{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QEQVEMNAUQI2T7EHELBMM6WHSU","short_pith_number":"pith:QEQVEMNA","schema_version":"1.0","canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","source":{"kind":"arxiv","id":"1305.0734","version":1},"attestation_state":"computed","paper":{"title":"Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"P. Somberg","submitted_at":"2013-05-03T14:49:07Z","abstract_excerpt":"For a finite reflection subgroup $G\\leq O(n+1,1,\\mR)$ of the conformal group of the sphere with standard conformal structure $(S^n,[g_0])$, we geometrically derive differential-difference Dunkl version of the series of conformally invariant differential operators with symbols given by powers of Laplace operator. The construction can be regarded as a deformation of the Fefferman-Graham ambient metric construction of GJMS operators."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.0734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-03T14:49:07Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"20bb7acc3c0419248ff6e8fbb439684261d5af98420fc1e9b1a31a1fbae97320","abstract_canon_sha256":"008323e299ca69d848267a9a826da5c8dbea0a4a983fdc52ccd6a77b4283bb71"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:32.971940Z","signature_b64":"+7RDKlmNrmDOalIVS5zCN5I5Zy45inUZNv3i9Bruv/7M2TkoLGaZukRNzrp5HYymzwV0dmr0gey+HWlqp06xCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","last_reissued_at":"2026-05-18T03:26:32.971408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:32.971408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.DG","authors_text":"P. Somberg","submitted_at":"2013-05-03T14:49:07Z","abstract_excerpt":"For a finite reflection subgroup $G\\leq O(n+1,1,\\mR)$ of the conformal group of the sphere with standard conformal structure $(S^n,[g_0])$, we geometrically derive differential-difference Dunkl version of the series of conformally invariant differential operators with symbols given by powers of Laplace operator. The construction can be regarded as a deformation of the Fefferman-Graham ambient metric construction of GJMS operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0734","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.0734","created_at":"2026-05-18T03:26:32.971499+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0734v1","created_at":"2026-05-18T03:26:32.971499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0734","created_at":"2026-05-18T03:26:32.971499+00:00"},{"alias_kind":"pith_short_12","alias_value":"QEQVEMNAUQI2","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QEQVEMNAUQI2T7EH","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QEQVEMNA","created_at":"2026-05-18T12:27:57.521954+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU","json":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU.json","graph_json":"https://pith.science/api/pith-number/QEQVEMNAUQI2T7EHELBMM6WHSU/graph.json","events_json":"https://pith.science/api/pith-number/QEQVEMNAUQI2T7EHELBMM6WHSU/events.json","paper":"https://pith.science/paper/QEQVEMNA"},"agent_actions":{"view_html":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU","download_json":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU.json","view_paper":"https://pith.science/paper/QEQVEMNA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0734&json=true","fetch_graph":"https://pith.science/api/pith-number/QEQVEMNAUQI2T7EHELBMM6WHSU/graph.json","fetch_events":"https://pith.science/api/pith-number/QEQVEMNAUQI2T7EHELBMM6WHSU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/action/storage_attestation","attest_author":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/action/author_attestation","sign_citation":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/action/citation_signature","submit_replication":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/action/replication_record"}},"created_at":"2026-05-18T03:26:32.971499+00:00","updated_at":"2026-05-18T03:26:32.971499+00:00"}