{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:2HS76UHXEOX4FLJSCGOIOEJSZJ","short_pith_number":"pith:2HS76UHX","schema_version":"1.0","canonical_sha256":"d1e5ff50f723afc2ad32119c871132ca6a590242539ab37acdf7fdd47b27fb55","source":{"kind":"arxiv","id":"1302.1249","version":1},"attestation_state":"computed","paper":{"title":"A note on Yamabe constants of products with hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guillermo Henry, Jimmy Petean","submitted_at":"2013-02-06T02:46:10Z","abstract_excerpt":"We study the H^n-Yamabe constants of Riemannian products (H^n \\times M^m, g_h^n +g), where (M,g) is a compact Riemannian manifold of constant scalar curvature and g_h^n is the hyperbolic metric on H^n. Numerical calculations can be carried out due to the uniqueness of (positive, finite energy) solutions of the equation \\Delta u -\\lambda u + u^q =0 on hyperbolic space H^n under appropriate bounds on the parameters \\lambda, q, as shown by G. Mancini and K. Sandeep. We do explicit numerical estimates in the cases (n,m)=(2,2),(2,3) and (3,2)."},"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":"1302.1249","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-06T02:46:10Z","cross_cats_sorted":[],"title_canon_sha256":"b2e00519c5f71e00aee37afcf32625b1a2eabc4339c7c4276806b839d43d3303","abstract_canon_sha256":"b76022cc5a4d0f48374505808164cf145a623f219dd8e3cebe399c2999755540"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:24.780075Z","signature_b64":"RrAOXIqp14L77PWZsEoTSPW2RGnuOu1L0F8vmTYSiwNaVPam79pf+JN9SeClolo3DqpEmszyhCOlRqAhfyhrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1e5ff50f723afc2ad32119c871132ca6a590242539ab37acdf7fdd47b27fb55","last_reissued_at":"2026-05-18T03:34:24.779654Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:24.779654Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on Yamabe constants of products with hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Guillermo Henry, Jimmy Petean","submitted_at":"2013-02-06T02:46:10Z","abstract_excerpt":"We study the H^n-Yamabe constants of Riemannian products (H^n \\times M^m, g_h^n +g), where (M,g) is a compact Riemannian manifold of constant scalar curvature and g_h^n is the hyperbolic metric on H^n. Numerical calculations can be carried out due to the uniqueness of (positive, finite energy) solutions of the equation \\Delta u -\\lambda u + u^q =0 on hyperbolic space H^n under appropriate bounds on the parameters \\lambda, q, as shown by G. Mancini and K. Sandeep. We do explicit numerical estimates in the cases (n,m)=(2,2),(2,3) and (3,2)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1249","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":"1302.1249","created_at":"2026-05-18T03:34:24.779712+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.1249v1","created_at":"2026-05-18T03:34:24.779712+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1249","created_at":"2026-05-18T03:34:24.779712+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HS76UHXEOX4","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HS76UHXEOX4FLJS","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HS76UHX","created_at":"2026-05-18T12:27:30.460161+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/2HS76UHXEOX4FLJSCGOIOEJSZJ","json":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ.json","graph_json":"https://pith.science/api/pith-number/2HS76UHXEOX4FLJSCGOIOEJSZJ/graph.json","events_json":"https://pith.science/api/pith-number/2HS76UHXEOX4FLJSCGOIOEJSZJ/events.json","paper":"https://pith.science/paper/2HS76UHX"},"agent_actions":{"view_html":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ","download_json":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ.json","view_paper":"https://pith.science/paper/2HS76UHX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.1249&json=true","fetch_graph":"https://pith.science/api/pith-number/2HS76UHXEOX4FLJSCGOIOEJSZJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2HS76UHXEOX4FLJSCGOIOEJSZJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ/action/storage_attestation","attest_author":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ/action/author_attestation","sign_citation":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ/action/citation_signature","submit_replication":"https://pith.science/pith/2HS76UHXEOX4FLJSCGOIOEJSZJ/action/replication_record"}},"created_at":"2026-05-18T03:34:24.779712+00:00","updated_at":"2026-05-18T03:34:24.779712+00:00"}