{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:K3VPGMIYRR2YU7TG4JJ647L57K","short_pith_number":"pith:K3VPGMIY","canonical_record":{"source":{"id":"1608.05690","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-19T18:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"ff9216a2920ec7ddce770ffa67a9bbc5ccb6aa932a3b214e26363ac48370c581","abstract_canon_sha256":"fa142a27cabb002a21159ab7e7362b6740ac682d4146caca94eecf0f00c42c5d"},"schema_version":"1.0"},"canonical_sha256":"56eaf331188c758a7e66e253ee7d7dfab23e5f4a05b3a2f6167017f7e3f9be97","source":{"kind":"arxiv","id":"1608.05690","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05690","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05690v5","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05690","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"K3VPGMIYRR2Y","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K3VPGMIYRR2YU7TG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K3VPGMIY","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:K3VPGMIYRR2YU7TG4JJ647L57K","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05690","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-19T18:36:20Z","cross_cats_sorted":[],"title_canon_sha256":"ff9216a2920ec7ddce770ffa67a9bbc5ccb6aa932a3b214e26363ac48370c581","abstract_canon_sha256":"fa142a27cabb002a21159ab7e7362b6740ac682d4146caca94eecf0f00c42c5d"},"schema_version":"1.0"},"canonical_sha256":"56eaf331188c758a7e66e253ee7d7dfab23e5f4a05b3a2f6167017f7e3f9be97","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:53.530818Z","signature_b64":"5qpJvuhbRi6yfAg9UB8njkyvj+mRQdeOXXlB+QCytKO8ho8s9BUFueta39ve+eY3YnWmenLbwVwqCn4mJHhhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"56eaf331188c758a7e66e253ee7d7dfab23e5f4a05b3a2f6167017f7e3f9be97","last_reissued_at":"2026-05-18T00:41:53.530279Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:53.530279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05690","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dT8tCsQKnbkjE4+YjH47N3K4RqZDnbHsqqusJzHQBh5gG3DazZq0QzkaOpBKYvrnlMVB0D3+WExo9WBNS4KmBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:09:16.936977Z"},"content_sha256":"5e329191c5d951b168d060e9447ad46390cedb460bee8b64c103b490a3f706a6","schema_version":"1.0","event_id":"sha256:5e329191c5d951b168d060e9447ad46390cedb460bee8b64c103b490a3f706a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:K3VPGMIYRR2YU7TG4JJ647L57K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Singular Equivalences of Morita Type and Universal Deformation Rings for Gorenstein Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hernan Giraldo, Jose A. Velez-Marulanda, Viktor Bekkert","submitted_at":"2016-08-19T18:36:20Z","abstract_excerpt":"Let $\\Lambda$ be a finite-dimensional algebra over a fixed algebraically closed field $\\mathbf{k}$ of arbitrary characteristic, and let $V$ be a finitely generated $\\Lambda$-module. It follows from results previously obtained by F.M. Bleher and the third author that $V$ has a well-defined versal deformation ring $R(\\Lambda, V)$, which is a complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$. The third author also proved that if $\\Lambda$ is a Gorenstein $\\mathbf{k}$-algebra and $V$ is a Cohen-Macaulay $\\Lambda$-module whose stable endomorphism ring is iso"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05690","kind":"arxiv","version":5},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzDDW/o3PYTWpZP9oc28s4Xc9j/T4PHmGLfeH7ONqRY8FrbxTwSWE+0ZSZ2drhtn00ArbXYcsc3G9WIF9dlDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T11:09:16.937335Z"},"content_sha256":"c938e02359c9ff7edf6a0309149e9214d880da01174d1583eb8256d22bc5e56d","schema_version":"1.0","event_id":"sha256:c938e02359c9ff7edf6a0309149e9214d880da01174d1583eb8256d22bc5e56d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K3VPGMIYRR2YU7TG4JJ647L57K/bundle.json","state_url":"https://pith.science/pith/K3VPGMIYRR2YU7TG4JJ647L57K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K3VPGMIYRR2YU7TG4JJ647L57K/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-05T11:09:16Z","links":{"resolver":"https://pith.science/pith/K3VPGMIYRR2YU7TG4JJ647L57K","bundle":"https://pith.science/pith/K3VPGMIYRR2YU7TG4JJ647L57K/bundle.json","state":"https://pith.science/pith/K3VPGMIYRR2YU7TG4JJ647L57K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K3VPGMIYRR2YU7TG4JJ647L57K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:K3VPGMIYRR2YU7TG4JJ647L57K","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":"fa142a27cabb002a21159ab7e7362b6740ac682d4146caca94eecf0f00c42c5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-19T18:36:20Z","title_canon_sha256":"ff9216a2920ec7ddce770ffa67a9bbc5ccb6aa932a3b214e26363ac48370c581"},"schema_version":"1.0","source":{"id":"1608.05690","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05690","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05690v5","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05690","created_at":"2026-05-18T00:41:53Z"},{"alias_kind":"pith_short_12","alias_value":"K3VPGMIYRR2Y","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"K3VPGMIYRR2YU7TG","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"K3VPGMIY","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:c938e02359c9ff7edf6a0309149e9214d880da01174d1583eb8256d22bc5e56d","target":"graph","created_at":"2026-05-18T00:41:53Z","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 $\\Lambda$ be a finite-dimensional algebra over a fixed algebraically closed field $\\mathbf{k}$ of arbitrary characteristic, and let $V$ be a finitely generated $\\Lambda$-module. It follows from results previously obtained by F.M. Bleher and the third author that $V$ has a well-defined versal deformation ring $R(\\Lambda, V)$, which is a complete local commutative Noetherian $\\mathbf{k}$-algebra with residue field $\\mathbf{k}$. The third author also proved that if $\\Lambda$ is a Gorenstein $\\mathbf{k}$-algebra and $V$ is a Cohen-Macaulay $\\Lambda$-module whose stable endomorphism ring is iso","authors_text":"Hernan Giraldo, Jose A. Velez-Marulanda, Viktor Bekkert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-19T18:36:20Z","title":"On Singular Equivalences of Morita Type and Universal Deformation Rings for Gorenstein Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05690","kind":"arxiv","version":5},"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":"sha256:5e329191c5d951b168d060e9447ad46390cedb460bee8b64c103b490a3f706a6","target":"record","created_at":"2026-05-18T00:41:53Z","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":"fa142a27cabb002a21159ab7e7362b6740ac682d4146caca94eecf0f00c42c5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-08-19T18:36:20Z","title_canon_sha256":"ff9216a2920ec7ddce770ffa67a9bbc5ccb6aa932a3b214e26363ac48370c581"},"schema_version":"1.0","source":{"id":"1608.05690","kind":"arxiv","version":5}},"canonical_sha256":"56eaf331188c758a7e66e253ee7d7dfab23e5f4a05b3a2f6167017f7e3f9be97","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56eaf331188c758a7e66e253ee7d7dfab23e5f4a05b3a2f6167017f7e3f9be97","first_computed_at":"2026-05-18T00:41:53.530279Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:53.530279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5qpJvuhbRi6yfAg9UB8njkyvj+mRQdeOXXlB+QCytKO8ho8s9BUFueta39ve+eY3YnWmenLbwVwqCn4mJHhhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:53.530818Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05690","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e329191c5d951b168d060e9447ad46390cedb460bee8b64c103b490a3f706a6","sha256:c938e02359c9ff7edf6a0309149e9214d880da01174d1583eb8256d22bc5e56d"],"state_sha256":"ba3a36f018144f6eaa92d47c487495f715d738f81e45fac58d4b7f2a287e0d38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BkcFEHgubq9ZU6aeTJyonTiugbeQLzUj1Iy4RPCB2gm2lvA0ipAR79rdogTT/reKvnf1+FKCeGRk97lQJwhsDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T11:09:16.939231Z","bundle_sha256":"91c971aec593522f7168efa852aa37287a10f1d2e26b0272089e8daeae3b0531"}}