{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VQZRBLW57ZALCR2VHHE3PFN4EV","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":"c6dbd0ce286a80dfadaa55c7d585493cbf60537e752a70a2266c86e734d8f194","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T21:26:02Z","title_canon_sha256":"6028b7894b4a9122bc52531d9c1c1f729b97f14e989995022a6de3555c394550"},"schema_version":"1.0","source":{"id":"1901.05048","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.05048","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"arxiv_version","alias_value":"1901.05048v1","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.05048","created_at":"2026-05-17T23:56:12Z"},{"alias_kind":"pith_short_12","alias_value":"VQZRBLW57ZAL","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"VQZRBLW57ZALCR2V","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"VQZRBLW5","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2f8a673b0dea322673ad3cc7ac7940464335b7ebdbcbf8b79273e1ed8a8143d8","target":"graph","created_at":"2026-05-17T23:56:12Z","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":"We consider harmonic maps$u(z): \\mathcal{X}_z\\to N$ in a fixed homotopy class from Riemann surfaces $\\mathcal{X}_z$ of genus $g\\geq 2$ varying in the Teichm\\\"u{}ller space $\\mathcal T$ to a Riemannian manifold $N$ with non-positive Hermitian sectional curvature.\n  The energy function $E(z)=E(u(z))$ can be viewed as a function on $\\mathcal T$ and we study its first and the second variations. We prove that the reciprocal energy function $E(z)^{-1}$ is plurisuperharmonic on Teichm\\\"uller space. We also obtain the (strict) plurisubharmonicity of $\\log E(z)$ and $E(z)$. As an application, we get th","authors_text":"Genkai Zhang, Inkang Kim, Xueyuan Wan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T21:26:02Z","title":"Plurisuperharmonicity of reciprocal energy function on Teichmuller space and Weil-Petersson metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.05048","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:e29f0fdb7e98742eae3ecc24417969b618bf0cc3991370de9898c3ee6a097780","target":"record","created_at":"2026-05-17T23:56:12Z","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":"c6dbd0ce286a80dfadaa55c7d585493cbf60537e752a70a2266c86e734d8f194","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-01-15T21:26:02Z","title_canon_sha256":"6028b7894b4a9122bc52531d9c1c1f729b97f14e989995022a6de3555c394550"},"schema_version":"1.0","source":{"id":"1901.05048","kind":"arxiv","version":1}},"canonical_sha256":"ac3310aeddfe40b1475539c9b795bc25708a5c8a583953d1d0e972b39b2b905f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac3310aeddfe40b1475539c9b795bc25708a5c8a583953d1d0e972b39b2b905f","first_computed_at":"2026-05-17T23:56:12.120017Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:12.120017Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3YDiL0CAzUZ3YQVWnBDvcG9t/E0yPoXENrzgaPOs5yHzH0SZ8XlltctA9XTsFBQe0GkwNClri4r6V2iXAX/DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:12.120628Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.05048","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e29f0fdb7e98742eae3ecc24417969b618bf0cc3991370de9898c3ee6a097780","sha256:2f8a673b0dea322673ad3cc7ac7940464335b7ebdbcbf8b79273e1ed8a8143d8"],"state_sha256":"bc03e20bc3dd2cd9ce1a480fb143d88e4ae893f6e14fd3d112cab411094e27fd"}