{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:ERAA3XDBIXEI3LUGDSCFB4JXLO","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":"7b44778fa6f58cee21dcbedf24647ad611e6cf34c485713a353186146a6f7a85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-19T21:10:32Z","title_canon_sha256":"ccdf7f1b51c1a2f6f000eb67979dc21935d20f09d5671037540c7fc0c8b5f844"},"schema_version":"1.0","source":{"id":"1206.4341","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4341","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4341v2","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4341","created_at":"2026-05-18T03:35:54Z"},{"alias_kind":"pith_short_12","alias_value":"ERAA3XDBIXEI","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"ERAA3XDBIXEI3LUG","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"ERAA3XDB","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:025b97a42e0978b0e45a4a08a594d4769fe8f9ff3580e8c6a3ec2d97e601c8a0","target":"graph","created_at":"2026-05-18T03:35:54Z","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 prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the $p$-Laplacian operator with Dirichlet boundary conditions on a bounded domain having nontrivial topology and discrete symmetry. Pioneering works related to the case $p=2$ are H. Brezis and L. Nirenberg [4], J.-M. Coron [10], and A. Bahri and J.-M. Coron [3]. A global compactness analysis is given for the Palais-Smale sequences in the presence of symmetries.","authors_text":"Carlo Mercuri, Filomena Pacella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-19T21:10:32Z","title":"On the pure critical exponent problem for the $p$-Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4341","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":"sha256:5864bf6c0adb0874e377be12f4d359e57e4bb6c968ae86bf3fc72d0d7519c74d","target":"record","created_at":"2026-05-18T03:35:54Z","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":"7b44778fa6f58cee21dcbedf24647ad611e6cf34c485713a353186146a6f7a85","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-19T21:10:32Z","title_canon_sha256":"ccdf7f1b51c1a2f6f000eb67979dc21935d20f09d5671037540c7fc0c8b5f844"},"schema_version":"1.0","source":{"id":"1206.4341","kind":"arxiv","version":2}},"canonical_sha256":"24400ddc6145c88dae861c8450f1375b889903d1dc23fc0559a8f3afbee03f7f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24400ddc6145c88dae861c8450f1375b889903d1dc23fc0559a8f3afbee03f7f","first_computed_at":"2026-05-18T03:35:54.060132Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:54.060132Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eocb6I6PaIkNm7eceJsCOdLifcOPKva2R8dAzsuVUFKtDElxwYCzfbRZWZJSbva/Qnxzka6nFzjEj632+Ig0DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:54.060705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4341","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5864bf6c0adb0874e377be12f4d359e57e4bb6c968ae86bf3fc72d0d7519c74d","sha256:025b97a42e0978b0e45a4a08a594d4769fe8f9ff3580e8c6a3ec2d97e601c8a0"],"state_sha256":"9b29a4ca110a52a102e07552ca6ac593810b6279c909d702996a9eb1771bb46c"}