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All algebra structures on $E$ such that $\\pi : E \\to A$ becomes an algebra map are described and classified by an explicitly constructed global cohomological type object ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$. Any such algebra is isomorphic to a Hochschild product $A \\star V$, an algebra introduced as a generalization of a classical construction. We prove that ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$ is the coproduct of all non-abelian cohom"},"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":"1503.05364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-03-18T12:10:43Z","cross_cats_sorted":[],"title_canon_sha256":"3a9265393fb910096ef788a6a6bbe7739eb0e9d90545e08a2407e072907bc5e5","abstract_canon_sha256":"8ef99cad000bb1429114529054b5f4a708336d34f3c8d5b7ece0aebaa8439831"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:04.342641Z","signature_b64":"ylnP9YhGZJeHBPxPSxT5Yf+iofRjBAEiq7990W0Jbl/4RXEvh0VHeIm8oNg/MnI2SC7VxbNfIlEKgNns1ItQCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f53bf3cad22ed8e0338a58c1c48d1811826661c8d0fc2f5f2e1ccf0b5833e0c","last_reissued_at":"2026-05-18T00:52:04.342175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:04.342175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hochschild products and global non-abelian cohomology for algebras. 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