{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2KIOZNZLTLR4CR5O4MWY5C6YGO","short_pith_number":"pith:2KIOZNZL","canonical_record":{"source":{"id":"1407.6122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-23T08:00:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"328b0f02ec17429514bbba15e046685c99d281eed6b46b12e15b48fabb30a4be","abstract_canon_sha256":"f23daecc6aa4db29edbce7e84408eed9a762fe9c32021302ad3f6a1de552a9a2"},"schema_version":"1.0"},"canonical_sha256":"d290ecb72b9ae3c147aee32d8e8bd8339a911cc1ce5499e50ed7af859c04beb2","source":{"kind":"arxiv","id":"1407.6122","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6122","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6122v1","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6122","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"2KIOZNZLTLR4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KIOZNZLTLR4CR5O","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KIOZNZL","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2KIOZNZLTLR4CR5O4MWY5C6YGO","target":"record","payload":{"canonical_record":{"source":{"id":"1407.6122","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-23T08:00:33Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"328b0f02ec17429514bbba15e046685c99d281eed6b46b12e15b48fabb30a4be","abstract_canon_sha256":"f23daecc6aa4db29edbce7e84408eed9a762fe9c32021302ad3f6a1de552a9a2"},"schema_version":"1.0"},"canonical_sha256":"d290ecb72b9ae3c147aee32d8e8bd8339a911cc1ce5499e50ed7af859c04beb2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:58.919934Z","signature_b64":"PjRsbqXq4MF7vzuuBK6DSmgHdQh5xMs06ImXhDSQdHfFOlrx/nH5az9BRzpWwqG/Bdu3+SjCtgSjuUnPRTiJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d290ecb72b9ae3c147aee32d8e8bd8339a911cc1ce5499e50ed7af859c04beb2","last_reissued_at":"2026-05-18T02:46:58.919125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:58.919125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.6122","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":"2026-05-18T02:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7exwj/uY13wMti15OmS0DhhU1gZaPvV69g8W/qYfeOYfoxu/3klXS5iLiTAero5aJbM9XFb5lQBFV/QVjOw7AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:18:51.839428Z"},"content_sha256":"403ff2823be20c529a2002a1bddc5f5a91652b0e64a34a4a23fa41e93158860a","schema_version":"1.0","event_id":"sha256:403ff2823be20c529a2002a1bddc5f5a91652b0e64a34a4a23fa41e93158860a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2KIOZNZLTLR4CR5O4MWY5C6YGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of spherical GJMS determinants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"J.S. Dowker, Toufik Mansour","submitted_at":"2014-07-23T08:00:33Z","abstract_excerpt":"An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. This is formalised and expanded by an analytical treatment of the integral which produces an explicit combinatorial expression directly in terms of the Riemann zeta function, and $\\log2$. An incidental byproduct is a (known) expression for the central factorial coefficients in terms of higher Bernoulli numbers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6122","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":"2026-05-18T02:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g0lVF2a5t+mWp/50T6J4pe+LRNXOuV5qunm2xCIP1ZobX1ufi8KE6r7i8KpCN2YVWJET+7aBd8Uq/PvzjmVfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:18:51.839780Z"},"content_sha256":"906ae825d9c1d25153ab917ad62d4aaf2cd94635c176d20b1eba97fd0fb07af9","schema_version":"1.0","event_id":"sha256:906ae825d9c1d25153ab917ad62d4aaf2cd94635c176d20b1eba97fd0fb07af9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/bundle.json","state_url":"https://pith.science/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/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":"2026-06-01T19:18:51Z","links":{"resolver":"https://pith.science/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO","bundle":"https://pith.science/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/bundle.json","state":"https://pith.science/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2KIOZNZLTLR4CR5O4MWY5C6YGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2KIOZNZLTLR4CR5O4MWY5C6YGO","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":"f23daecc6aa4db29edbce7e84408eed9a762fe9c32021302ad3f6a1de552a9a2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-23T08:00:33Z","title_canon_sha256":"328b0f02ec17429514bbba15e046685c99d281eed6b46b12e15b48fabb30a4be"},"schema_version":"1.0","source":{"id":"1407.6122","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6122","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6122v1","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6122","created_at":"2026-05-18T02:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"2KIOZNZLTLR4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"2KIOZNZLTLR4CR5O","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"2KIOZNZL","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:906ae825d9c1d25153ab917ad62d4aaf2cd94635c176d20b1eba97fd0fb07af9","target":"graph","created_at":"2026-05-18T02:46:58Z","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":"An expression in the form of an easily computed integral is given for the determinant of the scalar GJMS operator on an odd--dimensional sphere. Manipulation yields a sum formula for the logdet in terms of the logdets of the ordinary conformal Laplacian for other dimensions. This is formalised and expanded by an analytical treatment of the integral which produces an explicit combinatorial expression directly in terms of the Riemann zeta function, and $\\log2$. An incidental byproduct is a (known) expression for the central factorial coefficients in terms of higher Bernoulli numbers.","authors_text":"J.S. Dowker, Toufik Mansour","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-23T08:00:33Z","title":"Evaluation of spherical GJMS determinants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6122","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":"sha256:403ff2823be20c529a2002a1bddc5f5a91652b0e64a34a4a23fa41e93158860a","target":"record","created_at":"2026-05-18T02:46:58Z","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":"f23daecc6aa4db29edbce7e84408eed9a762fe9c32021302ad3f6a1de552a9a2","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-07-23T08:00:33Z","title_canon_sha256":"328b0f02ec17429514bbba15e046685c99d281eed6b46b12e15b48fabb30a4be"},"schema_version":"1.0","source":{"id":"1407.6122","kind":"arxiv","version":1}},"canonical_sha256":"d290ecb72b9ae3c147aee32d8e8bd8339a911cc1ce5499e50ed7af859c04beb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d290ecb72b9ae3c147aee32d8e8bd8339a911cc1ce5499e50ed7af859c04beb2","first_computed_at":"2026-05-18T02:46:58.919125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:58.919125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PjRsbqXq4MF7vzuuBK6DSmgHdQh5xMs06ImXhDSQdHfFOlrx/nH5az9BRzpWwqG/Bdu3+SjCtgSjuUnPRTiJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:58.919934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6122","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:403ff2823be20c529a2002a1bddc5f5a91652b0e64a34a4a23fa41e93158860a","sha256:906ae825d9c1d25153ab917ad62d4aaf2cd94635c176d20b1eba97fd0fb07af9"],"state_sha256":"d51c12a09f32878e20f73f4a1c31063ceb4fb112a1129169cfee1fb411459569"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jkQNNZCV2qwTLhE+aPYssxb4cWQILrpePqujyGSk4y5DNO+3BEROIhUpNJqE34lEZb+5UsfjuVqDLLJ9KVOfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:18:51.841763Z","bundle_sha256":"46ad4b8d6637be567cb003d8c49955a56788bbbcad9113e17a130bd210038cf8"}}