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The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be $C^2$-smooth. Overall however, the Wu metric is shown to be continuous when $m=1/2$ and even $C^1$-smooth for each $m>1/2$, and in all cases, a non-K\\\"ahler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents."},"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":"1503.02787","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-10T07:13:08Z","cross_cats_sorted":[],"title_canon_sha256":"2a17243bf59f161966f0719f8b8185dbbdf05cc5b757e7a195b36ddc7bb69cd3","abstract_canon_sha256":"94064f06816997bc5ba56a6179d20f57198f44f600c42faf4b074b1d1937b074"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:13.098803Z","signature_b64":"tSmXECn3DAUNTjcL8/7L9coy5F0l2EBucC1KuCyneBsdcVvkZ+spsr4dNn37INZLOrdi82qfKW9kbMNoYuiaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4cf9e9c7a370d78a1258247c3351a92328c560b2d0e001435a5a7b77a26bc495","last_reissued_at":"2026-05-18T02:25:13.098374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:13.098374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analyzing the Wu metric on a class of eggs in $\\mathbb{C}^n$ -- I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"G. P. Balakumar, Prachi Mahajan","submitted_at":"2015-03-10T07:13:08Z","abstract_excerpt":"We study the Wu metric on convex egg domains of the form \\[ E_{2m} = \\big\\{ z \\in \\mathbb{C}^n : \\vert z_1 \\vert^{2m} + \\vert z_2 \\vert^2 + \\ldots + \\vert z_{n-1} \\vert^2 + \\vert z_n \\vert^{2} <1 \\big\\} \\] where $m \\geq 1/2, m \\neq 1$. The Wu metric is shown to be real analytic everywhere except on a lower dimensional subvariety where it fails to be $C^2$-smooth. Overall however, the Wu metric is shown to be continuous when $m=1/2$ and even $C^1$-smooth for each $m>1/2$, and in all cases, a non-K\\\"ahler Hermitian metric with its holomorphic curvature strongly negative in the sense of currents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02787","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":"1503.02787","created_at":"2026-05-18T02:25:13.098438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02787v1","created_at":"2026-05-18T02:25:13.098438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02787","created_at":"2026-05-18T02:25:13.098438+00:00"},{"alias_kind":"pith_short_12","alias_value":"JT46TR5DODLY","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JT46TR5DODLYUESY","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JT46TR5D","created_at":"2026-05-18T12:29:27.538025+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/JT46TR5DODLYUESYER6DGUNJEM","json":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM.json","graph_json":"https://pith.science/api/pith-number/JT46TR5DODLYUESYER6DGUNJEM/graph.json","events_json":"https://pith.science/api/pith-number/JT46TR5DODLYUESYER6DGUNJEM/events.json","paper":"https://pith.science/paper/JT46TR5D"},"agent_actions":{"view_html":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM","download_json":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM.json","view_paper":"https://pith.science/paper/JT46TR5D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02787&json=true","fetch_graph":"https://pith.science/api/pith-number/JT46TR5DODLYUESYER6DGUNJEM/graph.json","fetch_events":"https://pith.science/api/pith-number/JT46TR5DODLYUESYER6DGUNJEM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM/action/storage_attestation","attest_author":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM/action/author_attestation","sign_citation":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM/action/citation_signature","submit_replication":"https://pith.science/pith/JT46TR5DODLYUESYER6DGUNJEM/action/replication_record"}},"created_at":"2026-05-18T02:25:13.098438+00:00","updated_at":"2026-05-18T02:25:13.098438+00:00"}