{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DQCIMEVFUO3BVNWI5KBJMQTT5K","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":"13c25927023c6a3855b24f0cfcd91758bfd3b1e372a340e65966fc42fd238fe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-17T13:54:03Z","title_canon_sha256":"be9da6247e0f2e482074476bda188ff8e95f19443789518c2fe3e0577af322d8"},"schema_version":"1.0","source":{"id":"0909.3222","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.3222","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0909.3222v4","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.3222","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"DQCIMEVFUO3B","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DQCIMEVFUO3BVNWI","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DQCIMEVF","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8d1bdc73d0a4b5d33a5b8e8e824de97a5c4ba12e86be3827b04368a51520fdd5","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"This paper investigates if a differential graded algebra can have more than one $A_\\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\\infty$-structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave's notion of derived $A_\\infty$-algebras after introducing a notion of Hochschild cohomology that applies to this.","authors_text":"Constanze Roitzheim, Sarah Whitehouse","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-17T13:54:03Z","title":"Uniqueness of $A_\\infty$-structures and Hochschild cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3222","kind":"arxiv","version":4},"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:d936756d8855c22f6f83a624170b9a36ac0258136c7b726043e2372aa599d8bd","target":"record","created_at":"2026-05-18T02:41:51Z","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":"13c25927023c6a3855b24f0cfcd91758bfd3b1e372a340e65966fc42fd238fe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-09-17T13:54:03Z","title_canon_sha256":"be9da6247e0f2e482074476bda188ff8e95f19443789518c2fe3e0577af322d8"},"schema_version":"1.0","source":{"id":"0909.3222","kind":"arxiv","version":4}},"canonical_sha256":"1c048612a5a3b61ab6c8ea82964273ea94b00254480589d08634ee3d0a9390e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c048612a5a3b61ab6c8ea82964273ea94b00254480589d08634ee3d0a9390e1","first_computed_at":"2026-05-18T02:41:51.156566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.156566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s3M4OnvMAdvmY+NQTdWWk63QEadKN1h+LikdSsezvnEKdC/L6tHL4HqLew7F/k6XPzdKJFfVbsV0bRZ5889JCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.157146Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.3222","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d936756d8855c22f6f83a624170b9a36ac0258136c7b726043e2372aa599d8bd","sha256:8d1bdc73d0a4b5d33a5b8e8e824de97a5c4ba12e86be3827b04368a51520fdd5"],"state_sha256":"7fa1c53aee1602c373cd528c98b62a36873a80186fee09cfcba29c2530972aa5"}