{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HTFPSHFYWF6IHVX2M7NB5FNJDF","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":"ce19a1eb2f155f68a500228fa8ce425e33193b1bc0e4fdfd1e7343cccbebcd4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:39:35Z","title_canon_sha256":"01d9fbcf7f308c9175085564e587d50afc22c2326537b319fd52882b9f3d3928"},"schema_version":"1.0","source":{"id":"1012.5670","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5670","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5670v1","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5670","created_at":"2026-05-18T04:32:22Z"},{"alias_kind":"pith_short_12","alias_value":"HTFPSHFYWF6I","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HTFPSHFYWF6IHVX2","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HTFPSHFY","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:267f197d984877f60704a18ae43e1ea69ab94e3899f16cb83bdfdb303600e7d0","target":"graph","created_at":"2026-05-18T04:32:22Z","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 consider the problem -{\\epsilon}^2\\Delta_gu+u = |u|^{p-2}u in M, where (M,g) is a symmetric Riemannian manifold. We give a multiplicity result for antisymmetric changing sign solutions.","authors_text":"Anna Maria Micheletti, Marco G. Ghimenti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:39:35Z","title":"On the number of nodal solutions for a nonlinear elliptic problem on symmetric Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5670","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":"sha256:455a306552c2e9e4586c83d6c601ab335dc298f761d15765d690c40083263c55","target":"record","created_at":"2026-05-18T04:32:22Z","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":"ce19a1eb2f155f68a500228fa8ce425e33193b1bc0e4fdfd1e7343cccbebcd4a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-27T21:39:35Z","title_canon_sha256":"01d9fbcf7f308c9175085564e587d50afc22c2326537b319fd52882b9f3d3928"},"schema_version":"1.0","source":{"id":"1012.5670","kind":"arxiv","version":1}},"canonical_sha256":"3ccaf91cb8b17c83d6fa67da1e95a91974a415e88e462065a231b087d80878dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ccaf91cb8b17c83d6fa67da1e95a91974a415e88e462065a231b087d80878dc","first_computed_at":"2026-05-18T04:32:22.604597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:22.604597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KneDnrrMwXgovKoMB8mQFN/ScC7WqWwZ1Gef/V1AA49EE0KTWXwTY+UsJ89FyPDl5z4PsZe2/EJRo2tC1onACA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:22.605441Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5670","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455a306552c2e9e4586c83d6c601ab335dc298f761d15765d690c40083263c55","sha256:267f197d984877f60704a18ae43e1ea69ab94e3899f16cb83bdfdb303600e7d0"],"state_sha256":"38a336190ff54364b5733c6fdc6f5a93e699975046854c82f53c4ac8793b3d5b"}