{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DDBRSROT7QABHAEUME7NQOWRUA","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":"1b9d6a5b24947bf04f40de420e7efd4842b6716cb931e4f78c799ddf16f12438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T14:03:35Z","title_canon_sha256":"c5c74d23749a43fc1b7eea87b862facbfe2481756a747fb27186085776a1343e"},"schema_version":"1.0","source":{"id":"1301.4868","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.4868","created_at":"2026-05-18T03:18:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.4868v2","created_at":"2026-05-18T03:18:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.4868","created_at":"2026-05-18T03:18:29Z"},{"alias_kind":"pith_short_12","alias_value":"DDBRSROT7QAB","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"DDBRSROT7QABHAEU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"DDBRSROT","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:978e5fab789447f67d3079db71a76db3ea611cb2be861ddffe73ae11816d4df1","target":"graph","created_at":"2026-05-18T03:18:29Z","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 equation $\\Ds u+u=u^p$, with $s\\in(0,1)$ in the subcritical range of $p$. We prove that if $s$ is sufficiently close to 1 the equation possesses a unique minimizer, which is nondegenerate.","authors_text":"Enrico Valdinoci, Mouhamed Moustapha Fall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T14:03:35Z","title":"Uniqueness and nondegeneracy of positive solutions of $\\Ds u+u=u^p$ in $\\R^N$ when $s$ is close to 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4868","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:d86d9d76095c62a2e065b8ab9f306cd4cc75d02b73a136656572e6c8c634a571","target":"record","created_at":"2026-05-18T03:18:29Z","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":"1b9d6a5b24947bf04f40de420e7efd4842b6716cb931e4f78c799ddf16f12438","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-01-21T14:03:35Z","title_canon_sha256":"c5c74d23749a43fc1b7eea87b862facbfe2481756a747fb27186085776a1343e"},"schema_version":"1.0","source":{"id":"1301.4868","kind":"arxiv","version":2}},"canonical_sha256":"18c31945d3fc00138094613ed83ad1a0128c232a7db12a4ffc325d366a2e4d88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18c31945d3fc00138094613ed83ad1a0128c232a7db12a4ffc325d366a2e4d88","first_computed_at":"2026-05-18T03:18:29.233103Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:29.233103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oYH1b8ZZPlCogF2eKpRah1Luzkd3JBy6X4l/4gtUJSwlZNifER4Jb/X70S9w9qKypdx0KcycUtIDaxmz4K59BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:29.233889Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.4868","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d86d9d76095c62a2e065b8ab9f306cd4cc75d02b73a136656572e6c8c634a571","sha256:978e5fab789447f67d3079db71a76db3ea611cb2be861ddffe73ae11816d4df1"],"state_sha256":"0ff0c8c015a85ec6ed92d926cf8216f6215f973af95e99cbf8c55265f9747a37"}