{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:TYUIBTGX7E23FKTIXJBQYUI4AF","short_pith_number":"pith:TYUIBTGX","canonical_record":{"source":{"id":"2004.00780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-02T02:47:02Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1bd44c7174c861a0cd181a5510c03bf9a646550c55cd1478026396f233d06c2b","abstract_canon_sha256":"2efa2869afe41f1c07314be6292bfa8456d50005a64f0ffe4074369def751366"},"schema_version":"1.0"},"canonical_sha256":"9e2880ccd7f935b2aa68ba430c511c01728653e49f316f5b893d25395ccb2a77","source":{"kind":"arxiv","id":"2004.00780","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.00780","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"2004.00780v1","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.00780","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"TYUIBTGX7E23","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_16","alias_value":"TYUIBTGX7E23FKTI","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_8","alias_value":"TYUIBTGX","created_at":"2026-07-05T00:52:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:TYUIBTGX7E23FKTIXJBQYUI4AF","target":"record","payload":{"canonical_record":{"source":{"id":"2004.00780","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-02T02:47:02Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"1bd44c7174c861a0cd181a5510c03bf9a646550c55cd1478026396f233d06c2b","abstract_canon_sha256":"2efa2869afe41f1c07314be6292bfa8456d50005a64f0ffe4074369def751366"},"schema_version":"1.0"},"canonical_sha256":"9e2880ccd7f935b2aa68ba430c511c01728653e49f316f5b893d25395ccb2a77","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:52:20.643800Z","signature_b64":"VYxiQvV9JVekil6Bif7kd/RhfExItYFNnQemUjci1JSu5qMvtfGT5M7zaZzrxKGln/rn3suGPFOMMSTgzL/JBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9e2880ccd7f935b2aa68ba430c511c01728653e49f316f5b893d25395ccb2a77","last_reissued_at":"2026-07-05T00:52:20.643447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:52:20.643447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.00780","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":"2026-07-05T00:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lhTzhvZ+6wyiANpTFX/TUygDiCWMqqbmrZNymgRAe1jJPUXlLqsVgTAu1/xbQTkf8IyPbjNlqj8K7XedgI7CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:57:13.878909Z"},"content_sha256":"147e72ba2b7284febfbd9a29f0273ab301494907adf1d4d7e130fc7aa8ea71f1","schema_version":"1.0","event_id":"sha256:147e72ba2b7284febfbd9a29f0273ab301494907adf1d4d7e130fc7aa8ea71f1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:TYUIBTGX7E23FKTIXJBQYUI4AF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cup product on Hochschild cohomology of a family of quiver algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.RA","authors_text":"Tolulope Oke","submitted_at":"2020-04-02T02:47:02Z","abstract_excerpt":"Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where N is the ideal generated by homogeneous nilpotent elements. We explicitly construct non-nilpotent Hochschild cocycles which cannot be generated by lower homological degree elements, thus disproving the Snashall-Solberg finite generation conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.00780","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.00780/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:52:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZxB5JaFRATyYB7+ijf0pX+52HXNFTUv3Rrb2h81oZ93T9JKN6z1zrMSkdPVpD4QH5wpuIUAVmVRNso0Zlb0EAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T15:57:13.879277Z"},"content_sha256":"13c2b9b1173c91f0683aa07753fb63f169a4193762aa0f99e9360df0ea47f3ac","schema_version":"1.0","event_id":"sha256:13c2b9b1173c91f0683aa07753fb63f169a4193762aa0f99e9360df0ea47f3ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/bundle.json","state_url":"https://pith.science/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/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":"2026-07-06T15:57:13Z","links":{"resolver":"https://pith.science/pith/TYUIBTGX7E23FKTIXJBQYUI4AF","bundle":"https://pith.science/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/bundle.json","state":"https://pith.science/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TYUIBTGX7E23FKTIXJBQYUI4AF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:TYUIBTGX7E23FKTIXJBQYUI4AF","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":"2efa2869afe41f1c07314be6292bfa8456d50005a64f0ffe4074369def751366","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-02T02:47:02Z","title_canon_sha256":"1bd44c7174c861a0cd181a5510c03bf9a646550c55cd1478026396f233d06c2b"},"schema_version":"1.0","source":{"id":"2004.00780","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.00780","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"arxiv_version","alias_value":"2004.00780v1","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.00780","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_12","alias_value":"TYUIBTGX7E23","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_16","alias_value":"TYUIBTGX7E23FKTI","created_at":"2026-07-05T00:52:20Z"},{"alias_kind":"pith_short_8","alias_value":"TYUIBTGX","created_at":"2026-07-05T00:52:20Z"}],"graph_snapshots":[{"event_id":"sha256:13c2b9b1173c91f0683aa07753fb63f169a4193762aa0f99e9360df0ea47f3ac","target":"graph","created_at":"2026-07-05T00:52:20Z","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/2004.00780/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let k be a field, q in k. We derive a cup product formula on the Hochschild cohomology ring of a family Lambda_q of quiver algebras. Using this formula, we determine a subalgebra of k[x,y] isomorphic to Hochschild cohomology modulo N, where N is the ideal generated by homogeneous nilpotent elements. We explicitly construct non-nilpotent Hochschild cocycles which cannot be generated by lower homological degree elements, thus disproving the Snashall-Solberg finite generation conjecture.","authors_text":"Tolulope Oke","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-02T02:47:02Z","title":"Cup product on Hochschild cohomology of a family of quiver algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.00780","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":"sha256:147e72ba2b7284febfbd9a29f0273ab301494907adf1d4d7e130fc7aa8ea71f1","target":"record","created_at":"2026-07-05T00:52:20Z","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":"2efa2869afe41f1c07314be6292bfa8456d50005a64f0ffe4074369def751366","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2020-04-02T02:47:02Z","title_canon_sha256":"1bd44c7174c861a0cd181a5510c03bf9a646550c55cd1478026396f233d06c2b"},"schema_version":"1.0","source":{"id":"2004.00780","kind":"arxiv","version":1}},"canonical_sha256":"9e2880ccd7f935b2aa68ba430c511c01728653e49f316f5b893d25395ccb2a77","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e2880ccd7f935b2aa68ba430c511c01728653e49f316f5b893d25395ccb2a77","first_computed_at":"2026-07-05T00:52:20.643447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:52:20.643447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VYxiQvV9JVekil6Bif7kd/RhfExItYFNnQemUjci1JSu5qMvtfGT5M7zaZzrxKGln/rn3suGPFOMMSTgzL/JBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:52:20.643800Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.00780","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:147e72ba2b7284febfbd9a29f0273ab301494907adf1d4d7e130fc7aa8ea71f1","sha256:13c2b9b1173c91f0683aa07753fb63f169a4193762aa0f99e9360df0ea47f3ac"],"state_sha256":"dfbf07ecaf42fa12d9fc5b04067e2fca3970deff8a6597950128a164af9b090e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FlNCdslHX4/3baqDdciWjOf2zSgBbvhbf7/KSzd+1PBB4vV+dL9eMkgCWAvfi4DKdA+ChKbbV7ucp/KEnUh1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T15:57:13.881185Z","bundle_sha256":"4500f442562aa3e521f38e71fbd74dfe5e61aa19c89ff86cf30bd6895d3e54f3"}}