{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OWDSHZ5EVZXVZ2LFYEWONEIIDP","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":"eb769ac6b511134fe5bcc6761d7538f836e5dec03b2e3fd02a028d68ee785f40","cross_cats_sorted":["hep-th","math.DG","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-11T16:04:42Z","title_canon_sha256":"82e144137162737d3096106085a42b6659f12d486de0a720814fcd51a50e1ce0"},"schema_version":"1.0","source":{"id":"1309.2873","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.2873","created_at":"2026-05-18T02:50:03Z"},{"alias_kind":"arxiv_version","alias_value":"1309.2873v1","created_at":"2026-05-18T02:50:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.2873","created_at":"2026-05-18T02:50:03Z"},{"alias_kind":"pith_short_12","alias_value":"OWDSHZ5EVZXV","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OWDSHZ5EVZXVZ2LF","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OWDSHZ5E","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:4ab2241fe2cab9adeb71f225caf9723964fd6b3c5f300bb2c1a69a400ab36ffa","target":"graph","created_at":"2026-05-18T02:50:03Z","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":"A numerical expression in the form of an integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a curious sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. A few graphs are drawn.","authors_text":"J.S.Dowker","cross_cats":["hep-th","math.DG","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-11T16:04:42Z","title":"Numerical evaluation of spherical GJMS determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.2873","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":"sha256:7a47067b22ab5644e733da3c2b54d7b88c0434c13061bbc7981ddad7975bfd06","target":"record","created_at":"2026-05-18T02:50:03Z","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":"eb769ac6b511134fe5bcc6761d7538f836e5dec03b2e3fd02a028d68ee785f40","cross_cats_sorted":["hep-th","math.DG","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-09-11T16:04:42Z","title_canon_sha256":"82e144137162737d3096106085a42b6659f12d486de0a720814fcd51a50e1ce0"},"schema_version":"1.0","source":{"id":"1309.2873","kind":"arxiv","version":1}},"canonical_sha256":"758723e7a4ae6f5ce965c12ce691081bf71d244186eedf8392fff7fe410b9dd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"758723e7a4ae6f5ce965c12ce691081bf71d244186eedf8392fff7fe410b9dd5","first_computed_at":"2026-05-18T02:50:03.344537Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:03.344537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V+Yxu44JqEbxHdom5J10k+6W9lWtzz69urDPkCfb1ieA2aRw0CAnkf+jK7byMklls/njFNbPuCSNLkyWfhpDBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:03.345361Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.2873","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a47067b22ab5644e733da3c2b54d7b88c0434c13061bbc7981ddad7975bfd06","sha256:4ab2241fe2cab9adeb71f225caf9723964fd6b3c5f300bb2c1a69a400ab36ffa"],"state_sha256":"40761424a2c56e4bfaaed5c637a7c78dd6c2dda849ae44135992edfe59300d20"}