{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:5IMYUDT2MEDM2KQHITOXYWKBBQ","short_pith_number":"pith:5IMYUDT2","canonical_record":{"source":{"id":"1404.2667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-10T01:48:20Z","cross_cats_sorted":[],"title_canon_sha256":"2b938f74e2929ace42db6660f71bd3678ed761db278778442ad20de8c41650c8","abstract_canon_sha256":"ba00d9b87c2471fc3198622c37375ef82cd65b1a94cfa8ba52dd45da44122cc4"},"schema_version":"1.0"},"canonical_sha256":"ea198a0e7a6106cd2a0744dd7c59410c36618fd532faa2963ad55b3bfb93b2bb","source":{"kind":"arxiv","id":"1404.2667","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2667","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2667v1","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2667","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"5IMYUDT2MEDM","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5IMYUDT2MEDM2KQH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5IMYUDT2","created_at":"2026-05-18T12:28:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:5IMYUDT2MEDM2KQHITOXYWKBBQ","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-10T01:48:20Z","cross_cats_sorted":[],"title_canon_sha256":"2b938f74e2929ace42db6660f71bd3678ed761db278778442ad20de8c41650c8","abstract_canon_sha256":"ba00d9b87c2471fc3198622c37375ef82cd65b1a94cfa8ba52dd45da44122cc4"},"schema_version":"1.0"},"canonical_sha256":"ea198a0e7a6106cd2a0744dd7c59410c36618fd532faa2963ad55b3bfb93b2bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:29.862775Z","signature_b64":"zPldX1DKcOJj3nxz+rtIjx5kV5mDbtRKopukRUZVMAG3NGj1MsJw1ufWD1LHq/Fb+hNsExPSz98dc+Y+psPMCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea198a0e7a6106cd2a0744dd7c59410c36618fd532faa2963ad55b3bfb93b2bb","last_reissued_at":"2026-05-18T02:54:29.862306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:29.862306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2667","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":"2026-05-18T02:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gB9JGrYSH9Z5y/dpOSZlaxW35UYuhiNp34vLFp306oUH6IGS2bzIthOXBjwvN9eW+WR7NG7wTZWtrU0LF5xLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:08:33.970074Z"},"content_sha256":"b0a9b105bd0db4765fa0ac9c9ffff2a455fee9ce9a1cd4b3a28d49c21de74a9c","schema_version":"1.0","event_id":"sha256:b0a9b105bd0db4765fa0ac9c9ffff2a455fee9ce9a1cd4b3a28d49c21de74a9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:5IMYUDT2MEDM2KQHITOXYWKBBQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Operations on the Secondary Hochschild Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Alin Stancu, Mihai D. Staic","submitted_at":"2014-04-10T01:48:20Z","abstract_excerpt":"We show that the secondary Hochschild cohomology associated to a triple $(A,B,\\varepsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove the existence of the cup and Lie products, discuss the connection with extensions of $B$-algebras, and give a Hodge type decomposition of the secondary Hochschild cohomology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2667","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":"2026-05-18T02:54:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oL1pF2yh5oQ4YsAgoMOjJeTKwXx4gKR2F16S/BSSCSMfulaWs7woNmvcILD+k3EGyQRcmQjqAo1iJ4y4IQjVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T03:08:33.970425Z"},"content_sha256":"21cc1aefe95f263dd27c6cd3600f95606afe40f4bd93aa87d1811c46cf8c3c56","schema_version":"1.0","event_id":"sha256:21cc1aefe95f263dd27c6cd3600f95606afe40f4bd93aa87d1811c46cf8c3c56"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/bundle.json","state_url":"https://pith.science/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/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":"2026-06-21T03:08:33Z","links":{"resolver":"https://pith.science/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ","bundle":"https://pith.science/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/bundle.json","state":"https://pith.science/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5IMYUDT2MEDM2KQHITOXYWKBBQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5IMYUDT2MEDM2KQHITOXYWKBBQ","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":"ba00d9b87c2471fc3198622c37375ef82cd65b1a94cfa8ba52dd45da44122cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-10T01:48:20Z","title_canon_sha256":"2b938f74e2929ace42db6660f71bd3678ed761db278778442ad20de8c41650c8"},"schema_version":"1.0","source":{"id":"1404.2667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2667","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2667v1","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2667","created_at":"2026-05-18T02:54:29Z"},{"alias_kind":"pith_short_12","alias_value":"5IMYUDT2MEDM","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5IMYUDT2MEDM2KQH","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5IMYUDT2","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:21cc1aefe95f263dd27c6cd3600f95606afe40f4bd93aa87d1811c46cf8c3c56","target":"graph","created_at":"2026-05-18T02:54:29Z","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 show that the secondary Hochschild cohomology associated to a triple $(A,B,\\varepsilon)$ has several of the properties of the usual Hochschild cohomology. Among others, we prove the existence of the cup and Lie products, discuss the connection with extensions of $B$-algebras, and give a Hodge type decomposition of the secondary Hochschild cohomology.","authors_text":"Alin Stancu, Mihai D. Staic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-10T01:48:20Z","title":"Operations on the Secondary Hochschild Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2667","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:b0a9b105bd0db4765fa0ac9c9ffff2a455fee9ce9a1cd4b3a28d49c21de74a9c","target":"record","created_at":"2026-05-18T02:54:29Z","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":"ba00d9b87c2471fc3198622c37375ef82cd65b1a94cfa8ba52dd45da44122cc4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-04-10T01:48:20Z","title_canon_sha256":"2b938f74e2929ace42db6660f71bd3678ed761db278778442ad20de8c41650c8"},"schema_version":"1.0","source":{"id":"1404.2667","kind":"arxiv","version":1}},"canonical_sha256":"ea198a0e7a6106cd2a0744dd7c59410c36618fd532faa2963ad55b3bfb93b2bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea198a0e7a6106cd2a0744dd7c59410c36618fd532faa2963ad55b3bfb93b2bb","first_computed_at":"2026-05-18T02:54:29.862306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:29.862306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zPldX1DKcOJj3nxz+rtIjx5kV5mDbtRKopukRUZVMAG3NGj1MsJw1ufWD1LHq/Fb+hNsExPSz98dc+Y+psPMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:29.862775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0a9b105bd0db4765fa0ac9c9ffff2a455fee9ce9a1cd4b3a28d49c21de74a9c","sha256:21cc1aefe95f263dd27c6cd3600f95606afe40f4bd93aa87d1811c46cf8c3c56"],"state_sha256":"6a68410a1c628969a6340cf0f03ee978aa2741d07963c0cb160e182dbd0b5ac3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYa3JhHU4woidhu8AUjSl2VhF4wMfbO8UB/akAfYzs53w1UfxtVpFRbpL52z8SG/gwyrgFdlop7aB1pg9+j+AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T03:08:33.972279Z","bundle_sha256":"188f9bef65514b7a7dc93eef4c2c524eba4918e2185908f1e3b91228382ecdd7"}}