{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XOZSOZLMNSLPGREXW52V3PJ3SY","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":"ea1c46e1f86e7ee804dff87bd0a44c8ec973a829333dc5c0b2924669a41b6fc7","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2003-06-23T18:03:49Z","title_canon_sha256":"7d71955e69057fef92b86253662c7cf2cbfdcb7bf24a6ce452230838a8621146"},"schema_version":"1.0","source":{"id":"math/0306332","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0306332","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"math/0306332v2","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306332","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"XOZSOZLMNSLP","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XOZSOZLMNSLPGREX","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XOZSOZLM","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d6c369c41ec1ff219a1b49c7f38535663ab810a1434fcb705cacb68b80792b93","target":"graph","created_at":"2026-05-18T04:36:18Z","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 discuss general properties of $A_\\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\\infty$-algebras and cyclic $A_\\infty$-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic $A_\\infty$-isomorphic to each other. The same results h","authors_text":"Hiroshige Kajiura","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-06-23T18:03:49Z","title":"Noncommutative homotopy algebras associated with open strings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306332","kind":"arxiv","version":2},"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":"sha256:932b769d3f302cb122b5e91d87e59b12829f5440f128cb69b1cff58d6e6a32df","target":"record","created_at":"2026-05-18T04:36:18Z","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":"ea1c46e1f86e7ee804dff87bd0a44c8ec973a829333dc5c0b2924669a41b6fc7","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2003-06-23T18:03:49Z","title_canon_sha256":"7d71955e69057fef92b86253662c7cf2cbfdcb7bf24a6ce452230838a8621146"},"schema_version":"1.0","source":{"id":"math/0306332","kind":"arxiv","version":2}},"canonical_sha256":"bbb327656c6c96f34497b7755dbd3b9637b5e6ca9ef218b216f3f38bb882b130","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bbb327656c6c96f34497b7755dbd3b9637b5e6ca9ef218b216f3f38bb882b130","first_computed_at":"2026-05-18T04:36:18.958727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:18.958727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ITHkI4H3UZ1iencMq4+if0iwXi5X6x/Xfko3qbvRzLU5OUnw0q1FJrn4sOCMGRByGVFmfYhjTLM4vU2s2pcSCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:18.959284Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0306332","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:932b769d3f302cb122b5e91d87e59b12829f5440f128cb69b1cff58d6e6a32df","sha256:d6c369c41ec1ff219a1b49c7f38535663ab810a1434fcb705cacb68b80792b93"],"state_sha256":"1497d22a7d612e7d5d9ed9f2544a505b47b83e85d90b10968bcdd619281d16a5"}