{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:5S2IJ4FRRAVG3435VDV7JS6AGO","short_pith_number":"pith:5S2IJ4FR","schema_version":"1.0","canonical_sha256":"ecb484f0b1882a6df37da8ebf4cbc033a08c35b34b5603cb34db7a28aa253646","source":{"kind":"arxiv","id":"1507.00053","version":1},"attestation_state":"computed","paper":{"title":"Solutions to the singular $\\sigma_2-$Yamabe problem with isolated singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Almir Silva Santos","submitted_at":"2015-06-30T22:28:51Z","abstract_excerpt":"Given $(M,g_0)$ a closed Riemannian manifold and a nonempty closed subset $X$ in $M$, the singular $\\sigma_k-$Yamabe problem asks for a complete metric $g$ on $M\\backslash X$ conformal to $g_0$ with constant $\\sigma_k-$curvature. The $\\sigma_k-$curvature is defined as the $k-$th elementary symmetric function of the eigenvalues of the Schouten tensor of a Riemannian metric. The main goal of this paper is to find solutions to the singular $\\sigma_2-$Yamabe problem with isolated singularities in any compact non-degenerate manifold such that the Weyl tensor vanishing to sufficiently high order at "},"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":"1507.00053","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-06-30T22:28:51Z","cross_cats_sorted":[],"title_canon_sha256":"4291411a6337d652b97b9d83ea2afd90c02c5541525adb1eed4bc8514fa01aad","abstract_canon_sha256":"732a7ba5e6431ca3a929d3d882b0523dafe3627032d69e9f4a4fc87e3a79cb8f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:30.747060Z","signature_b64":"5wpRPB4MNj0bM76LOJvR+Jdm98ts21YTXHpIx2eWe2i+k4JuzCYvI8ATLk+MlPlnsXP9R/+LADAIoTBatdNeDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecb484f0b1882a6df37da8ebf4cbc033a08c35b34b5603cb34db7a28aa253646","last_reissued_at":"2026-05-18T01:37:30.746213Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:30.746213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Solutions to the singular $\\sigma_2-$Yamabe problem with isolated singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Almir Silva Santos","submitted_at":"2015-06-30T22:28:51Z","abstract_excerpt":"Given $(M,g_0)$ a closed Riemannian manifold and a nonempty closed subset $X$ in $M$, the singular $\\sigma_k-$Yamabe problem asks for a complete metric $g$ on $M\\backslash X$ conformal to $g_0$ with constant $\\sigma_k-$curvature. The $\\sigma_k-$curvature is defined as the $k-$th elementary symmetric function of the eigenvalues of the Schouten tensor of a Riemannian metric. The main goal of this paper is to find solutions to the singular $\\sigma_2-$Yamabe problem with isolated singularities in any compact non-degenerate manifold such that the Weyl tensor vanishing to sufficiently high order at "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00053","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":"1507.00053","created_at":"2026-05-18T01:37:30.746372+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.00053v1","created_at":"2026-05-18T01:37:30.746372+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00053","created_at":"2026-05-18T01:37:30.746372+00:00"},{"alias_kind":"pith_short_12","alias_value":"5S2IJ4FRRAVG","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"5S2IJ4FRRAVG3435","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"5S2IJ4FR","created_at":"2026-05-18T12:29:07.941421+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/5S2IJ4FRRAVG3435VDV7JS6AGO","json":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO.json","graph_json":"https://pith.science/api/pith-number/5S2IJ4FRRAVG3435VDV7JS6AGO/graph.json","events_json":"https://pith.science/api/pith-number/5S2IJ4FRRAVG3435VDV7JS6AGO/events.json","paper":"https://pith.science/paper/5S2IJ4FR"},"agent_actions":{"view_html":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO","download_json":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO.json","view_paper":"https://pith.science/paper/5S2IJ4FR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.00053&json=true","fetch_graph":"https://pith.science/api/pith-number/5S2IJ4FRRAVG3435VDV7JS6AGO/graph.json","fetch_events":"https://pith.science/api/pith-number/5S2IJ4FRRAVG3435VDV7JS6AGO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO/action/storage_attestation","attest_author":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO/action/author_attestation","sign_citation":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO/action/citation_signature","submit_replication":"https://pith.science/pith/5S2IJ4FRRAVG3435VDV7JS6AGO/action/replication_record"}},"created_at":"2026-05-18T01:37:30.746372+00:00","updated_at":"2026-05-18T01:37:30.746372+00:00"}