{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RDVXDGMIMQFVG6WNZIFX7MFYPT","short_pith_number":"pith:RDVXDGMI","schema_version":"1.0","canonical_sha256":"88eb719988640b537acdca0b7fb0b87cd9a5e79f937b3b124e5e9d2e6d367c20","source":{"kind":"arxiv","id":"1911.12892","version":1},"attestation_state":"computed","paper":{"title":"Explicit fundamental gap estimates for some convex domains in $\\mathbb H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alina Stancu, Guofang Wei, Julie Clutterbuck, Theodora Bourni, Valentina-Mira Wheeler, Xuan Hien Nguyen","submitted_at":"2019-11-28T22:57:30Z","abstract_excerpt":"Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane $\\mathbb H^2$, showing that for some of them $\\lambda_2 - \\lambda_1 < \\frac{3\\pi^2}{D^2}$, where $D$ is the diameter of the domain and $\\lambda_1$, $\\lambda_2$ are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in $\\mathbb R^n $ or $\\mathbb S^n$, where $\\lambda_2 - \\lambda_1 \\geq \\frac{3 \\pi^2}{D^2}$ for convex domains. We also show that the fundamental gap of the example in Shih's article is still great"},"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":"1911.12892","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-11-28T22:57:30Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"af8571fe247e78c89aa0f82f9057d45ff65bfe4fbaad09615aeb5a7d677b74c0","abstract_canon_sha256":"be902823b6abe4ab786b79b4f412f1c57bce3c185c99042974030dca29bbe63a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:22:49.992805Z","signature_b64":"2Gc/slFa9Y66zPNnZ7BvTAjYX58kUemwG1UKI8gT8B7WozLnoqBVdp8HvtC84aDbJVKNkl86exhmeJgrk369DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88eb719988640b537acdca0b7fb0b87cd9a5e79f937b3b124e5e9d2e6d367c20","last_reissued_at":"2026-07-05T00:22:49.992366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:22:49.992366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit fundamental gap estimates for some convex domains in $\\mathbb H^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Alina Stancu, Guofang Wei, Julie Clutterbuck, Theodora Bourni, Valentina-Mira Wheeler, Xuan Hien Nguyen","submitted_at":"2019-11-28T22:57:30Z","abstract_excerpt":"Motivated by an example of Shih, we compute the fundamental gap of a family of convex domains in the hyperbolic plane $\\mathbb H^2$, showing that for some of them $\\lambda_2 - \\lambda_1 < \\frac{3\\pi^2}{D^2}$, where $D$ is the diameter of the domain and $\\lambda_1$, $\\lambda_2$ are the first and second Dirichlet eigenvalues of the Laplace operator on the domain. The result contrasts with what is known in $\\mathbb R^n $ or $\\mathbb S^n$, where $\\lambda_2 - \\lambda_1 \\geq \\frac{3 \\pi^2}{D^2}$ for convex domains. We also show that the fundamental gap of the example in Shih's article is still great"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.12892","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1911.12892/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1911.12892","created_at":"2026-07-05T00:22:49.992431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1911.12892v1","created_at":"2026-07-05T00:22:49.992431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.12892","created_at":"2026-07-05T00:22:49.992431+00:00"},{"alias_kind":"pith_short_12","alias_value":"RDVXDGMIMQFV","created_at":"2026-07-05T00:22:49.992431+00:00"},{"alias_kind":"pith_short_16","alias_value":"RDVXDGMIMQFVG6WN","created_at":"2026-07-05T00:22:49.992431+00:00"},{"alias_kind":"pith_short_8","alias_value":"RDVXDGMI","created_at":"2026-07-05T00:22:49.992431+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/RDVXDGMIMQFVG6WNZIFX7MFYPT","json":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT.json","graph_json":"https://pith.science/api/pith-number/RDVXDGMIMQFVG6WNZIFX7MFYPT/graph.json","events_json":"https://pith.science/api/pith-number/RDVXDGMIMQFVG6WNZIFX7MFYPT/events.json","paper":"https://pith.science/paper/RDVXDGMI"},"agent_actions":{"view_html":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT","download_json":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT.json","view_paper":"https://pith.science/paper/RDVXDGMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1911.12892&json=true","fetch_graph":"https://pith.science/api/pith-number/RDVXDGMIMQFVG6WNZIFX7MFYPT/graph.json","fetch_events":"https://pith.science/api/pith-number/RDVXDGMIMQFVG6WNZIFX7MFYPT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT/action/storage_attestation","attest_author":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT/action/author_attestation","sign_citation":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT/action/citation_signature","submit_replication":"https://pith.science/pith/RDVXDGMIMQFVG6WNZIFX7MFYPT/action/replication_record"}},"created_at":"2026-07-05T00:22:49.992431+00:00","updated_at":"2026-07-05T00:22:49.992431+00:00"}