{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RMPKZKYHSDT77TRD3KR6SXUCFR","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":"faa233dfc244f01eef9c84c73ad7db1029890ba277897d466040e5a964516369","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-02T00:15:02Z","title_canon_sha256":"11077e2f4a4a93861307d11f847b2b469787dfb47cea2cbf0be10b023be6ec95"},"schema_version":"1.0","source":{"id":"1001.0269","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0269","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0269v3","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0269","created_at":"2026-05-18T04:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"RMPKZKYHSDT7","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RMPKZKYHSDT77TRD","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RMPKZKYH","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:5c4d13aec925352ab00b92bf58da65b3b447e3f3f438b3ded7cd17db4b31e9c7","target":"graph","created_at":"2026-05-18T04:23:33Z","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 present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\\RN$, for $N\\ge 3$. In particular, in the first part of the paper we are interested in studying the existence of a positive solution to the elliptic Kirchhoff equation under the effect of a nonlinearity satisfying the general Berestycki-Lions assumptions. In the second part we look for ground states using minimizing arguments on a suitable natural constraint.","authors_text":"Antonio Azzollini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-02T00:15:02Z","title":"The elliptic Kirchhoff equation in $\\R^N$ perturbed by a local nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0269","kind":"arxiv","version":3},"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:f3ccb31eab666a6f4f742c3a6078e36962a539f2ae9de78ccb8f2260826ecf8b","target":"record","created_at":"2026-05-18T04:23:33Z","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":"faa233dfc244f01eef9c84c73ad7db1029890ba277897d466040e5a964516369","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-01-02T00:15:02Z","title_canon_sha256":"11077e2f4a4a93861307d11f847b2b469787dfb47cea2cbf0be10b023be6ec95"},"schema_version":"1.0","source":{"id":"1001.0269","kind":"arxiv","version":3}},"canonical_sha256":"8b1eacab0790e7ffce23daa3e95e822c4706cec0230b76a84573df087bfbd31c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b1eacab0790e7ffce23daa3e95e822c4706cec0230b76a84573df087bfbd31c","first_computed_at":"2026-05-18T04:23:33.285552Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:33.285552Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VYTsL1lr+/bD6ZEDOxQtrnzMBBVo7XqWsVM697Ewj0WcYDn08y/JmUFFBgowUsGZQUujPOl8HHi6q70Igv8+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:33.286209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0269","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3ccb31eab666a6f4f742c3a6078e36962a539f2ae9de78ccb8f2260826ecf8b","sha256:5c4d13aec925352ab00b92bf58da65b3b447e3f3f438b3ded7cd17db4b31e9c7"],"state_sha256":"8070d66a7403e552a42389c914c982b7d72dc29ed41d4fdca44a2d629646a69e"}