{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:QZGZCX4DQDCUCRLCHKUVT7K6UI","short_pith_number":"pith:QZGZCX4D","schema_version":"1.0","canonical_sha256":"864d915f8380c54145623aa959fd5ea2257d89c483113a4ce5ccb3004c512ef2","source":{"kind":"arxiv","id":"1503.02791","version":1},"attestation_state":"computed","paper":{"title":"Analyzing the Wu metric on a class of eggs in $\\mathbb{C}^n$ -- II","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":"2015-03-10T07:24:22Z","abstract_excerpt":"We study the Wu metric for the non-convex 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 $ 0 < m < 1/2$. Explicit expressions for the Kobayashi metric and the Wu metric on such pseudo-eggs $E_{2m}$ are obtained. The Wu metric is then verified to be a continuous Hermitian metric on $ E_{2m} $ which is real analytic everywhere except along the complex hypersurface $ Z = \\{ (0, z_2, \\ldots, z_n ) \\in E_{2m} \\} $. We also show that the holomorphic sectional curvature of"},"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":"1503.02791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-10T07:24:22Z","cross_cats_sorted":[],"title_canon_sha256":"957c0e70af44b1c73575f0207375453ef11f6c5195e6d612929feb5e93692fc2","abstract_canon_sha256":"431e22b196e804ba88708eee3246a8c08757432fe223e308059f7ae4a3bd6772"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:13.086602Z","signature_b64":"wlFMSquicMav71aqsJz2FyolEPqhAU9XPyg8fLIuyvmI+FxB96dWv7MWCcduBsQqWwMnrpEIwLzEgh70HWtAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"864d915f8380c54145623aa959fd5ea2257d89c483113a4ce5ccb3004c512ef2","last_reissued_at":"2026-05-18T02:25:13.086160Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:13.086160Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analyzing the Wu metric on a class of eggs in $\\mathbb{C}^n$ -- II","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":"2015-03-10T07:24:22Z","abstract_excerpt":"We study the Wu metric for the non-convex 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 $ 0 < m < 1/2$. Explicit expressions for the Kobayashi metric and the Wu metric on such pseudo-eggs $E_{2m}$ are obtained. The Wu metric is then verified to be a continuous Hermitian metric on $ E_{2m} $ which is real analytic everywhere except along the complex hypersurface $ Z = \\{ (0, z_2, \\ldots, z_n ) \\in E_{2m} \\} $. We also show that the holomorphic sectional curvature of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02791","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":"1503.02791","created_at":"2026-05-18T02:25:13.086226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.02791v1","created_at":"2026-05-18T02:25:13.086226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.02791","created_at":"2026-05-18T02:25:13.086226+00:00"},{"alias_kind":"pith_short_12","alias_value":"QZGZCX4DQDCU","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_16","alias_value":"QZGZCX4DQDCUCRLC","created_at":"2026-05-18T12:29:39.896362+00:00"},{"alias_kind":"pith_short_8","alias_value":"QZGZCX4D","created_at":"2026-05-18T12:29:39.896362+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/QZGZCX4DQDCUCRLCHKUVT7K6UI","json":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI.json","graph_json":"https://pith.science/api/pith-number/QZGZCX4DQDCUCRLCHKUVT7K6UI/graph.json","events_json":"https://pith.science/api/pith-number/QZGZCX4DQDCUCRLCHKUVT7K6UI/events.json","paper":"https://pith.science/paper/QZGZCX4D"},"agent_actions":{"view_html":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI","download_json":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI.json","view_paper":"https://pith.science/paper/QZGZCX4D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.02791&json=true","fetch_graph":"https://pith.science/api/pith-number/QZGZCX4DQDCUCRLCHKUVT7K6UI/graph.json","fetch_events":"https://pith.science/api/pith-number/QZGZCX4DQDCUCRLCHKUVT7K6UI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI/action/storage_attestation","attest_author":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI/action/author_attestation","sign_citation":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI/action/citation_signature","submit_replication":"https://pith.science/pith/QZGZCX4DQDCUCRLCHKUVT7K6UI/action/replication_record"}},"created_at":"2026-05-18T02:25:13.086226+00:00","updated_at":"2026-05-18T02:25:13.086226+00:00"}