{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5UFQIRD2HTFGX33EJ3YB27MZXB","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":"4e2c8c187df5c6846f602ef5f45a8d7dcc723431fea6cf594f81894b60f4abbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-30T06:53:17Z","title_canon_sha256":"663eeec34afb27049041c337596ffbaa5ab6cc83a44508eddc915840f122e153"},"schema_version":"1.0","source":{"id":"1807.11191","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.11191","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.11191v1","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.11191","created_at":"2026-05-18T00:09:32Z"},{"alias_kind":"pith_short_12","alias_value":"5UFQIRD2HTFG","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5UFQIRD2HTFGX33E","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5UFQIRD2","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:a435a938c98540dc281249f7fafc63452eef3f99a3672aac7a17a31c746c58af","target":"graph","created_at":"2026-05-18T00:09:32Z","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 show the existence and multiplicity of positive solutions of the following fractional Kirchhoff system\\\\ \\begin{equation} \\left\\{ \\begin{array}{rllll} \\mc L_M(u)&=\\lambda f(x)|u|^{q-2}u+ \\frac{2\\alpha}{\\alpha+\\beta}\\left|u\\right|^{\\alpha-2}u|v|^\\beta & \\text{in } \\Omega,\\\\ \\mc L_M(v)&=\\mu g(x)|v|^{q-2}v+ \\frac{2\\beta}{\\alpha+\\beta}\\left|u\\right|^{\\alpha}|v|^{\\beta-2}v & \\text{in } \\Omega,\\\\ u&=v=0 &\\mbox{in } \\mathbb{R}^{N}\\setminus \\Omega, \\end{array} \\right. \\end{equation} where $\\mc L_M(u)=M\\left(\\displaystyle \\int_\\Omega|(-\\Delta)^{\\frac{s}{2}}u|^2dx\\right)(-\\Delta)^{s} u","authors_text":"J. Giacomoni, J.M. do \\'O, P.K. Mishra","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-30T06:53:17Z","title":"Nehari Manifold for fractional Kirchhoff system with critical nonlinearity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11191","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":"sha256:585f3420d132606bb70e740ea792f9cafeb68e147027f10a3c00a3c62bb18652","target":"record","created_at":"2026-05-18T00:09:32Z","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":"4e2c8c187df5c6846f602ef5f45a8d7dcc723431fea6cf594f81894b60f4abbb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-30T06:53:17Z","title_canon_sha256":"663eeec34afb27049041c337596ffbaa5ab6cc83a44508eddc915840f122e153"},"schema_version":"1.0","source":{"id":"1807.11191","kind":"arxiv","version":1}},"canonical_sha256":"ed0b04447a3cca6bef644ef01d7d99b85ab25272aabc2e2a95bdaaa6974103d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed0b04447a3cca6bef644ef01d7d99b85ab25272aabc2e2a95bdaaa6974103d1","first_computed_at":"2026-05-18T00:09:32.691465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:32.691465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w4Lo25QkP12W36vwW3PbPNMta94nanb+mHvhmBUnIRBw/ftfydSzku4+XZl3X86j1G62Mh1vTNkspnwvMXwEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:32.691845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.11191","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:585f3420d132606bb70e740ea792f9cafeb68e147027f10a3c00a3c62bb18652","sha256:a435a938c98540dc281249f7fafc63452eef3f99a3672aac7a17a31c746c58af"],"state_sha256":"a89c0e954fd97c5952f760b6a157779aecddd1b71ee214ca38b6668b460a7600"}