{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SJN7IQ3HEGTC4GEIBRH7SVPSP3","short_pith_number":"pith:SJN7IQ3H","canonical_record":{"source":{"id":"1107.5840","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T22:20:03Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"ecdced07f8c5fe768f4fe49ece26aeeba3cd55036d341a5effec56c730f4ff3b","abstract_canon_sha256":"2c3d25d372de4b32dcb5bf24067981630a0f9ef484516ded3b7709f8aa5f0cc5"},"schema_version":"1.0"},"canonical_sha256":"925bf4436721a62e18880c4ff955f27ec0f751f7d02472d1a6393d7d0d1c7c46","source":{"kind":"arxiv","id":"1107.5840","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5840","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5840v4","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5840","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"pith_short_12","alias_value":"SJN7IQ3HEGTC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SJN7IQ3HEGTC4GEI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SJN7IQ3H","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SJN7IQ3HEGTC4GEIBRH7SVPSP3","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5840","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T22:20:03Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"ecdced07f8c5fe768f4fe49ece26aeeba3cd55036d341a5effec56c730f4ff3b","abstract_canon_sha256":"2c3d25d372de4b32dcb5bf24067981630a0f9ef484516ded3b7709f8aa5f0cc5"},"schema_version":"1.0"},"canonical_sha256":"925bf4436721a62e18880c4ff955f27ec0f751f7d02472d1a6393d7d0d1c7c46","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:49.845438Z","signature_b64":"c+udYkBysFroPUWUlYV5Z7JvqJ6TJ97HC6IfY1b7dL6yLBKpZvQvjsIkxkk1CUwMH9ocSpQxLKrphku2gsVkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"925bf4436721a62e18880c4ff955f27ec0f751f7d02472d1a6393d7d0d1c7c46","last_reissued_at":"2026-05-18T02:27:49.845034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:49.845034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5840","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:27:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"brhX80imiYttmFSTwILDFWm0wi0ezL1PCLx4dfF4/fJypUNiyiaSqCb9gTGMwUPuuP1UQUN83PM51SOc6TlUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:43:36.627389Z"},"content_sha256":"9461ad930116b9bf702814581fcf71ff821d387532fc0224dd2aaf622344ee76","schema_version":"1.0","event_id":"sha256:9461ad930116b9bf702814581fcf71ff821d387532fc0224dd2aaf622344ee76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SJN7IQ3HEGTC4GEIBRH7SVPSP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher Symmetries of the Laplacian via Quantization","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.DG","authors_text":"Jean-Philippe Michel","submitted_at":"2011-07-28T22:20:03Z","abstract_excerpt":"We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and \\v{S}ilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined with a symplectic reduction, this leads to a quantization of the minimal nilpotent coadjoi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5840","kind":"arxiv","version":4},"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":"2026-05-18T02:27:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bor3zJnlakyMTv6EkG56boHWFllen1U0GCAgDk7/R45UpqQyaaj6s4Of7QvtgQ9OB03otm4U+Z6ulJIb2/e5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T23:43:36.627782Z"},"content_sha256":"ad08cd09344d1b808c194a572520f8fb34b57996268f321384ff37e7c9c93611","schema_version":"1.0","event_id":"sha256:ad08cd09344d1b808c194a572520f8fb34b57996268f321384ff37e7c9c93611"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/bundle.json","state_url":"https://pith.science/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/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":"2026-05-25T23:43:36Z","links":{"resolver":"https://pith.science/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3","bundle":"https://pith.science/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/bundle.json","state":"https://pith.science/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SJN7IQ3HEGTC4GEIBRH7SVPSP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SJN7IQ3HEGTC4GEIBRH7SVPSP3","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":"2c3d25d372de4b32dcb5bf24067981630a0f9ef484516ded3b7709f8aa5f0cc5","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T22:20:03Z","title_canon_sha256":"ecdced07f8c5fe768f4fe49ece26aeeba3cd55036d341a5effec56c730f4ff3b"},"schema_version":"1.0","source":{"id":"1107.5840","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5840","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5840v4","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5840","created_at":"2026-05-18T02:27:49Z"},{"alias_kind":"pith_short_12","alias_value":"SJN7IQ3HEGTC","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SJN7IQ3HEGTC4GEI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SJN7IQ3H","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:ad08cd09344d1b808c194a572520f8fb34b57996268f321384ff37e7c9c93611","target":"graph","created_at":"2026-05-18T02:27:49Z","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":"We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and \\v{S}ilhan. In particular, conformally equivariant quantization establishes a correspondence between the algebra of Hamiltonian symmetries of the null geodesic flow and the algebra of higher symmetries of the conformal Laplacian. Combined with a symplectic reduction, this leads to a quantization of the minimal nilpotent coadjoi","authors_text":"Jean-Philippe Michel","cross_cats":["math-ph","math.MP","math.RT"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T22:20:03Z","title":"Higher Symmetries of the Laplacian via Quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5840","kind":"arxiv","version":4},"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":"sha256:9461ad930116b9bf702814581fcf71ff821d387532fc0224dd2aaf622344ee76","target":"record","created_at":"2026-05-18T02:27:49Z","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":"2c3d25d372de4b32dcb5bf24067981630a0f9ef484516ded3b7709f8aa5f0cc5","cross_cats_sorted":["math-ph","math.MP","math.RT"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.DG","submitted_at":"2011-07-28T22:20:03Z","title_canon_sha256":"ecdced07f8c5fe768f4fe49ece26aeeba3cd55036d341a5effec56c730f4ff3b"},"schema_version":"1.0","source":{"id":"1107.5840","kind":"arxiv","version":4}},"canonical_sha256":"925bf4436721a62e18880c4ff955f27ec0f751f7d02472d1a6393d7d0d1c7c46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"925bf4436721a62e18880c4ff955f27ec0f751f7d02472d1a6393d7d0d1c7c46","first_computed_at":"2026-05-18T02:27:49.845034Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:49.845034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c+udYkBysFroPUWUlYV5Z7JvqJ6TJ97HC6IfY1b7dL6yLBKpZvQvjsIkxkk1CUwMH9ocSpQxLKrphku2gsVkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:49.845438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5840","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9461ad930116b9bf702814581fcf71ff821d387532fc0224dd2aaf622344ee76","sha256:ad08cd09344d1b808c194a572520f8fb34b57996268f321384ff37e7c9c93611"],"state_sha256":"92c73ecd0a1400436e843de97c8847e6477ae2f4ed41adcfd4707e5e5836eefc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"22QL/SCohooVEQeusjmKEUxHw5Y5AI/oGVQwCreoKfIZRujgv3AG3nwIIiBa6VUc0SnB/W3Hk0/hoeaoS+xIAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T23:43:36.631283Z","bundle_sha256":"50c40a2d290fe8ab06440c9dc612a8eb75222823fa31cb23a36d87d750a1ec91"}}