{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LMEKWYZXFTF6SWPOUTH4TEQQLX","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":"32ef702b216366100f10cd688c8f8b98887a67187502a096b9833420308361a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-01-22T03:29:36Z","title_canon_sha256":"be672c2a009a3079be0b53c64b9dd9d24e2ae5ee50336ae66f362d3df9ad0fcb"},"schema_version":"1.0","source":{"id":"1801.06943","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.06943","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.06943v1","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.06943","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"pith_short_12","alias_value":"LMEKWYZXFTF6","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LMEKWYZXFTF6SWPO","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LMEKWYZX","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:e0f2fbdfacaf6e53f03a65a2f26e1b003441fcc23172d17f0e8a593f58b2d718","target":"graph","created_at":"2026-05-18T00:25:22Z","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":"Given a graded module over a commutative ring, we define a dg-Lie algebra whose Maurer-Cartan elements are the strictly unital A-infinity algebra structures on that module. We use this to generalize Positselski's result that a curvature term on the bar construction compensates for a lack of augmentation, from a field to arbitrary commutative base ring. We also use this to show that the reduced Hochschild cochains control the strictly unital deformation functor. We motivate these results by giving a full development of the deformation theory of a nonunital A-infinity algebra.","authors_text":"Jesse Burke","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-01-22T03:29:36Z","title":"Strictly unital A-infinity algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06943","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":"sha256:968cb67ff09bdfc9bc75fb2a53bfa73a9410e7dab1fcb8076aee2ae8470abdc8","target":"record","created_at":"2026-05-18T00:25:22Z","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":"32ef702b216366100f10cd688c8f8b98887a67187502a096b9833420308361a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2018-01-22T03:29:36Z","title_canon_sha256":"be672c2a009a3079be0b53c64b9dd9d24e2ae5ee50336ae66f362d3df9ad0fcb"},"schema_version":"1.0","source":{"id":"1801.06943","kind":"arxiv","version":1}},"canonical_sha256":"5b08ab63372ccbe959eea4cfc992105dee2596c8848d8e1c81202b598af613d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b08ab63372ccbe959eea4cfc992105dee2596c8848d8e1c81202b598af613d2","first_computed_at":"2026-05-18T00:25:22.736708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:22.736708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WL4loJqubbLCNABfn5lv4gT9brDWMxYpg3ioaGzPPrW3i7Jut+x8MLLuH2F8Bm+W94sUCJytsnFXC5apJfQMDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:22.737389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.06943","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:968cb67ff09bdfc9bc75fb2a53bfa73a9410e7dab1fcb8076aee2ae8470abdc8","sha256:e0f2fbdfacaf6e53f03a65a2f26e1b003441fcc23172d17f0e8a593f58b2d718"],"state_sha256":"b4b44a0117acbd19514672c75d44e51e53babbc148d1f764a3adac804b017c91"}