{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7AKIX47OJGU4OWY7LN5RHT6MLG","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":"84461e8942cdd7da9a4247834adede033b7fbea2977f84993646544edbd2bbc4","cross_cats_sorted":["math-ph","math.CO","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-09-28T17:58:37Z","title_canon_sha256":"4303273753d2fd73392aecb9c71bc39d9e660571d985ec2a2ec1e0605327e6cc"},"schema_version":"1.0","source":{"id":"2309.16664","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.16664","created_at":"2026-07-05T07:33:20Z"},{"alias_kind":"arxiv_version","alias_value":"2309.16664v2","created_at":"2026-07-05T07:33:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.16664","created_at":"2026-07-05T07:33:20Z"},{"alias_kind":"pith_short_12","alias_value":"7AKIX47OJGU4","created_at":"2026-07-05T07:33:20Z"},{"alias_kind":"pith_short_16","alias_value":"7AKIX47OJGU4OWY7","created_at":"2026-07-05T07:33:20Z"},{"alias_kind":"pith_short_8","alias_value":"7AKIX47O","created_at":"2026-07-05T07:33:20Z"}],"graph_snapshots":[{"event_id":"sha256:a18aa7834f10502679d5e03acc91d9327cecf82383be0a00cdadb3a74dbdb461","target":"graph","created_at":"2026-07-05T07:33:20Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2309.16664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The formula $\\star$ mod $\\bar{o}(\\hbar^k)$ of Kontsevich's star-product with harmonic propagators was known in full at $\\hbar^{k\\leqslant 6}$ since 2018 for generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We discover that the mechanism of associativity for the star-product up to $\\bar{o}(\\hbar^6)$ is different from the mechanism at order $7$ for both the full star-product and the affine star-product. Namely, at lower orders the needed consequences of the Jacobi identity are immediately obtained from the associator mod $\\bar{o}(\\hbar^6)$, whereas at order $\\hbar^7$ a","authors_text":"Arthemy V. Kiselev, Ricardo Buring","cross_cats":["math-ph","math.CO","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-09-28T17:58:37Z","title":"Associativity certificates for Kontsevich's star-product $\\star$ mod $\\bar{o}(\\hbar^k)$: $k\\leqslant 6$ unlike $k\\geqslant7$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.16664","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":"sha256:8a33d3bab57f6569c862c71a02d3e3a3220058a02e12824f8bf34588533dde25","target":"record","created_at":"2026-07-05T07:33:20Z","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":"84461e8942cdd7da9a4247834adede033b7fbea2977f84993646544edbd2bbc4","cross_cats_sorted":["math-ph","math.CO","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2023-09-28T17:58:37Z","title_canon_sha256":"4303273753d2fd73392aecb9c71bc39d9e660571d985ec2a2ec1e0605327e6cc"},"schema_version":"1.0","source":{"id":"2309.16664","kind":"arxiv","version":2}},"canonical_sha256":"f8148bf3ee49a9c75b1f5b7b13cfcc599900641b4e42d19c219bf9aa9c289069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8148bf3ee49a9c75b1f5b7b13cfcc599900641b4e42d19c219bf9aa9c289069","first_computed_at":"2026-07-05T07:33:20.068786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:20.068786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"52tTKJyrTsDX8PSLdWTfKmlXVsFX30LwYU0Quc7Rmz3NbdH0qpdbmEg/IcO+J+HZM6+sR7NLkEJkqZinwTzsAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:20.069198Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.16664","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a33d3bab57f6569c862c71a02d3e3a3220058a02e12824f8bf34588533dde25","sha256:a18aa7834f10502679d5e03acc91d9327cecf82383be0a00cdadb3a74dbdb461"],"state_sha256":"a5760f4f74cf05a265fe2401f5422aaae1201f7281ac6ed9c55c9f38418a1d6a"}