{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EV6RXMF5VF775MG5SE33KDQFR3","short_pith_number":"pith:EV6RXMF5","canonical_record":{"source":{"id":"1403.1425","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-06T12:03:12Z","cross_cats_sorted":[],"title_canon_sha256":"97491fd65ef63f19adfae0161cbf66f9105607f9c89defe8dbede141c7dbd277","abstract_canon_sha256":"de650d09adc70a5d692500f3b1918f513e1cf0f9bcd4d96dd2c6971413294c72"},"schema_version":"1.0"},"canonical_sha256":"257d1bb0bda97ffeb0dd9137b50e058ef7a5420307a91bd4da07c8e87a138ebb","source":{"kind":"arxiv","id":"1403.1425","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1425","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1425v5","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1425","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"EV6RXMF5VF77","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EV6RXMF5VF775MG5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EV6RXMF5","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EV6RXMF5VF775MG5SE33KDQFR3","target":"record","payload":{"canonical_record":{"source":{"id":"1403.1425","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-06T12:03:12Z","cross_cats_sorted":[],"title_canon_sha256":"97491fd65ef63f19adfae0161cbf66f9105607f9c89defe8dbede141c7dbd277","abstract_canon_sha256":"de650d09adc70a5d692500f3b1918f513e1cf0f9bcd4d96dd2c6971413294c72"},"schema_version":"1.0"},"canonical_sha256":"257d1bb0bda97ffeb0dd9137b50e058ef7a5420307a91bd4da07c8e87a138ebb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:51.784854Z","signature_b64":"eBlhc7vILjPiOCRPOijEV7EKbI51BK7aGHxs/4pYwNBff2974ZuyTkiJdyoIn7HwcvL4LgGHgabwWHBERX2QBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"257d1bb0bda97ffeb0dd9137b50e058ef7a5420307a91bd4da07c8e87a138ebb","last_reissued_at":"2026-05-18T01:36:51.784175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:51.784175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.1425","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":"2026-05-18T01:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RTTBCWJfN3t1LUEqHNe01SrqRxdzwWy0fleNdGJaet+rUij63qrT10iY0oVbmFYnOjrX85g8oB0fgmb6bB+GAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:06:59.897189Z"},"content_sha256":"0a6f6b59ab972334588df973574e6053d5cb2dd6a0d03efeb14f9de43cd56042","schema_version":"1.0","event_id":"sha256:0a6f6b59ab972334588df973574e6053d5cb2dd6a0d03efeb14f9de43cd56042"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EV6RXMF5VF775MG5SE33KDQFR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohomology of finite groups without homological algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Nikolay N. Mostovsky, Sergei O. Ivanov","submitted_at":"2014-03-06T12:03:12Z","abstract_excerpt":"We prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$ and a commutative ring $k.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1425","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":"2026-05-18T01:36:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xgkn7+3BH4Xhl+4/gM0Ioew4STuCM+8iLWZRGqeSi+pdJU7VQORyOsdH18VYxeq6ZEsGkBqgRagxKIXNffvHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:06:59.897866Z"},"content_sha256":"7052d843951e5d5a39497ce0bbce7a6ec8b63739d56214446494eddb63056dc2","schema_version":"1.0","event_id":"sha256:7052d843951e5d5a39497ce0bbce7a6ec8b63739d56214446494eddb63056dc2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EV6RXMF5VF775MG5SE33KDQFR3/bundle.json","state_url":"https://pith.science/pith/EV6RXMF5VF775MG5SE33KDQFR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EV6RXMF5VF775MG5SE33KDQFR3/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":"2026-06-08T03:06:59Z","links":{"resolver":"https://pith.science/pith/EV6RXMF5VF775MG5SE33KDQFR3","bundle":"https://pith.science/pith/EV6RXMF5VF775MG5SE33KDQFR3/bundle.json","state":"https://pith.science/pith/EV6RXMF5VF775MG5SE33KDQFR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EV6RXMF5VF775MG5SE33KDQFR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EV6RXMF5VF775MG5SE33KDQFR3","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":"de650d09adc70a5d692500f3b1918f513e1cf0f9bcd4d96dd2c6971413294c72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-06T12:03:12Z","title_canon_sha256":"97491fd65ef63f19adfae0161cbf66f9105607f9c89defe8dbede141c7dbd277"},"schema_version":"1.0","source":{"id":"1403.1425","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.1425","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"arxiv_version","alias_value":"1403.1425v5","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.1425","created_at":"2026-05-18T01:36:51Z"},{"alias_kind":"pith_short_12","alias_value":"EV6RXMF5VF77","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EV6RXMF5VF775MG5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EV6RXMF5","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:7052d843951e5d5a39497ce0bbce7a6ec8b63739d56214446494eddb63056dc2","target":"graph","created_at":"2026-05-18T01:36:51Z","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 prove explicit and elementary formulas for the group homology and cohomology of a finite group with coefficients in any module. We describe in elementary terms the cohomology algebra $H^*(G,k)$ as a graded algebra for a finite group $G$ and a commutative ring $k.$","authors_text":"Nikolay N. Mostovsky, Sergei O. Ivanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-06T12:03:12Z","title":"Cohomology of finite groups without homological algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1425","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":"sha256:0a6f6b59ab972334588df973574e6053d5cb2dd6a0d03efeb14f9de43cd56042","target":"record","created_at":"2026-05-18T01:36:51Z","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":"de650d09adc70a5d692500f3b1918f513e1cf0f9bcd4d96dd2c6971413294c72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-03-06T12:03:12Z","title_canon_sha256":"97491fd65ef63f19adfae0161cbf66f9105607f9c89defe8dbede141c7dbd277"},"schema_version":"1.0","source":{"id":"1403.1425","kind":"arxiv","version":5}},"canonical_sha256":"257d1bb0bda97ffeb0dd9137b50e058ef7a5420307a91bd4da07c8e87a138ebb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"257d1bb0bda97ffeb0dd9137b50e058ef7a5420307a91bd4da07c8e87a138ebb","first_computed_at":"2026-05-18T01:36:51.784175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:51.784175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eBlhc7vILjPiOCRPOijEV7EKbI51BK7aGHxs/4pYwNBff2974ZuyTkiJdyoIn7HwcvL4LgGHgabwWHBERX2QBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:51.784854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.1425","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a6f6b59ab972334588df973574e6053d5cb2dd6a0d03efeb14f9de43cd56042","sha256:7052d843951e5d5a39497ce0bbce7a6ec8b63739d56214446494eddb63056dc2"],"state_sha256":"fbbdad5a85bc9f01179956156288396426607f49ed596e2a0941ca09bacc21d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MNUg9TcGHLl0WvNx6dOqcwuwBxhVYREfQ6XN3q+ILJoczvKZfQprclhqEpxgZhMEKVTXi/yKw64BZk1M1JHYBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:06:59.900711Z","bundle_sha256":"a042d5370bae7840feb7b946ed15bc313fead830476e435fa3f5791a49d926cc"}}