{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SCDLSTO5QQ5KY6MCGBE3DCXRCG","short_pith_number":"pith:SCDLSTO5","canonical_record":{"source":{"id":"1511.08348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-26T10:40:55Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"175a086a2186b98276432baf4c4f634e81a51663194af1ff2eb65d439a18b044","abstract_canon_sha256":"4045ec466b35e30657764f3c5fae00d8b7805a228a9e934d7022c45547f0d861"},"schema_version":"1.0"},"canonical_sha256":"9086b94ddd843aac79823049b18af111adeb4e077ca4fe26dd728af2304bf43b","source":{"kind":"arxiv","id":"1511.08348","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08348","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08348v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08348","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"SCDLSTO5QQ5K","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SCDLSTO5QQ5KY6MC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SCDLSTO5","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SCDLSTO5QQ5KY6MCGBE3DCXRCG","target":"record","payload":{"canonical_record":{"source":{"id":"1511.08348","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-26T10:40:55Z","cross_cats_sorted":["math.KT","math.RA"],"title_canon_sha256":"175a086a2186b98276432baf4c4f634e81a51663194af1ff2eb65d439a18b044","abstract_canon_sha256":"4045ec466b35e30657764f3c5fae00d8b7805a228a9e934d7022c45547f0d861"},"schema_version":"1.0"},"canonical_sha256":"9086b94ddd843aac79823049b18af111adeb4e077ca4fe26dd728af2304bf43b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.871502Z","signature_b64":"St6BGwX4JAFxfiQ8PHJJxkI908S9jQ8aMm7tLi8SvCVbdZxZY5NmmVJQrrcn+BxA644gdSsfzIjUMhXh+G/dAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9086b94ddd843aac79823049b18af111adeb4e077ca4fe26dd728af2304bf43b","last_reissued_at":"2026-05-17T23:56:48.871126Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.871126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.08348","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"35/0GmlelkSbNmTi/ayr+27Sglnf09vn3ioXv4USKnn0tUzpDsC1wnJsEQ69MsrLrntpo5m1+D7cOd32hlYmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:43:35.223919Z"},"content_sha256":"8dedd44ebb0e18048aa67253d249d91ef736957807343775ed44abf84c4aa39e","schema_version":"1.0","event_id":"sha256:8dedd44ebb0e18048aa67253d249d91ef736957807343775ed44abf84c4aa39e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SCDLSTO5QQ5KY6MCGBE3DCXRCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tate-Hochschild Cohomology of Radical Square Zero Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RA"],"primary_cat":"math.RT","authors_text":"Zhengfang Wang","submitted_at":"2015-11-26T10:40:55Z","abstract_excerpt":"For algebras with radical square zero, we give a combinatorial description to the Tate-Hochschild cohomology. We compute the Gerstenhaber algebra structure on the Tate-Hochschild cohomology for some classes of such algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08348","kind":"arxiv","version":2},"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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uyburI93Md9McRkDI0sxSVqFK8oZtDlY3FTWwaNDcI/uFtjVFRR7Gs/lASuJk5GXuQXessNKv239y/JvAkghCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:43:35.224591Z"},"content_sha256":"069ae735ed0d7968c255c7c4a784c20b7ba70f2831e4a882f45715138c068450","schema_version":"1.0","event_id":"sha256:069ae735ed0d7968c255c7c4a784c20b7ba70f2831e4a882f45715138c068450"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/bundle.json","state_url":"https://pith.science/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/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":"2026-05-29T14:43:35Z","links":{"resolver":"https://pith.science/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG","bundle":"https://pith.science/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/bundle.json","state":"https://pith.science/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SCDLSTO5QQ5KY6MCGBE3DCXRCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SCDLSTO5QQ5KY6MCGBE3DCXRCG","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":"4045ec466b35e30657764f3c5fae00d8b7805a228a9e934d7022c45547f0d861","cross_cats_sorted":["math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-26T10:40:55Z","title_canon_sha256":"175a086a2186b98276432baf4c4f634e81a51663194af1ff2eb65d439a18b044"},"schema_version":"1.0","source":{"id":"1511.08348","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.08348","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1511.08348v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.08348","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"SCDLSTO5QQ5K","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"SCDLSTO5QQ5KY6MC","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"SCDLSTO5","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:069ae735ed0d7968c255c7c4a784c20b7ba70f2831e4a882f45715138c068450","target":"graph","created_at":"2026-05-17T23:56:48Z","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":"For algebras with radical square zero, we give a combinatorial description to the Tate-Hochschild cohomology. We compute the Gerstenhaber algebra structure on the Tate-Hochschild cohomology for some classes of such algebras.","authors_text":"Zhengfang Wang","cross_cats":["math.KT","math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-26T10:40:55Z","title":"Tate-Hochschild Cohomology of Radical Square Zero Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08348","kind":"arxiv","version":2},"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":"sha256:8dedd44ebb0e18048aa67253d249d91ef736957807343775ed44abf84c4aa39e","target":"record","created_at":"2026-05-17T23:56:48Z","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":"4045ec466b35e30657764f3c5fae00d8b7805a228a9e934d7022c45547f0d861","cross_cats_sorted":["math.KT","math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-11-26T10:40:55Z","title_canon_sha256":"175a086a2186b98276432baf4c4f634e81a51663194af1ff2eb65d439a18b044"},"schema_version":"1.0","source":{"id":"1511.08348","kind":"arxiv","version":2}},"canonical_sha256":"9086b94ddd843aac79823049b18af111adeb4e077ca4fe26dd728af2304bf43b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9086b94ddd843aac79823049b18af111adeb4e077ca4fe26dd728af2304bf43b","first_computed_at":"2026-05-17T23:56:48.871126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:48.871126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"St6BGwX4JAFxfiQ8PHJJxkI908S9jQ8aMm7tLi8SvCVbdZxZY5NmmVJQrrcn+BxA644gdSsfzIjUMhXh+G/dAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:48.871502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.08348","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dedd44ebb0e18048aa67253d249d91ef736957807343775ed44abf84c4aa39e","sha256:069ae735ed0d7968c255c7c4a784c20b7ba70f2831e4a882f45715138c068450"],"state_sha256":"b4fc9b27dc25896eca1d9debfbdee8690589e462539a1c71e6c8f098bbe45474"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lVvoD7N4yt5H/DQlyLJ6RV+Kuw2vobTa9HFuaGRqgSNfmEbn74Kk1cXIscYtc/YqCO9qxvsqnkdd8nlxxi+kCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:43:35.227936Z","bundle_sha256":"16f742684787a986ddab913b2691f0a6ae71effd6635aba22472d831a66f8039"}}