{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SWDQVHNGO3XTHZRTSIBAY35N7D","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":"665b71cb1e2be612b1e44e72f3da6a1ab7cafe3cded9d1eb54e1db9237c6ef26","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-07-09T11:24:08Z","title_canon_sha256":"576b55bffdaa44ab18b992bdd596f23ed30ffad680112c3db2d2bd270bfd686b"},"schema_version":"1.0","source":{"id":"0907.1505","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1505","created_at":"2026-05-18T04:14:46Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1505v2","created_at":"2026-05-18T04:14:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1505","created_at":"2026-05-18T04:14:46Z"},{"alias_kind":"pith_short_12","alias_value":"SWDQVHNGO3XT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SWDQVHNGO3XTHZRT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SWDQVHNG","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:18b0695be62a2f85d777e76923fc57d84fd32a7e85c36a1276535a2511880f66","target":"graph","created_at":"2026-05-18T04:14:46Z","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 investigate operads for various n-ary algebras. As a useful tool we introduce galgalim - analogs of the Lie-hedra for n-ary algebras. We then focus to algebras with one anti-associative operation. We describe the relevant part of the deformation cohomology for this type of algebras using the minimal model for the anti-associative operad. We also discuss free partially associative algebras and formulate some open problems.","authors_text":"Elisabeth Remm, Martin Markl","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-07-09T11:24:08Z","title":"(Non-)Koszulness of operads for n-ary algebras, galgalim and other curiosities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1505","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":"sha256:74910786f838192a164e9200eec8c4af2d041254f905238421158c1049fc684c","target":"record","created_at":"2026-05-18T04:14:46Z","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":"665b71cb1e2be612b1e44e72f3da6a1ab7cafe3cded9d1eb54e1db9237c6ef26","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-07-09T11:24:08Z","title_canon_sha256":"576b55bffdaa44ab18b992bdd596f23ed30ffad680112c3db2d2bd270bfd686b"},"schema_version":"1.0","source":{"id":"0907.1505","kind":"arxiv","version":2}},"canonical_sha256":"95870a9da676ef33e63392020c6fadf8e5e2b9733c05e6bae8d8d19900a00171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"95870a9da676ef33e63392020c6fadf8e5e2b9733c05e6bae8d8d19900a00171","first_computed_at":"2026-05-18T04:14:46.285249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:46.285249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ILSNxc0sgcSMZHimopHrWSxFoX2crMC6Q+puOJZ8VdG709/y+9D5YpZPAXnHP674wkP9PDIyQUYxelQhYkxWDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:46.285837Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.1505","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74910786f838192a164e9200eec8c4af2d041254f905238421158c1049fc684c","sha256:18b0695be62a2f85d777e76923fc57d84fd32a7e85c36a1276535a2511880f66"],"state_sha256":"080e8a52265b0d283e6e97d7a127d7dcb95231483f06a820e2d84cd8115a408d"}