{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:FAYWAK3TBNZUAYWAADHRCA3BVG","short_pith_number":"pith:FAYWAK3T","schema_version":"1.0","canonical_sha256":"2831602b730b734062c000cf110361a99cc4c6a6d673f5a9f8041190e88b5d55","source":{"kind":"arxiv","id":"1005.2356","version":1},"attestation_state":"computed","paper":{"title":"Curvatures on the Teichm\\\"uller curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ren Guo, Subhojoy Gupta, Zheng Huang","submitted_at":"2010-05-13T15:53:34Z","abstract_excerpt":"The Teichm\\\"{u}ller curve is the fiber space over Teichm\\\"{u}ller space of closed Riemann surfaces, where the fiber over a point in Teichm\\\"{u}ller space is the underlying surface. We derive formulas for sectional curvatures on the Teichm\\\"{u}ller curve. In particular, our method can be applied to investigate the geometry of the Weil-Petersson geodesic as a three-manifold, and the degeneration of the curvatures near the infinity of the augmented Teichm\\\"{u}ller space along a Weil-Petersson geodesic, as well as the minimality of hyperbolic surfaces in this three-manifold."},"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":"1005.2356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-05-13T15:53:34Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"66ed29e366b55668d25c58427aa16bf41fe1441aea8156eed190d9895e87fc37","abstract_canon_sha256":"267b385e68a9e22d58159e7b15a3891c4d37bfd502d813496853e78fabfd0281"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:00.443304Z","signature_b64":"2qMVDIx5yPLrG6FoaSOoARVWWG+EZS79HNN00+LFyuo02RFyI1sqev4AjAo6zTJwmAn7L4Xz35GxMA/4rQJ3CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2831602b730b734062c000cf110361a99cc4c6a6d673f5a9f8041190e88b5d55","last_reissued_at":"2026-05-18T03:26:00.442602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:00.442602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Curvatures on the Teichm\\\"uller curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ren Guo, Subhojoy Gupta, Zheng Huang","submitted_at":"2010-05-13T15:53:34Z","abstract_excerpt":"The Teichm\\\"{u}ller curve is the fiber space over Teichm\\\"{u}ller space of closed Riemann surfaces, where the fiber over a point in Teichm\\\"{u}ller space is the underlying surface. We derive formulas for sectional curvatures on the Teichm\\\"{u}ller curve. In particular, our method can be applied to investigate the geometry of the Weil-Petersson geodesic as a three-manifold, and the degeneration of the curvatures near the infinity of the augmented Teichm\\\"{u}ller space along a Weil-Petersson geodesic, as well as the minimality of hyperbolic surfaces in this three-manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2356","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":"1005.2356","created_at":"2026-05-18T03:26:00.442713+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.2356v1","created_at":"2026-05-18T03:26:00.442713+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.2356","created_at":"2026-05-18T03:26:00.442713+00:00"},{"alias_kind":"pith_short_12","alias_value":"FAYWAK3TBNZU","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"FAYWAK3TBNZUAYWA","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"FAYWAK3T","created_at":"2026-05-18T12:26:06.534383+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/FAYWAK3TBNZUAYWAADHRCA3BVG","json":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG.json","graph_json":"https://pith.science/api/pith-number/FAYWAK3TBNZUAYWAADHRCA3BVG/graph.json","events_json":"https://pith.science/api/pith-number/FAYWAK3TBNZUAYWAADHRCA3BVG/events.json","paper":"https://pith.science/paper/FAYWAK3T"},"agent_actions":{"view_html":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG","download_json":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG.json","view_paper":"https://pith.science/paper/FAYWAK3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.2356&json=true","fetch_graph":"https://pith.science/api/pith-number/FAYWAK3TBNZUAYWAADHRCA3BVG/graph.json","fetch_events":"https://pith.science/api/pith-number/FAYWAK3TBNZUAYWAADHRCA3BVG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG/action/storage_attestation","attest_author":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG/action/author_attestation","sign_citation":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG/action/citation_signature","submit_replication":"https://pith.science/pith/FAYWAK3TBNZUAYWAADHRCA3BVG/action/replication_record"}},"created_at":"2026-05-18T03:26:00.442713+00:00","updated_at":"2026-05-18T03:26:00.442713+00:00"}