{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:2MB4PJEDHEILNSMKJ63MUYJGWP","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":"ee7fa279be609f1c344148ee476a44e43e5ec3f59296a27f17af8faece2b6bfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-09T21:34:17Z","title_canon_sha256":"c58251e2561cbd7ebfee93abbb17ecb6e7b81c8e357366c305295bbea1649d3e"},"schema_version":"1.0","source":{"id":"0902.1543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.1543","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"arxiv_version","alias_value":"0902.1543v1","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.1543","created_at":"2026-05-18T02:14:48Z"},{"alias_kind":"pith_short_12","alias_value":"2MB4PJEDHEIL","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"2MB4PJEDHEILNSMK","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"2MB4PJED","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:775278d5c8fe7e239aa4997bfa8bdb37fc88454246424736a81c702c9d238741","target":"graph","created_at":"2026-05-18T02:14:48Z","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 [5], P. Lecomte conjectured the existence of a natural and conformally invariant quantization. In [7], we gave a proof of this theorem thanks to the theory of Cartan connections. In this paper, we give an explicit formula for the natural and conformally invariant quantization of trace-free symbols thanks to the method used in [7] and to tools already used in [8] in the projective setting. This formula is extremely similar to the one giving the natural and projectively invariant quantization in [8].","authors_text":"F. Radoux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-09T21:34:17Z","title":"An explicit formula for the natural and conformally invariant quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.1543","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:bf4e11500a51f4966cc2c0b76b62ffb6b659ae73a599d9947089dbf3aa03a364","target":"record","created_at":"2026-05-18T02:14:48Z","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":"ee7fa279be609f1c344148ee476a44e43e5ec3f59296a27f17af8faece2b6bfa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-02-09T21:34:17Z","title_canon_sha256":"c58251e2561cbd7ebfee93abbb17ecb6e7b81c8e357366c305295bbea1649d3e"},"schema_version":"1.0","source":{"id":"0902.1543","kind":"arxiv","version":1}},"canonical_sha256":"d303c7a4833910b6c98a4fb6ca6126b3fea1ed09927d90f2cc0820d1e4f8c43a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d303c7a4833910b6c98a4fb6ca6126b3fea1ed09927d90f2cc0820d1e4f8c43a","first_computed_at":"2026-05-18T02:14:48.594464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:48.594464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lmZ5Nt5B43IB1rdD2ZLvMxMt/tbPkYGmUt+0wwGLP6E+6AszptB/oK/MEhVU3FxC8g/lOHJ/uRt75dnnGU5+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:48.595185Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.1543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf4e11500a51f4966cc2c0b76b62ffb6b659ae73a599d9947089dbf3aa03a364","sha256:775278d5c8fe7e239aa4997bfa8bdb37fc88454246424736a81c702c9d238741"],"state_sha256":"9d180c2885b09cf50590fd2c467293e2d363f4e541f7079ed5a16a6c03a8aea2"}