{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:JBTNTQ3KDT3JDL2XCLRHXJZLXE","short_pith_number":"pith:JBTNTQ3K","canonical_record":{"source":{"id":"0707.1412","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-07-10T11:26:06Z","cross_cats_sorted":[],"title_canon_sha256":"421836817b230e93c989dada979969850cbdd972681fd6a0d59e075030767461","abstract_canon_sha256":"de2575a03f1f54f6ec89196304d3636e2a1b841daf11d8ed5708b7fead23e06e"},"schema_version":"1.0"},"canonical_sha256":"4866d9c36a1cf691af5712e27ba72bb9098e357084f9331ef02b4ff885071f28","source":{"kind":"arxiv","id":"0707.1412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1412","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1412v1","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1412","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"JBTNTQ3KDT3J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JBTNTQ3KDT3JDL2X","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JBTNTQ3K","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:JBTNTQ3KDT3JDL2XCLRHXJZLXE","target":"record","payload":{"canonical_record":{"source":{"id":"0707.1412","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2007-07-10T11:26:06Z","cross_cats_sorted":[],"title_canon_sha256":"421836817b230e93c989dada979969850cbdd972681fd6a0d59e075030767461","abstract_canon_sha256":"de2575a03f1f54f6ec89196304d3636e2a1b841daf11d8ed5708b7fead23e06e"},"schema_version":"1.0"},"canonical_sha256":"4866d9c36a1cf691af5712e27ba72bb9098e357084f9331ef02b4ff885071f28","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:12.574502Z","signature_b64":"jGL1jcBD6iav4b7bRPHUgbIJGF2C47asJkXmhAB0AVKgs50AZN0Vr6mlxUnpkmEJhUIFZpjoJSbRwN1yjDMqAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4866d9c36a1cf691af5712e27ba72bb9098e357084f9331ef02b4ff885071f28","last_reissued_at":"2026-05-18T02:58:12.573701Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:12.573701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0707.1412","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":"2026-05-18T02:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WRIpq46K1emz66NiApHmo3y8JJ2YoCJUXD6m+D4PqAM8PvJuJuZ3A06l4AGrp8ogLSOThzEabP7ui9FwTgARBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:45:56.768664Z"},"content_sha256":"c638dda7e391a7b536bdd3a87659f78d30f3b5c49ced2e01d8321a82d2273a22","schema_version":"1.0","event_id":"sha256:c638dda7e391a7b536bdd3a87659f78d30f3b5c49ced2e01d8321a82d2273a22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:JBTNTQ3KDT3JDL2XCLRHXJZLXE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On natural and conformally equivariant quantizations","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"F. Radoux, P. Mathonet","submitted_at":"2007-07-10T11:26:06Z","abstract_excerpt":"The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in \\cite{DLO} for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold $M$, that depends on a pseudo-Riemannian metric, is natural and is invariant with respect to a conformal change of the metric. The existence of such a procedure was conjectured by P. Lecomte in \\cite{Leconj} and proved by C. Duva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1412","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":"2026-05-18T02:58:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4UbMnaYEKxCeu+ccADNr7Dy66DPuZ4Uwpc0Xg+N+JYwYcJUtvDNUiZAcFgl25qiID8h/DQx8YJ0GyzCHUjlgBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:45:56.769009Z"},"content_sha256":"38391b5239ed20b187f788a460772b917a1fce2025f431b6cee3d86cbcdf6155","schema_version":"1.0","event_id":"sha256:38391b5239ed20b187f788a460772b917a1fce2025f431b6cee3d86cbcdf6155"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/bundle.json","state_url":"https://pith.science/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/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":"2026-06-28T12:45:56Z","links":{"resolver":"https://pith.science/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE","bundle":"https://pith.science/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/bundle.json","state":"https://pith.science/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBTNTQ3KDT3JDL2XCLRHXJZLXE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:JBTNTQ3KDT3JDL2XCLRHXJZLXE","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":"de2575a03f1f54f6ec89196304d3636e2a1b841daf11d8ed5708b7fead23e06e","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-07-10T11:26:06Z","title_canon_sha256":"421836817b230e93c989dada979969850cbdd972681fd6a0d59e075030767461"},"schema_version":"1.0","source":{"id":"0707.1412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1412","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1412v1","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1412","created_at":"2026-05-18T02:58:12Z"},{"alias_kind":"pith_short_12","alias_value":"JBTNTQ3KDT3J","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"JBTNTQ3KDT3JDL2X","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"JBTNTQ3K","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:38391b5239ed20b187f788a460772b917a1fce2025f431b6cee3d86cbcdf6155","target":"graph","created_at":"2026-05-18T02:58:12Z","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":"The concept of conformally equivariant quantizations was introduced by Duval, Lecomte and Ovsienko in \\cite{DLO} for manifolds endowed with flat conformal structures. They obtained results of existence and uniqueness (up to normalization) of such a quantization procedure. A natural generalization of this concept is to seek for a quantization procedure, over a manifold $M$, that depends on a pseudo-Riemannian metric, is natural and is invariant with respect to a conformal change of the metric. The existence of such a procedure was conjectured by P. Lecomte in \\cite{Leconj} and proved by C. Duva","authors_text":"F. Radoux, P. Mathonet","cross_cats":[],"headline":"","license":"","primary_cat":"math.DG","submitted_at":"2007-07-10T11:26:06Z","title":"On natural and conformally equivariant quantizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1412","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:c638dda7e391a7b536bdd3a87659f78d30f3b5c49ced2e01d8321a82d2273a22","target":"record","created_at":"2026-05-18T02:58:12Z","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":"de2575a03f1f54f6ec89196304d3636e2a1b841daf11d8ed5708b7fead23e06e","cross_cats_sorted":[],"license":"","primary_cat":"math.DG","submitted_at":"2007-07-10T11:26:06Z","title_canon_sha256":"421836817b230e93c989dada979969850cbdd972681fd6a0d59e075030767461"},"schema_version":"1.0","source":{"id":"0707.1412","kind":"arxiv","version":1}},"canonical_sha256":"4866d9c36a1cf691af5712e27ba72bb9098e357084f9331ef02b4ff885071f28","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4866d9c36a1cf691af5712e27ba72bb9098e357084f9331ef02b4ff885071f28","first_computed_at":"2026-05-18T02:58:12.573701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:12.573701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jGL1jcBD6iav4b7bRPHUgbIJGF2C47asJkXmhAB0AVKgs50AZN0Vr6mlxUnpkmEJhUIFZpjoJSbRwN1yjDMqAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:12.574502Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.1412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c638dda7e391a7b536bdd3a87659f78d30f3b5c49ced2e01d8321a82d2273a22","sha256:38391b5239ed20b187f788a460772b917a1fce2025f431b6cee3d86cbcdf6155"],"state_sha256":"b66101d60c3cb98410e7207c01120db12f18d2f93bfbee357bbe58fbcc477439"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHCEmEykTNp58liw+x5u0lIsoQF9bdlc+3RLnucmDii2dpWn90E2FQUVFvWImBz2zBqp9wycon+G2Bkeli3NBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:45:56.770933Z","bundle_sha256":"32b041f5b841d4e9d3f5eeea01e0be3d6c0646a0155efc91d64d6f2d45323427"}}