{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SEH5BIU7W42EIARLMY6BB53HCG","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":"b9c2a5eccf63c676fdbced88fe70fb2ee61ca5d5e898fb96d314e4d3e9740155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T14:12:39Z","title_canon_sha256":"3783208af77ba6e3efdb13b4c63c11f0ed96153095aa46e175c0dc090ccf18bd"},"schema_version":"1.0","source":{"id":"1407.6226","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6226","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6226v3","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6226","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"SEH5BIU7W42E","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SEH5BIU7W42EIARL","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SEH5BIU7","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:959dbbfd08b46e971c40ab5035a889ecbe7c3830aa3666a79cbe64d1c5a77d23","target":"graph","created_at":"2026-05-18T02:00:02Z","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 derive a family of weighted Hardy-type inequalities in the variable exponent Lebesgue space with an additional term of the form\n  \\[ \\int_\\Omega\\ |\\xi|^{p(x)} \\mu_{1,\\beta}(dx)\\leqslant \\int_\\Omega |\\nabla \\xi|^{p(x)}\\mu_{2,\\beta}(dx)+\\int_\\Omega \\left|\\xi{\\log \\xi} \\right|^{p(x)} \\mu_{3,\\beta}(dx), \\] where $\\xi$ is any compactly supported Lipschitz function. The involved measures depend on a certain solution to the partial differential inequality involving $p(x)$-Laplacian ${-}\\Delta_{p(x)} u\\geqslant \\Phi$, where $\\Phi$ is a given locally integrable function, and $u$ is defined on an ope","authors_text":"Iwona Skrzypczak, Sylwia Dudek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T14:12:39Z","title":"Hardy-type inequality in variable exponent Lebesgue spaces derived from nonlinear problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6226","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":"sha256:81acae0575dda2fed70db05c558629ed96663c1257ff819ea30d15196f66ef39","target":"record","created_at":"2026-05-18T02:00:02Z","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":"b9c2a5eccf63c676fdbced88fe70fb2ee61ca5d5e898fb96d314e4d3e9740155","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-23T14:12:39Z","title_canon_sha256":"3783208af77ba6e3efdb13b4c63c11f0ed96153095aa46e175c0dc090ccf18bd"},"schema_version":"1.0","source":{"id":"1407.6226","kind":"arxiv","version":3}},"canonical_sha256":"910fd0a29fb73444022b663c10f76711ba5eeecb48d9acea348eb6257e6e7b94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"910fd0a29fb73444022b663c10f76711ba5eeecb48d9acea348eb6257e6e7b94","first_computed_at":"2026-05-18T02:00:02.619144Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:02.619144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JlWqJ/kJlWeMgdluwpN/fdBPGsJ9XsamTw/xnDKM9XK8LWiZ0wLeA2Fl7kmuIlzOpzWFla4FaWLUsrwTixiVDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:02.619622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6226","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81acae0575dda2fed70db05c558629ed96663c1257ff819ea30d15196f66ef39","sha256:959dbbfd08b46e971c40ab5035a889ecbe7c3830aa3666a79cbe64d1c5a77d23"],"state_sha256":"7c90f1a4ba4fb215131e12786e79f0e79e6ed72540ca240a18ccdbd89eb15ea7"}