{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5Z7EJW4MXIW6GIFVIWBPD667LG","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":"d08b1d764470088bd447b6cd0fe15bde86d9927d544991a32a35ad865bb168a3","cross_cats_sorted":["gr-qc","math-ph","math.DG","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-10-04T12:35:07Z","title_canon_sha256":"5990333619afb3a40d57028a24291fcdaef5db99a39567a0c849d6d7a81c59a0"},"schema_version":"1.0","source":{"id":"1010.0566","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.0566","created_at":"2026-05-18T04:27:38Z"},{"alias_kind":"arxiv_version","alias_value":"1010.0566v5","created_at":"2026-05-18T04:27:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.0566","created_at":"2026-05-18T04:27:38Z"},{"alias_kind":"pith_short_12","alias_value":"5Z7EJW4MXIW6","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5Z7EJW4MXIW6GIFV","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5Z7EJW4M","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:e6a2bd3f90eb7176280be688ea445ccea1c48ce4497aa9a90f4f2121aa189125","target":"graph","created_at":"2026-05-18T04:27:38Z","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 conformal anomalies and functional determinants of the Branson--GJMS operators, P_{2k}, on the d-dimensional sphere are evaluated in explicit terms for any d and k such that k < d/2+1 (if d is even). The determinants are given in terms of multiple gamma functions and a rational multiplicative anomaly, which vanishes for odd d. Taking the mode system on the sphere as the union of Neumann and Dirichlet ones on the hemisphere is a basic part of the method and leads to a heuristic explanation of the non--existence of `super--critical' operators, 2k>d for even d. Significant use is made of the ","authors_text":"J.S.Dowker","cross_cats":["gr-qc","math-ph","math.DG","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-10-04T12:35:07Z","title":"Determinants and conformal anomalies of GJMS operators on spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.0566","kind":"arxiv","version":5},"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":"sha256:9d471d8d8e477bc7dbc81e645fb192b6615802acb8d92915e2e2215a9abe8c0d","target":"record","created_at":"2026-05-18T04:27:38Z","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":"d08b1d764470088bd447b6cd0fe15bde86d9927d544991a32a35ad865bb168a3","cross_cats_sorted":["gr-qc","math-ph","math.DG","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-10-04T12:35:07Z","title_canon_sha256":"5990333619afb3a40d57028a24291fcdaef5db99a39567a0c849d6d7a81c59a0"},"schema_version":"1.0","source":{"id":"1010.0566","kind":"arxiv","version":5}},"canonical_sha256":"ee7e44db8cba2de320b54582f1fbdf59b5f903c9d4b5b25675c68429ef95aebc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7e44db8cba2de320b54582f1fbdf59b5f903c9d4b5b25675c68429ef95aebc","first_computed_at":"2026-05-18T04:27:38.008216Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:38.008216Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njRdbEj1MSGXr4r6f/aVzAXMdSI3cU4MO0Sc0rBYaQJxLXLG7tH4ryOSXxGnghQhgDUCW9jZXagES2GH6wBnAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:38.008662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.0566","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d471d8d8e477bc7dbc81e645fb192b6615802acb8d92915e2e2215a9abe8c0d","sha256:e6a2bd3f90eb7176280be688ea445ccea1c48ce4497aa9a90f4f2121aa189125"],"state_sha256":"8965e7c7c945c7a025c67af7c961e8e5cf38d2486b6108b4a067af769c278683"}