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We show that it is also necessary when we assume that $\\theta_1,\\theta_2,\\dots,\\theta_n \\not\\in \\mathbb{N}$."},"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":"1704.04823","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-16T21:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"13e82f8be0a82f0bc0543b886be86575be948e572b60520caf5ed2d87225f72c","abstract_canon_sha256":"942f914e099d6ed00241ad5323e973970a9a1e5f5fdfdce987355359977a8810"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:44.533527Z","signature_b64":"2xksebPXaGKtix/uNQEFuiuAZuR3WXeMuLB6oxoovT0QrXSsEoD3QzU3DdTKEFUAjUIktKIm1cUTWiRhgqQKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a755bae37e0f40def94e16fb608f72d855a676094eb4b281e933454938ff0e8","last_reissued_at":"2026-05-17T23:53:44.532921Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:44.532921Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spherical metrics with conical singularities on 2-spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Subhadip Dey","submitted_at":"2017-04-16T21:46:39Z","abstract_excerpt":"Suppose that $\\theta_1,\\theta_2,\\dots,\\theta_n$ are positive numbers and $n\\ge 3$. 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