{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I3N2TF5J7NIMB2NWBVTCY4KHCA","short_pith_number":"pith:I3N2TF5J","schema_version":"1.0","canonical_sha256":"46dba997a9fb50c0e9b60d662c7147102fcc8464018f5fd63478701f7b2a32dc","source":{"kind":"arxiv","id":"1104.1786","version":2},"attestation_state":"computed","paper":{"title":"Hermitian Curvature and Plurisubharmonicity of Energy on Teichm\\\"uller Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Domingo Toledo","submitted_at":"2011-04-10T18:04:23Z","abstract_excerpt":"Let $M$ be a closed Riemann surface, $N$ a Riemannian manifold of Hermitian non-positive curvature, $f:M\\to N$ a continuous map, and $E$ the function on the Teichm\\\"uller space of $M$ that assigns to a complex structure on $M$ the energy of the harmonic map homotopic to $f$. We show that $E$ is a plurisubharmonic function on the Teichm\\\"uller space of $M$. If $N$ has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of $E$ vanishes."},"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":"1104.1786","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-10T18:04:23Z","cross_cats_sorted":[],"title_canon_sha256":"1c72e052afb79ff6778ec27e0ff86c46656d8b04d84ee03e0ee344e0f089c478","abstract_canon_sha256":"9d2bec737b8e1844874be8acce5299e53a5ed13260180a12e0e34c2f60d487e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:12.367646Z","signature_b64":"SdG/l9GbQbc0gzy1xTtfp+or1fyN4YtS6IVN9vYCyRsvNbLQ2BNezL9IdOOBHgzohZoVxq85GXwE3m1Rdww4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46dba997a9fb50c0e9b60d662c7147102fcc8464018f5fd63478701f7b2a32dc","last_reissued_at":"2026-05-18T03:59:12.366975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:12.366975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hermitian Curvature and Plurisubharmonicity of Energy on Teichm\\\"uller Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Domingo Toledo","submitted_at":"2011-04-10T18:04:23Z","abstract_excerpt":"Let $M$ be a closed Riemann surface, $N$ a Riemannian manifold of Hermitian non-positive curvature, $f:M\\to N$ a continuous map, and $E$ the function on the Teichm\\\"uller space of $M$ that assigns to a complex structure on $M$ the energy of the harmonic map homotopic to $f$. We show that $E$ is a plurisubharmonic function on the Teichm\\\"uller space of $M$. If $N$ has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of $E$ vanishes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1786","kind":"arxiv","version":2},"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":"1104.1786","created_at":"2026-05-18T03:59:12.367078+00:00"},{"alias_kind":"arxiv_version","alias_value":"1104.1786v2","created_at":"2026-05-18T03:59:12.367078+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1786","created_at":"2026-05-18T03:59:12.367078+00:00"},{"alias_kind":"pith_short_12","alias_value":"I3N2TF5J7NIM","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I3N2TF5J7NIMB2NW","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I3N2TF5J","created_at":"2026-05-18T12:26:30.835961+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/I3N2TF5J7NIMB2NWBVTCY4KHCA","json":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA.json","graph_json":"https://pith.science/api/pith-number/I3N2TF5J7NIMB2NWBVTCY4KHCA/graph.json","events_json":"https://pith.science/api/pith-number/I3N2TF5J7NIMB2NWBVTCY4KHCA/events.json","paper":"https://pith.science/paper/I3N2TF5J"},"agent_actions":{"view_html":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA","download_json":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA.json","view_paper":"https://pith.science/paper/I3N2TF5J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1104.1786&json=true","fetch_graph":"https://pith.science/api/pith-number/I3N2TF5J7NIMB2NWBVTCY4KHCA/graph.json","fetch_events":"https://pith.science/api/pith-number/I3N2TF5J7NIMB2NWBVTCY4KHCA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA/action/storage_attestation","attest_author":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA/action/author_attestation","sign_citation":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA/action/citation_signature","submit_replication":"https://pith.science/pith/I3N2TF5J7NIMB2NWBVTCY4KHCA/action/replication_record"}},"created_at":"2026-05-18T03:59:12.367078+00:00","updated_at":"2026-05-18T03:59:12.367078+00:00"}