{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:V2XS5FJTWAO33FAYMK6V2YVCHY","short_pith_number":"pith:V2XS5FJT","schema_version":"1.0","canonical_sha256":"aeaf2e9533b01dbd941862bd5d62a23e2b78bdbbcfeac13722d0e3ca1e898a6a","source":{"kind":"arxiv","id":"1608.05466","version":2},"attestation_state":"computed","paper":{"title":"Higher Order Hochschild (Co)homology of Noncommutative Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.RA","authors_text":"Bruce R. Corrigan-Salter","submitted_at":"2016-08-19T00:53:05Z","abstract_excerpt":"Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the (co)homology of any commutative algebra with symmetric coefficient bimodules, however traditional Hochschild (co)homology is able to be computed for any associative algebra with not necessarily symmetric coefficient bimodules. In a previous paper, the author generalized higher order Hochschild cohomology for multimodule coefficients (which need not be symmetric"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1608.05466","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-08-19T00:53:05Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"e9da1082eb659316e749889117d8e08b600ba37fbf0a6d58990f25669dbcd802","abstract_canon_sha256":"3e8af0699f4d10babdfd6acc258e5cb1d0bb25a2ce1a23f75cbab86243d510b7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:10.929724Z","signature_b64":"QIpcpgcTK9DJCrA0zZidV6mNyaGZ6i7rQGp34KNF1mKS/fs6fntai3l0iNRBP0XbchB1uxedxgDjz0Tj9877AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aeaf2e9533b01dbd941862bd5d62a23e2b78bdbbcfeac13722d0e3ca1e898a6a","last_reissued_at":"2026-05-18T00:29:10.929227Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:10.929227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher Order Hochschild (Co)homology of Noncommutative Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.RA","authors_text":"Bruce R. Corrigan-Salter","submitted_at":"2016-08-19T00:53:05Z","abstract_excerpt":"Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the (co)homology of any commutative algebra with symmetric coefficient bimodules, however traditional Hochschild (co)homology is able to be computed for any associative algebra with not necessarily symmetric coefficient bimodules. In a previous paper, the author generalized higher order Hochschild cohomology for multimodule coefficients (which need not be symmetric"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05466","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1608.05466","created_at":"2026-05-18T00:29:10.929301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.05466v2","created_at":"2026-05-18T00:29:10.929301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05466","created_at":"2026-05-18T00:29:10.929301+00:00"},{"alias_kind":"pith_short_12","alias_value":"V2XS5FJTWAO3","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"V2XS5FJTWAO33FAY","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"V2XS5FJT","created_at":"2026-05-18T12:30:46.583412+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY","json":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY.json","graph_json":"https://pith.science/api/pith-number/V2XS5FJTWAO33FAYMK6V2YVCHY/graph.json","events_json":"https://pith.science/api/pith-number/V2XS5FJTWAO33FAYMK6V2YVCHY/events.json","paper":"https://pith.science/paper/V2XS5FJT"},"agent_actions":{"view_html":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY","download_json":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY.json","view_paper":"https://pith.science/paper/V2XS5FJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.05466&json=true","fetch_graph":"https://pith.science/api/pith-number/V2XS5FJTWAO33FAYMK6V2YVCHY/graph.json","fetch_events":"https://pith.science/api/pith-number/V2XS5FJTWAO33FAYMK6V2YVCHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY/action/storage_attestation","attest_author":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY/action/author_attestation","sign_citation":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY/action/citation_signature","submit_replication":"https://pith.science/pith/V2XS5FJTWAO33FAYMK6V2YVCHY/action/replication_record"}},"created_at":"2026-05-18T00:29:10.929301+00:00","updated_at":"2026-05-18T00:29:10.929301+00:00"}