{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7CJKUBJ6PYB557VV7RXVP75XMR","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":"a6e2d0288aefeb33a979cd2b14005a6b990881b970aae25c908c71fc589d1fb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-23T15:06:28Z","title_canon_sha256":"227ef8ef0bef2b0c3dfd3690004b5d8a3af2ae26e70a8421af71ba19bd441355"},"schema_version":"1.0","source":{"id":"1408.5502","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.5502","created_at":"2026-05-18T02:44:25Z"},{"alias_kind":"arxiv_version","alias_value":"1408.5502v1","created_at":"2026-05-18T02:44:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.5502","created_at":"2026-05-18T02:44:25Z"},{"alias_kind":"pith_short_12","alias_value":"7CJKUBJ6PYB5","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7CJKUBJ6PYB557VV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7CJKUBJ6","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:d85d6f1f1a4f3ce06e468a606b6a5f2248e0ca72a019a068a1fdc0118aff3049","target":"graph","created_at":"2026-05-18T02:44:25Z","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":"The purpose of this paper is to study the indefinite Kirchhoff type problem: \\begin{equation*} \\left\\{ \\begin{array}{ll} M\\left( \\int_{\\mathbb{R}^{N}}(|\\nabla u|^{2}+u^{2})dx\\right) \\left[ -\\Delta u+u\\right] =f(x,u) & \\text{in }\\mathbb{R}^{N}, \\\\ 0\\leq u\\in H^{1}\\left( \\mathbb{R}^{N}\\right), & \\end{array} \\right. \\end{equation*} where $N\\geq 1$, $M(t)=am\\left( t\\right) +b$, $m\\in C(\\mathbb{R}^{+})$ and $ f(x,u)=g(x,u)+h(x)u^{q-1}$. We require that $f$ is \\textquotedblleft local\\textquotedblright\\ sublinear at the origin and \\textquotedblleft local\\textquotedblright\\ linear at infinite. Using t","authors_text":"Juntao Sun, Tsung-fang Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-23T15:06:28Z","title":"On the indefinite Kirchhoff type problems with local sublinearity and linearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5502","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":"sha256:4ce3bdd89207358655f4c0bf5d1e4c87d70e726547b06ca6770cc1b9612130f0","target":"record","created_at":"2026-05-18T02:44:25Z","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":"a6e2d0288aefeb33a979cd2b14005a6b990881b970aae25c908c71fc589d1fb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-23T15:06:28Z","title_canon_sha256":"227ef8ef0bef2b0c3dfd3690004b5d8a3af2ae26e70a8421af71ba19bd441355"},"schema_version":"1.0","source":{"id":"1408.5502","kind":"arxiv","version":1}},"canonical_sha256":"f892aa053e7e03defeb5fc6f57ffb7645c4f7513185d1708a7c6c1677ce22a23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f892aa053e7e03defeb5fc6f57ffb7645c4f7513185d1708a7c6c1677ce22a23","first_computed_at":"2026-05-18T02:44:25.015405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:25.015405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xxdwlRLemqw2Gu2iAC3v7PHCzYzVACdjV2WHKIFRy/pgANcrINANxIBAvyKd9wCe3jR11e76ge8vsEBWgcPCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:25.015885Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.5502","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ce3bdd89207358655f4c0bf5d1e4c87d70e726547b06ca6770cc1b9612130f0","sha256:d85d6f1f1a4f3ce06e468a606b6a5f2248e0ca72a019a068a1fdc0118aff3049"],"state_sha256":"63331583d7e003296f1e0d479ceb8b541966cd01136f7cf7f225357b26e19de7"}