovukNCLSsIkmulmFVTtWiaT1loHkQGohIc1EY/BXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"84faebfc24740d0e77061ab5f01d55985527078b6deccd8333296075fc30d0f1","last_reissued_at":"2026-05-18T03:37:51.497705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:51.497705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Universal deformation rings of string modules over a certain symmetric special biserial algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jose A. Velez-Marulanda","submitted_at":"2012-12-23T02:36:35Z","abstract_excerpt":"Let $\\k$ be an algebraically closed field, let $\\A$ be a finite dimensional $\\k$-algebra and let $V$ be a $\\A$-module with stable endomorphism ring isomorphic to $\\k$. If $\\A$ is self-injective then $V$ has a universal deformation ring $R(\\A,V)$, which is a complete local commutative Noetherian $\\k$-algebra with residue field $\\k$. Moreover, if $\\Lambda$ is also a Frobenius $\\k$-algebra then $R(\\A,V)$ is stable under syzygies. We use these facts to determine the universal deformation rings of string $\\Ar$-modules whose stable endomorphism ring isomorphic to $\\k$, where $\\Ar$ is a symmetric spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5754","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":"1212.5754","created_at":"2026-05-18T03:37:51.497814+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.5754v1","created_at":"2026-05-18T03:37:51.497814+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.5754","created_at":"2026-05-18T03:37:51.497814+00:00"},{"alias_kind":"pith_short_12","alias_value":"QT5OX7BEOQGQ","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"QT5OX7BEOQGQ45YG","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"QT5OX7BE","created_at":"2026-05-18T12:27:18.751474+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/QT5OX7BEOQGQ45YGDK27AHKVTB","json":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB.json","graph_json":"https://pith.science/api/pith-number/QT5OX7BEOQGQ45YGDK27AHKVTB/graph.json","events_json":"https://pith.science/api/pith-number/QT5OX7BEOQGQ45YGDK27AHKVTB/events.json","paper":"https://pith.science/paper/QT5OX7BE"},"agent_actions":{"view_html":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB","download_json":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB.json","view_paper":"https://pith.science/paper/QT5OX7BE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.5754&json=true","fetch_graph":"https://pith.science/api/pith-number/QT5OX7BEOQGQ45YGDK27AHKVTB/graph.json","fetch_events":"https://pith.science/api/pith-number/QT5OX7BEOQGQ45YGDK27AHKVTB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB/action/storage_attestation","attest_author":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB/action/author_attestation","sign_citation":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB/action/citation_signature","submit_replication":"https://pith.science/pith/QT5OX7BEOQGQ45YGDK27AHKVTB/action/replication_record"}},"created_at":"2026-05-18T03:37:51.497814+00:00","updated_at":"2026-05-18T03:37:51.497814+00:00"}