{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:QEQVEMNAUQI2T7EHELBMM6WHSU","short_pith_number":"pith:QEQVEMNA","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"},"canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","source":{"kind":"arxiv","id":"1305.0734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0734","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0734v1","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0734","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"QEQVEMNAUQI2","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QEQVEMNAUQI2T7EH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QEQVEMNA","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:QEQVEMNAUQI2T7EHELBMM6WHSU","target":"record","payload":{"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"},"canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","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"},"source_kind":"arxiv","source_id":"1305.0734","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":"2026-05-18T03:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPcat3n3uKsGzcAWRYqvtnt7gm4LBuNHTO3MHlihUHnhN52Lexh9uXP8f1NfuD0wDDiP7E75GVC4CC4Eezm9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:34:54.450944Z"},"content_sha256":"0ab9f3c6762c73828b22e5be51f03377b91284d1d11e9322c325811bbafd245d","schema_version":"1.0","event_id":"sha256:0ab9f3c6762c73828b22e5be51f03377b91284d1d11e9322c325811bbafd245d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:QEQVEMNAUQI2T7EHELBMM6WHSU","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i43mtB+2W93CdhlxpfOl8RhiM4IgTJ4RrU0y+NYfFJjPQV2aWIhWA0bvZYR2Vh1oAhYoEcfKSCBdNXhwgs5fAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:34:54.451729Z"},"content_sha256":"69c43b4e54291a72d39847385cdad3d44fe660314ff08255a19a7e18083e63c0","schema_version":"1.0","event_id":"sha256:69c43b4e54291a72d39847385cdad3d44fe660314ff08255a19a7e18083e63c0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/bundle.json","state_url":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/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":"2026-05-31T22:34:54Z","links":{"resolver":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU","bundle":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/bundle.json","state":"https://pith.science/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QEQVEMNAUQI2T7EHELBMM6WHSU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QEQVEMNAUQI2T7EHELBMM6WHSU","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":"008323e299ca69d848267a9a826da5c8dbea0a4a983fdc52ccd6a77b4283bb71","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-03T14:49:07Z","title_canon_sha256":"20bb7acc3c0419248ff6e8fbb439684261d5af98420fc1e9b1a31a1fbae97320"},"schema_version":"1.0","source":{"id":"1305.0734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0734","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0734v1","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0734","created_at":"2026-05-18T03:26:32Z"},{"alias_kind":"pith_short_12","alias_value":"QEQVEMNAUQI2","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QEQVEMNAUQI2T7EH","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QEQVEMNA","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:69c43b4e54291a72d39847385cdad3d44fe660314ff08255a19a7e18083e63c0","target":"graph","created_at":"2026-05-18T03:26:32Z","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":"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.","authors_text":"P. Somberg","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-03T14:49:07Z","title":"Finite reflection groups and the Dunkl-Laplace differential-difference operators in conformal geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0734","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":"sha256:0ab9f3c6762c73828b22e5be51f03377b91284d1d11e9322c325811bbafd245d","target":"record","created_at":"2026-05-18T03:26:32Z","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":"008323e299ca69d848267a9a826da5c8dbea0a4a983fdc52ccd6a77b4283bb71","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-05-03T14:49:07Z","title_canon_sha256":"20bb7acc3c0419248ff6e8fbb439684261d5af98420fc1e9b1a31a1fbae97320"},"schema_version":"1.0","source":{"id":"1305.0734","kind":"arxiv","version":1}},"canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81215231a0a411a9fc8722c2c67ac7952b0f7e8c7a1561bae0b9e3ad6f6f449f","first_computed_at":"2026-05-18T03:26:32.971408Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:32.971408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+7RDKlmNrmDOalIVS5zCN5I5Zy45inUZNv3i9Bruv/7M2TkoLGaZukRNzrp5HYymzwV0dmr0gey+HWlqp06xCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:32.971940Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ab9f3c6762c73828b22e5be51f03377b91284d1d11e9322c325811bbafd245d","sha256:69c43b4e54291a72d39847385cdad3d44fe660314ff08255a19a7e18083e63c0"],"state_sha256":"d3350f1d14708c3dcbcee54e9ef0ca590dcb7b67a810fa51c04346cc3441fb1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8UnfDkwXjuvm+sunRcfPSXeCoucX5K6eSnpvt9ye88Rdb37GTtb6kLvQ8+RcrQwUc17YOOXLt8AQEXxLkGdmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:34:54.456085Z","bundle_sha256":"ff367f4205086ebc1c4944aca16e57d3bf7e4a6dc0fe9e4d6cfdbf2d06e1aeb1"}}