{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UFGVPNZGR3XJUIHMF6ET6J7PKD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c6c0fc0ec18c300a5eaa8cdcd42657f6d22d9ea50440e08b68e67df6e76db7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T06:55:47Z","title_canon_sha256":"31d0b9474693c4cf5b94a969c4c775a5b35708d65d663276b964a50ca69943b1"},"schema_version":"1.0","source":{"id":"1804.01687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.01687","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"arxiv_version","alias_value":"1804.01687v1","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.01687","created_at":"2026-05-18T00:19:10Z"},{"alias_kind":"pith_short_12","alias_value":"UFGVPNZGR3XJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UFGVPNZGR3XJUIHM","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UFGVPNZG","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:0296a3396235d8e84cedd0c61f6220a23a58ad8385d859014bcbc1d64115736a","target":"graph","created_at":"2026-05-18T00:19:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we build infinitely many non-radial sign-changing solutions to the critical problem: \\begin{equation*} \\left\\{\\begin{array}{rlll} -\\Delta u&=|u|^{\\frac{4}{N-2}}u, &\\hbox{ in }\\Omega,\\\\ u&=0, &\\hbox{ on }\\partial\\Omega. \\end{array}\\right. \\eqno(P) \\end{equation*} on the annulus $\\Omega:=\\{x\\in \\mathbb{R}^N: a<|x|<b\\}$, $N\\geq 3.$ In particular, for any integer $k$ large enough, we build a non-radial solution which look like the unique positive solution $u_0$ to $(P)$ crowned by $k$ negative bubbles arranged on a regular polygon with radius $r_0$ such that $r_0^{\\frac{N-2}{2}}u_0(","authors_text":"Angela Pistoia, Benniao Li, Shusen Yan, Yuxia Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T06:55:47Z","title":"Infinitely many non-radial solutions to a critical equation on annulus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01687","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:e3fbeb97731b3596577e699da5992d831cf33339a98fbedbf5c4af9705513af2","target":"record","created_at":"2026-05-18T00:19:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c6c0fc0ec18c300a5eaa8cdcd42657f6d22d9ea50440e08b68e67df6e76db7fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-05T06:55:47Z","title_canon_sha256":"31d0b9474693c4cf5b94a969c4c775a5b35708d65d663276b964a50ca69943b1"},"schema_version":"1.0","source":{"id":"1804.01687","kind":"arxiv","version":1}},"canonical_sha256":"a14d57b7268eee9a20ec2f893f27ef50d6eb6fe02ccfbc9510b57ab8e5fb0eb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a14d57b7268eee9a20ec2f893f27ef50d6eb6fe02ccfbc9510b57ab8e5fb0eb4","first_computed_at":"2026-05-18T00:19:10.360534Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:19:10.360534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q58wSRbdTjnLiEv9PutBvDggcIvetxueimz+K5zuv+GlkS9fH2P6AZV1a8CX4DMcMVR1/Co+SLrGHl8wWGEkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:19:10.361006Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.01687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3fbeb97731b3596577e699da5992d831cf33339a98fbedbf5c4af9705513af2","sha256:0296a3396235d8e84cedd0c61f6220a23a58ad8385d859014bcbc1d64115736a"],"state_sha256":"5469633cc9efa2153295e744700de8f0eca62f964e2d8bc33e0eaffdf5cec726"}