{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:UM7XI6KVVIBJZO2I22AJS24EUN","short_pith_number":"pith:UM7XI6KV","canonical_record":{"source":{"id":"1110.2347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-11T12:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"ca3dfe246dfdff9b41fb4a1e4850c661894b3b494a15b5b65bfbe57a52a26202","abstract_canon_sha256":"dfc2ed997361dd132787a2e4224744702dcf3d97aaed0a1ee6cf5c73e12d995e"},"schema_version":"1.0"},"canonical_sha256":"a33f747955aa029cbb48d680996b84a3457a26ee03979269f29a1397d2bd9d78","source":{"kind":"arxiv","id":"1110.2347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2347","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2347v1","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2347","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"pith_short_12","alias_value":"UM7XI6KVVIBJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UM7XI6KVVIBJZO2I","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UM7XI6KV","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:UM7XI6KVVIBJZO2I22AJS24EUN","target":"record","payload":{"canonical_record":{"source":{"id":"1110.2347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-11T12:29:52Z","cross_cats_sorted":[],"title_canon_sha256":"ca3dfe246dfdff9b41fb4a1e4850c661894b3b494a15b5b65bfbe57a52a26202","abstract_canon_sha256":"dfc2ed997361dd132787a2e4224744702dcf3d97aaed0a1ee6cf5c73e12d995e"},"schema_version":"1.0"},"canonical_sha256":"a33f747955aa029cbb48d680996b84a3457a26ee03979269f29a1397d2bd9d78","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:16.974469Z","signature_b64":"UQ659tE/Fjt9rvxl9pk5xh10OIsu5RKJtepvsWzE3+74dPgQVy7/TAQDPFkEYZXyKwV6YbVynV3/A/mDEtgACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a33f747955aa029cbb48d680996b84a3457a26ee03979269f29a1397d2bd9d78","last_reissued_at":"2026-05-18T04:11:16.973654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:16.973654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.2347","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y1ChyuLqVxg2LsUw8/BzDwTyOO5BJOBpDz9Y7byShtQvUMVcXk3rpnPY18E77CLEZ7o3uXJDqoQRqi0DNzPWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:57:41.211991Z"},"content_sha256":"db1ff4bf73d9d00b731b99fe4caec4ff5de3a05e86c23cf14d453fa4440adfac","schema_version":"1.0","event_id":"sha256:db1ff4bf73d9d00b731b99fe4caec4ff5de3a05e86c23cf14d453fa4440adfac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:UM7XI6KVVIBJZO2I22AJS24EUN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pre-Lie systems and obstruction to A_infty-structures over a ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Muriel Livernet (LAGA)","submitted_at":"2011-10-11T12:29:52Z","abstract_excerpt":"In this note, we prove an obstruction theorem for the existence of A infinite-structures over a commutative ring R on an algebra A associative up to homotopy, in terms of the Hochschild cohomology of the associative algebra H(A). The hidden purpose of the note is to show that there are no assumptions needed on the commutative ring R nor bounded assumptions on the complex A."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2347","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:11:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caIUMkFOVWhWG93WziyMqyR1MD+GIM6/mGkiCMHcJzGZK3ukT50qg0KzhutjVX5opa+rtShQePnPOGZRc22UBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:57:41.212341Z"},"content_sha256":"6560499d9e6c5a370cbeb529f96ee561284485b54930e9c5ea60af7dcbf9fc26","schema_version":"1.0","event_id":"sha256:6560499d9e6c5a370cbeb529f96ee561284485b54930e9c5ea60af7dcbf9fc26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UM7XI6KVVIBJZO2I22AJS24EUN/bundle.json","state_url":"https://pith.science/pith/UM7XI6KVVIBJZO2I22AJS24EUN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UM7XI6KVVIBJZO2I22AJS24EUN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-24T19:57:41Z","links":{"resolver":"https://pith.science/pith/UM7XI6KVVIBJZO2I22AJS24EUN","bundle":"https://pith.science/pith/UM7XI6KVVIBJZO2I22AJS24EUN/bundle.json","state":"https://pith.science/pith/UM7XI6KVVIBJZO2I22AJS24EUN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UM7XI6KVVIBJZO2I22AJS24EUN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UM7XI6KVVIBJZO2I22AJS24EUN","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":"dfc2ed997361dd132787a2e4224744702dcf3d97aaed0a1ee6cf5c73e12d995e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-11T12:29:52Z","title_canon_sha256":"ca3dfe246dfdff9b41fb4a1e4850c661894b3b494a15b5b65bfbe57a52a26202"},"schema_version":"1.0","source":{"id":"1110.2347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.2347","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"arxiv_version","alias_value":"1110.2347v1","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.2347","created_at":"2026-05-18T04:11:16Z"},{"alias_kind":"pith_short_12","alias_value":"UM7XI6KVVIBJ","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UM7XI6KVVIBJZO2I","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UM7XI6KV","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6560499d9e6c5a370cbeb529f96ee561284485b54930e9c5ea60af7dcbf9fc26","target":"graph","created_at":"2026-05-18T04:11:16Z","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":"In this note, we prove an obstruction theorem for the existence of A infinite-structures over a commutative ring R on an algebra A associative up to homotopy, in terms of the Hochschild cohomology of the associative algebra H(A). The hidden purpose of the note is to show that there are no assumptions needed on the commutative ring R nor bounded assumptions on the complex A.","authors_text":"Muriel Livernet (LAGA)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-11T12:29:52Z","title":"Pre-Lie systems and obstruction to A_infty-structures over a ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2347","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:db1ff4bf73d9d00b731b99fe4caec4ff5de3a05e86c23cf14d453fa4440adfac","target":"record","created_at":"2026-05-18T04:11:16Z","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":"dfc2ed997361dd132787a2e4224744702dcf3d97aaed0a1ee6cf5c73e12d995e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2011-10-11T12:29:52Z","title_canon_sha256":"ca3dfe246dfdff9b41fb4a1e4850c661894b3b494a15b5b65bfbe57a52a26202"},"schema_version":"1.0","source":{"id":"1110.2347","kind":"arxiv","version":1}},"canonical_sha256":"a33f747955aa029cbb48d680996b84a3457a26ee03979269f29a1397d2bd9d78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a33f747955aa029cbb48d680996b84a3457a26ee03979269f29a1397d2bd9d78","first_computed_at":"2026-05-18T04:11:16.973654Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:16.973654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UQ659tE/Fjt9rvxl9pk5xh10OIsu5RKJtepvsWzE3+74dPgQVy7/TAQDPFkEYZXyKwV6YbVynV3/A/mDEtgACA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:16.974469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.2347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db1ff4bf73d9d00b731b99fe4caec4ff5de3a05e86c23cf14d453fa4440adfac","sha256:6560499d9e6c5a370cbeb529f96ee561284485b54930e9c5ea60af7dcbf9fc26"],"state_sha256":"a25c605f87f6bb34cf9bb0cb5a479c889c4fb98c490f572fd6983a296c181637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IawlTZNPO6WVf7FT+dMOfnVzGX2i1J5UiKjjuJtlE+7fDNYnCKJda/rInNB6UXIh4hlUbyXq5euEACkPXA5TDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:57:41.214331Z","bundle_sha256":"45590c8a462349398dd310e45521e8a88f2955596630b3c5e4e90deb382bef45"}}