{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:UK2TUKUFZ5MSDBWGFA2NRVT7KF","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":"11f5df44ed965aadabd91dc80af33575fbd63d979c61396f4bdb390e43ceef62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T11:59:41Z","title_canon_sha256":"aef3028817d5b3c1f3fd02794b2b566f817b15e59570d8b13457f381cdce0f0c"},"schema_version":"1.0","source":{"id":"1208.5892","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.5892","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"arxiv_version","alias_value":"1208.5892v1","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.5892","created_at":"2026-05-18T01:29:13Z"},{"alias_kind":"pith_short_12","alias_value":"UK2TUKUFZ5MS","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"UK2TUKUFZ5MSDBWG","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"UK2TUKUF","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:2be29a7e615b17a2167c4b53a4112fe44fd7af9fd7ddd51b0a1f2f5f6a246fb2","target":"graph","created_at":"2026-05-18T01:29:13Z","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":"We study the existence of sign-changing solutions with multiple bubbles to the slightly subcritical problem $$-\\Delta u=|u|^{2^*-2-\\e}u \\hbox{in}\\Omega, \\quad u=0 \\hbox{on}\\partial \\Omega,$$ where $\\Omega$ is a smooth bounded domain in $\\R^N$, $N\\geq 3$, $2^*=\\frac{2N}{N-2}$ and $\\e>0$ is a small parameter. In particular we prove that if $\\Omega$ is convex and satisfies a certain symmetry, then a nodal four-bubble solution exists with two positive and two negative bubbles.","authors_text":"Angela Pistoia, Teresa D'Aprile, Thomas Bartsch","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T11:59:41Z","title":"Multi-bubble nodal solutions for slightly subcritical elliptic problems in domains with symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.5892","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":"sha256:4e54bd7631563bc6d7efec4708d8f0f932c6223834e05299887c072d7956e476","target":"record","created_at":"2026-05-18T01:29:13Z","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":"11f5df44ed965aadabd91dc80af33575fbd63d979c61396f4bdb390e43ceef62","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-08-29T11:59:41Z","title_canon_sha256":"aef3028817d5b3c1f3fd02794b2b566f817b15e59570d8b13457f381cdce0f0c"},"schema_version":"1.0","source":{"id":"1208.5892","kind":"arxiv","version":1}},"canonical_sha256":"a2b53a2a85cf592186c62834d8d67f51671035ccda2042e79ee8a506620c2f66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2b53a2a85cf592186c62834d8d67f51671035ccda2042e79ee8a506620c2f66","first_computed_at":"2026-05-18T01:29:13.631680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:13.631680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"py4TSSOmv1rnmMW6TO/upwB5uR2+jlGXzscg/QrafRu3TPahH7Aywiuq8iw/XnEAZdMSKX+wkBK9l2DwReioAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:13.632102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.5892","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e54bd7631563bc6d7efec4708d8f0f932c6223834e05299887c072d7956e476","sha256:2be29a7e615b17a2167c4b53a4112fe44fd7af9fd7ddd51b0a1f2f5f6a246fb2"],"state_sha256":"338d20e5aaa4139fc4d461d66d0416f5e3acc6737245ec98bab2b23e966f52ee"}