{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DW7RTNJSSF3EUD4GNK6OMBCDDJ","short_pith_number":"pith:DW7RTNJS","canonical_record":{"source":{"id":"1610.00092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa","abstract_canon_sha256":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf"},"schema_version":"1.0"},"canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","source":{"kind":"arxiv","id":"1610.00092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00092v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"DW7RTNJSSF3E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DW7RTNJSSF3EUD4G","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DW7RTNJS","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DW7RTNJSSF3EUD4GNK6OMBCDDJ","target":"record","payload":{"canonical_record":{"source":{"id":"1610.00092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa","abstract_canon_sha256":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf"},"schema_version":"1.0"},"canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:31.884903Z","signature_b64":"kh6xA2875bBqmQInFEEZqkjl4F++wDzOOS+F2LLG2kLLVyqQAx17j56luE8ytPoZtlSKYQkYPp38DPjoMHCtCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","last_reissued_at":"2026-05-18T01:03:31.884443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:31.884443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.00092","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":"2026-05-18T01:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aCy+ARa/tSYRy1Oez7vWqd7MaEEqjurHyPaIApc6EF2DPkVtFrvvyc/htpg5ilsOYqe5XI2jViAncgUFNeFgCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:20:12.409932Z"},"content_sha256":"caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c","schema_version":"1.0","event_id":"sha256:caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DW7RTNJSSF3EUD4GNK6OMBCDDJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.GR","authors_text":"Constantin-Cosmin Todea","submitted_at":"2016-10-01T05:57:56Z","abstract_excerpt":"We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a Product Formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For k an algebraically closed field of characteristic p and G a finite group we prove an additive decomposition and a Product Formula for the cohomology algebra of a defect group of a block ideal of kG with coefficients in the source alg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00092","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":"2026-05-18T01:03:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bFdj0U9ZGHVmxmiHpXysW6/ppFMaIdqOUlbGflvU+Y1hrKjtmArpnBmFhjlevlz2HsTXjDmOAuPRh0btRdmRAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:20:12.410615Z"},"content_sha256":"09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932","schema_version":"1.0","event_id":"sha256:09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/bundle.json","state_url":"https://pith.science/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/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":"2026-06-05T01:20:12Z","links":{"resolver":"https://pith.science/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ","bundle":"https://pith.science/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/bundle.json","state":"https://pith.science/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DW7RTNJSSF3EUD4GNK6OMBCDDJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DW7RTNJSSF3EUD4GNK6OMBCDDJ","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":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa"},"schema_version":"1.0","source":{"id":"1610.00092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00092v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00092","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"DW7RTNJSSF3E","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DW7RTNJSSF3EUD4G","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DW7RTNJS","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932","target":"graph","created_at":"2026-05-18T01:03:31Z","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":"We give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a Product Formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For k an algebraically closed field of characteristic p and G a finite group we prove an additive decomposition and a Product Formula for the cohomology algebra of a defect group of a block ideal of kG with coefficients in the source alg","authors_text":"Constantin-Cosmin Todea","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title":"Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00092","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:caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c","target":"record","created_at":"2026-05-18T01:03:31Z","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":"bf3bedb4c22cc96dce7cac97c001aa1df16ac057efcfdc838a9d9eaff8cdfbaf","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-10-01T05:57:56Z","title_canon_sha256":"1e5a05e3924451af1bb7672d898f81cb1c4cb80911cb15c2629a104a5a2e3baa"},"schema_version":"1.0","source":{"id":"1610.00092","kind":"arxiv","version":1}},"canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1dbf19b53291764a0f866abce604431a70ab3db50303574f28a4459c8e586231","first_computed_at":"2026-05-18T01:03:31.884443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.884443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kh6xA2875bBqmQInFEEZqkjl4F++wDzOOS+F2LLG2kLLVyqQAx17j56luE8ytPoZtlSKYQkYPp38DPjoMHCtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.884903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caa738dae328eaa5e3bf1b4d1947a71c4a1dbad3330d9f0902c898a44d4dac3c","sha256:09fbcaba6f96eaffbd55f6f96a768585808569a2c13779d6b2b5f8f597f97932"],"state_sha256":"eac5b6c99167b401dae52ff6677f38767cee49399d729559ce62616ec803c578"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYWBc6aY5OsXk3ZBw5bzVuh5UgWpW4sjHkjG1z8PBfzWrKSuB2npDNtW+iYc2YeUZPACHGDMC8m3TJZqsss/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:20:12.414014Z","bundle_sha256":"2e059fb0739396cd45127f9bcc4fc4f0db3f5e4e6f9a86d03557b0938369b64d"}}