{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:TOSZTFEGB7YZ2RKHQLVPHBA6NR","short_pith_number":"pith:TOSZTFEG","schema_version":"1.0","canonical_sha256":"9ba59994860ff19d454782eaf3841e6c5f2f0768cc0e49a4bee9f7ace2d66e15","source":{"kind":"arxiv","id":"1011.3095","version":1},"attestation_state":"computed","paper":{"title":"Factorization formulas for higher depth determinants of the Laplacian on the n-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yoshinori Yamasaki","submitted_at":"2010-11-13T03:32:14Z","abstract_excerpt":"We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere in terms of the multiple gamma functions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1011.3095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-11-13T03:32:14Z","cross_cats_sorted":[],"title_canon_sha256":"0f59f1f305f34c87d9f31ab5c4f067ce3a588123c5c3d58ad76c613af4f7aff7","abstract_canon_sha256":"9c1231d0db283d0713d3deaab94beb929a4ada29c1da50ebc91efe495edf3cac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:56.528112Z","signature_b64":"Ceyk4+mP+KHs0NIH2ZnkXbB/x+kNvJfZifcXuNAor5+DudFr0dpp/giu9MYSVIkGyyHzgLc+nQPRfxzh04QZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ba59994860ff19d454782eaf3841e6c5f2f0768cc0e49a4bee9f7ace2d66e15","last_reissued_at":"2026-05-18T04:35:56.527708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:56.527708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Factorization formulas for higher depth determinants of the Laplacian on the n-sphere","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yoshinori Yamasaki","submitted_at":"2010-11-13T03:32:14Z","abstract_excerpt":"We explicitly give factorization formulas for higher depth determinants, which are defined via derivatives of the spectral zeta function at non-positive integer points, of Laplacians on the n-sphere in terms of the multiple gamma functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3095","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1011.3095","created_at":"2026-05-18T04:35:56.527761+00:00"},{"alias_kind":"arxiv_version","alias_value":"1011.3095v1","created_at":"2026-05-18T04:35:56.527761+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.3095","created_at":"2026-05-18T04:35:56.527761+00:00"},{"alias_kind":"pith_short_12","alias_value":"TOSZTFEGB7YZ","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"TOSZTFEGB7YZ2RKH","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"TOSZTFEG","created_at":"2026-05-18T12:26:13.927090+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR","json":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR.json","graph_json":"https://pith.science/api/pith-number/TOSZTFEGB7YZ2RKHQLVPHBA6NR/graph.json","events_json":"https://pith.science/api/pith-number/TOSZTFEGB7YZ2RKHQLVPHBA6NR/events.json","paper":"https://pith.science/paper/TOSZTFEG"},"agent_actions":{"view_html":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR","download_json":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR.json","view_paper":"https://pith.science/paper/TOSZTFEG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1011.3095&json=true","fetch_graph":"https://pith.science/api/pith-number/TOSZTFEGB7YZ2RKHQLVPHBA6NR/graph.json","fetch_events":"https://pith.science/api/pith-number/TOSZTFEGB7YZ2RKHQLVPHBA6NR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR/action/storage_attestation","attest_author":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR/action/author_attestation","sign_citation":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR/action/citation_signature","submit_replication":"https://pith.science/pith/TOSZTFEGB7YZ2RKHQLVPHBA6NR/action/replication_record"}},"created_at":"2026-05-18T04:35:56.527761+00:00","updated_at":"2026-05-18T04:35:56.527761+00:00"}