{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HJVPCLY3HENH734I7JTX3QHRIH","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":"b7e9a80e377c4306c36606ce6290848a0669a44c82cb1e434bacc735a880abe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-13T08:37:12Z","title_canon_sha256":"53f10b4ac6e52b212a8bb4dd2bd36a12fb77c5245ff1072e3aec9d734cd19215"},"schema_version":"1.0","source":{"id":"2408.06726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.06726","created_at":"2026-07-05T09:04:11Z"},{"alias_kind":"arxiv_version","alias_value":"2408.06726v2","created_at":"2026-07-05T09:04:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.06726","created_at":"2026-07-05T09:04:11Z"},{"alias_kind":"pith_short_12","alias_value":"HJVPCLY3HENH","created_at":"2026-07-05T09:04:11Z"},{"alias_kind":"pith_short_16","alias_value":"HJVPCLY3HENH734I","created_at":"2026-07-05T09:04:11Z"},{"alias_kind":"pith_short_8","alias_value":"HJVPCLY3","created_at":"2026-07-05T09:04:11Z"}],"graph_snapshots":[{"event_id":"sha256:cbfa7ac19c3873ac27d00f2fa7a80b6d0dc9bb3b8a509cd2414aa2d57d1eeecf","target":"graph","created_at":"2026-07-05T09:04:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.06726/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we investigate the interior regularity theory for stationary solutions of the supercritical nonlinear elliptic equation $$ -\\Delta u=|u|^{p-1}u\\quad\\text{in }\\Omega,\\quad p>\\frac{n+2}{n-2}, $$ where $ \\Omega\\subset\\mathbb{R}^n $ is a bounded domain with $ n\\geq 3 $. Our primary focus is on the structure of stratification for the singular sets. We define the $ k $-th stratification $ S^k(u) $ of $ u $ based on the tangent functions and measures. We show that the Hausdorff dimension of $ S^k(u) $ is at most $ k $ and $ S^k(u) $ is $ k $-rectifiable, and establish estimates for vol","authors_text":"Haotong Fu, Wei Wang, Zhifei Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-13T08:37:12Z","title":"Quantitative stratification and sharp regularity estimates for supercritical semilinear elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06726","kind":"arxiv","version":2},"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":"sha256:80f3d9307601ab89216ca088d7461e75aaab3cd4a87906e34358a082856628d5","target":"record","created_at":"2026-07-05T09:04:11Z","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":"b7e9a80e377c4306c36606ce6290848a0669a44c82cb1e434bacc735a880abe1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-13T08:37:12Z","title_canon_sha256":"53f10b4ac6e52b212a8bb4dd2bd36a12fb77c5245ff1072e3aec9d734cd19215"},"schema_version":"1.0","source":{"id":"2408.06726","kind":"arxiv","version":2}},"canonical_sha256":"3a6af12f1b391a7fef88fa677dc0f141f6477a098bea0c2ea06005d6a2cf3219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a6af12f1b391a7fef88fa677dc0f141f6477a098bea0c2ea06005d6a2cf3219","first_computed_at":"2026-07-05T09:04:11.560084Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:04:11.560084Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lz3iiFbjHaY97p8XiJKKJ7Hl+04vyfZrcbgmENFXM5xnDxrVLVJ2lvrTltgzNliK3gFSoG8tvaguXmS5zKM5Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T09:04:11.560631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.06726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80f3d9307601ab89216ca088d7461e75aaab3cd4a87906e34358a082856628d5","sha256:cbfa7ac19c3873ac27d00f2fa7a80b6d0dc9bb3b8a509cd2414aa2d57d1eeecf"],"state_sha256":"1aadd1952fd7e8e3e34c1f30f93249236a5310fb101e658dd2088ae3bd3e1c0c"}