{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:3XFTJ7ENF6FL4QBS7ZNZJGRJP5","short_pith_number":"pith:3XFTJ7EN","schema_version":"1.0","canonical_sha256":"ddcb34fc8d2f8abe4032fe5b949a297f55033b042953109b179747d46ca860e0","source":{"kind":"arxiv","id":"1210.2244","version":1},"attestation_state":"computed","paper":{"title":"Sign-changing blow-up for scalar curvature type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Robert, J\\'er\\^ome V\\'etois","submitted_at":"2012-10-08T11:42:43Z","abstract_excerpt":"Given $(M,g)$ a compact Riemannian manifold of dimension $n\\geq 3$, we are interested in the existence of blowing-up sign-changing families $(\\ue)_{\\eps>0}\\in C^{2,\\theta}(M)$, $\\theta\\in (0,1)$, of solutions to $$\\Delta_g \\ue+h\\ue=|\\ue|^{\\frac{4}{n-2}-\\eps}\\ue\\hbox{ in }M\\,,$$ where $\\Delta_g:=-\\hbox{div}_g(\\nabla)$ and $h\\in C^{0,\\theta}(M)$ is a potential. We prove that such families exist in two main cases: in small dimension $n\\in \\{3,4,5,6\\}$ for any potential $h$ or in dimension $3\\leq n\\leq 9$ when $h\\equiv\\frac{n-2}{4(n-1)}\\Scal_g$. These examples yield a complete panorama of the comp"},"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":"1210.2244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-08T11:42:43Z","cross_cats_sorted":[],"title_canon_sha256":"ae80d85729e4ecb528c7a1a7fe5150d793147bfc96456b88d2af338445899e1c","abstract_canon_sha256":"99909111672c19a14ed2152fcb76d597921b876e4e4c3305300ff501fc9b3364"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:50.730985Z","signature_b64":"ZSZSNrj9CapSetnu7ByVFU6NWTAIEV2694BbKMTGp1IKsY68lrUhNs4QVYA4Fy2Ol6wu5W4F0Pq0/7kkWUyaAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddcb34fc8d2f8abe4032fe5b949a297f55033b042953109b179747d46ca860e0","last_reissued_at":"2026-05-18T03:43:50.730298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:50.730298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sign-changing blow-up for scalar curvature type equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fr\\'ed\\'eric Robert, J\\'er\\^ome V\\'etois","submitted_at":"2012-10-08T11:42:43Z","abstract_excerpt":"Given $(M,g)$ a compact Riemannian manifold of dimension $n\\geq 3$, we are interested in the existence of blowing-up sign-changing families $(\\ue)_{\\eps>0}\\in C^{2,\\theta}(M)$, $\\theta\\in (0,1)$, of solutions to $$\\Delta_g \\ue+h\\ue=|\\ue|^{\\frac{4}{n-2}-\\eps}\\ue\\hbox{ in }M\\,,$$ where $\\Delta_g:=-\\hbox{div}_g(\\nabla)$ and $h\\in C^{0,\\theta}(M)$ is a potential. We prove that such families exist in two main cases: in small dimension $n\\in \\{3,4,5,6\\}$ for any potential $h$ or in dimension $3\\leq n\\leq 9$ when $h\\equiv\\frac{n-2}{4(n-1)}\\Scal_g$. These examples yield a complete panorama of the comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2244","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":"1210.2244","created_at":"2026-05-18T03:43:50.730436+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.2244v1","created_at":"2026-05-18T03:43:50.730436+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.2244","created_at":"2026-05-18T03:43:50.730436+00:00"},{"alias_kind":"pith_short_12","alias_value":"3XFTJ7ENF6FL","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"3XFTJ7ENF6FL4QBS","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"3XFTJ7EN","created_at":"2026-05-18T12:26:53.410803+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/3XFTJ7ENF6FL4QBS7ZNZJGRJP5","json":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5.json","graph_json":"https://pith.science/api/pith-number/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/graph.json","events_json":"https://pith.science/api/pith-number/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/events.json","paper":"https://pith.science/paper/3XFTJ7EN"},"agent_actions":{"view_html":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5","download_json":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5.json","view_paper":"https://pith.science/paper/3XFTJ7EN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.2244&json=true","fetch_graph":"https://pith.science/api/pith-number/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/graph.json","fetch_events":"https://pith.science/api/pith-number/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/action/storage_attestation","attest_author":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/action/author_attestation","sign_citation":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/action/citation_signature","submit_replication":"https://pith.science/pith/3XFTJ7ENF6FL4QBS7ZNZJGRJP5/action/replication_record"}},"created_at":"2026-05-18T03:43:50.730436+00:00","updated_at":"2026-05-18T03:43:50.730436+00:00"}