{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:N2S3HEWPFK367AYYRLG5RFFOOB","short_pith_number":"pith:N2S3HEWP","canonical_record":{"source":{"id":"1905.01506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-04T14:52:14Z","cross_cats_sorted":[],"title_canon_sha256":"b42e4c1ae348c9d09d3b0804481375f5b73dabc35cd4b48701e4cbcdceca4d88","abstract_canon_sha256":"0bc61069d7d3a6120987921ca75e9964a8d9d3773cbc11c1c643aa844698a5f7"},"schema_version":"1.0"},"canonical_sha256":"6ea5b392cf2ab7ef83188acdd894ae706f4a7dba14a684a3a44bdc7cef60ee7c","source":{"kind":"arxiv","id":"1905.01506","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01506","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01506v1","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01506","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"N2S3HEWPFK36","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N2S3HEWPFK367AYY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N2S3HEWP","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:N2S3HEWPFK367AYYRLG5RFFOOB","target":"record","payload":{"canonical_record":{"source":{"id":"1905.01506","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-04T14:52:14Z","cross_cats_sorted":[],"title_canon_sha256":"b42e4c1ae348c9d09d3b0804481375f5b73dabc35cd4b48701e4cbcdceca4d88","abstract_canon_sha256":"0bc61069d7d3a6120987921ca75e9964a8d9d3773cbc11c1c643aa844698a5f7"},"schema_version":"1.0"},"canonical_sha256":"6ea5b392cf2ab7ef83188acdd894ae706f4a7dba14a684a3a44bdc7cef60ee7c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:58.363734Z","signature_b64":"n8Gs080/YHGP1j0vqa5lMbvntotzE/gRgEBU9WA52ALeE29l0XUYWwqauAnzfFYF0kKXhtFqgrGKoht/+ADzAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ea5b392cf2ab7ef83188acdd894ae706f4a7dba14a684a3a44bdc7cef60ee7c","last_reissued_at":"2026-05-17T23:46:58.363155Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:58.363155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.01506","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dAmGu03FIQy7yunsrK+zxQc/cOjhhqsvrKdRxaVakMRcb42Lq/3QBhJP2f/ZD7MkU9SMi2TxemQ5yJvUMl/lCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:58:41.430546Z"},"content_sha256":"1e9931001a96283046a3cfaa0b4bf122d34b412f602e582ad696e6896cd314e7","schema_version":"1.0","event_id":"sha256:1e9931001a96283046a3cfaa0b4bf122d34b412f602e582ad696e6896cd314e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:N2S3HEWPFK367AYYRLG5RFFOOB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local duality for the singularity category of a finite dimensional Gorenstein algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar","submitted_at":"2019-05-04T14:52:14Z","abstract_excerpt":"A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\\mathfrak{p}$-local and $\\mathfrak{p}$-torsion subcategories of the derived category, for each homogeneous prime ideal $\\mathfrak{p}$ arising from the action of a commutative ring via Hochschild cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01506","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXqas2gXCt1NdSwGqFzfz7a1AqNfWwp+KQAG/p+kkUa7cpRChHsfjPv1EUOwQSZftr+pjIZJZX0KYzhqPx+MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T04:58:41.430892Z"},"content_sha256":"abd965f9d4bf7614bb71f674112c42a5a7bddd9e143eb147129fc5fbaa33828c","schema_version":"1.0","event_id":"sha256:abd965f9d4bf7614bb71f674112c42a5a7bddd9e143eb147129fc5fbaa33828c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N2S3HEWPFK367AYYRLG5RFFOOB/bundle.json","state_url":"https://pith.science/pith/N2S3HEWPFK367AYYRLG5RFFOOB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N2S3HEWPFK367AYYRLG5RFFOOB/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":"2026-06-12T04:58:41Z","links":{"resolver":"https://pith.science/pith/N2S3HEWPFK367AYYRLG5RFFOOB","bundle":"https://pith.science/pith/N2S3HEWPFK367AYYRLG5RFFOOB/bundle.json","state":"https://pith.science/pith/N2S3HEWPFK367AYYRLG5RFFOOB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N2S3HEWPFK367AYYRLG5RFFOOB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:N2S3HEWPFK367AYYRLG5RFFOOB","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":"0bc61069d7d3a6120987921ca75e9964a8d9d3773cbc11c1c643aa844698a5f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-04T14:52:14Z","title_canon_sha256":"b42e4c1ae348c9d09d3b0804481375f5b73dabc35cd4b48701e4cbcdceca4d88"},"schema_version":"1.0","source":{"id":"1905.01506","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.01506","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1905.01506v1","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.01506","created_at":"2026-05-17T23:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"N2S3HEWPFK36","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"N2S3HEWPFK367AYY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"N2S3HEWP","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:abd965f9d4bf7614bb71f674112c42a5a7bddd9e143eb147129fc5fbaa33828c","target":"graph","created_at":"2026-05-17T23:46:58Z","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":"A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander-Reiten triangles for the $\\mathfrak{p}$-local and $\\mathfrak{p}$-torsion subcategories of the derived category, for each homogeneous prime ideal $\\mathfrak{p}$ arising from the action of a commutative ring via Hochschild cohomology.","authors_text":"Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-04T14:52:14Z","title":"Local duality for the singularity category of a finite dimensional Gorenstein algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.01506","kind":"arxiv","version":1},"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":"sha256:1e9931001a96283046a3cfaa0b4bf122d34b412f602e582ad696e6896cd314e7","target":"record","created_at":"2026-05-17T23:46:58Z","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":"0bc61069d7d3a6120987921ca75e9964a8d9d3773cbc11c1c643aa844698a5f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2019-05-04T14:52:14Z","title_canon_sha256":"b42e4c1ae348c9d09d3b0804481375f5b73dabc35cd4b48701e4cbcdceca4d88"},"schema_version":"1.0","source":{"id":"1905.01506","kind":"arxiv","version":1}},"canonical_sha256":"6ea5b392cf2ab7ef83188acdd894ae706f4a7dba14a684a3a44bdc7cef60ee7c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ea5b392cf2ab7ef83188acdd894ae706f4a7dba14a684a3a44bdc7cef60ee7c","first_computed_at":"2026-05-17T23:46:58.363155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:58.363155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8Gs080/YHGP1j0vqa5lMbvntotzE/gRgEBU9WA52ALeE29l0XUYWwqauAnzfFYF0kKXhtFqgrGKoht/+ADzAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:58.363734Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.01506","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e9931001a96283046a3cfaa0b4bf122d34b412f602e582ad696e6896cd314e7","sha256:abd965f9d4bf7614bb71f674112c42a5a7bddd9e143eb147129fc5fbaa33828c"],"state_sha256":"aedc592b56f5713db288527887a7af6d71c44216ba14579acfbb9d858fac501c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hf1JE0gzD3zaabZz8hIDzOGvb0lnx5xCD1LjkD+UQjr44jhsj295WMfJxMgi21+KzHMfL++7yhOk+QytapYQAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T04:58:41.432855Z","bundle_sha256":"2dba6bbe12c906831153828cd885ba0b669288b1ecb755d5ff6fd4ad8e26ae98"}}