{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IPSYJJ6NPZ7U4LK6B3BWZBPPAN","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":"a04215f71eb09421c11c02d29c4404fc8e50cbe01ddf6d4711b1d37273bd4a5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-04-10T22:06:33Z","title_canon_sha256":"f6dff452fb947307a833981c8e1985cd40fd8437afb27e3e7bbfd3ca98426fe8"},"schema_version":"1.0","source":{"id":"2604.09929","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.09929","created_at":"2026-06-03T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"2604.09929v2","created_at":"2026-06-03T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.09929","created_at":"2026-06-03T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"IPSYJJ6NPZ7U","created_at":"2026-06-03T01:05:12Z"},{"alias_kind":"pith_short_16","alias_value":"IPSYJJ6NPZ7U4LK6","created_at":"2026-06-03T01:05:12Z"},{"alias_kind":"pith_short_8","alias_value":"IPSYJJ6N","created_at":"2026-06-03T01:05:12Z"}],"graph_snapshots":[{"event_id":"sha256:9d48fcbe3d176ff4a60e52311df47f2127a129f64d84496b2a09f2ca1184a29f","target":"graph","created_at":"2026-06-03T01:05:12Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type p(·)-Laplacian problems involving an arbitrary growth and a sandwich-type growth s(·)∈(inf p, sup p)."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"Suitable assumptions on the data (growth conditions, Kirchhoff function, and variable exponents) that are not specified in the abstract but are required for the truncation and a priori estimate arguments to close."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Existence of positive bounded weak solutions is shown for Kirchhoff-type variable-exponent Laplacian problems with arbitrary and sandwich-type growth conditions."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions."}],"snapshot_sha256":"b26909fe4545b1e46497febeb741a63190480208654c43b1149179a0de7cfea4"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.09929/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type $p(\\cdot)$-Laplacian problems involving an arbitrary growth and a sandwich-type growth $s(\\cdot)\\in (\\inf p,\\sup p)$. This setting leads to substantial analytical difficulties in the variational analysis of the associated energy functional. By combining truncation arguments with a priori estimates, we prove the existence result under suitable assumptions on the data.","authors_text":"Ky Ho","cross_cats":[],"headline":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-04-10T22:06:33Z","title":"On Kirchhoff-type p(.)-Laplacian problems with sandwich-type and arbitrary growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.09929","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T16:44:29.284346Z","id":"24ab9253-a502-4bf1-8a41-a10e9c073a25","model_set":{"reader":"grok-4.3"},"one_line_summary":"Existence of positive bounded weak solutions is shown for Kirchhoff-type variable-exponent Laplacian problems with arbitrary and sandwich-type growth conditions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Kirchhoff-type p(·)-Laplacian problems with arbitrary and sandwich growth admit positive bounded weak solutions.","strongest_claim":"We establish the existence of a positive bounded weak solution for a class of Kirchhoff-type p(·)-Laplacian problems involving an arbitrary growth and a sandwich-type growth s(·)∈(inf p, sup p).","weakest_assumption":"Suitable assumptions on the data (growth conditions, Kirchhoff function, and variable exponents) that are not specified in the abstract but are required for the truncation and a priori estimate arguments to close."}},"verdict_id":"24ab9253-a502-4bf1-8a41-a10e9c073a25"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9b59b4d4d6f14e079041f21bef98f38019c9198a90e674bab13cb79aea08940e","target":"record","created_at":"2026-06-03T01:05:12Z","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":"a04215f71eb09421c11c02d29c4404fc8e50cbe01ddf6d4711b1d37273bd4a5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-04-10T22:06:33Z","title_canon_sha256":"f6dff452fb947307a833981c8e1985cd40fd8437afb27e3e7bbfd3ca98426fe8"},"schema_version":"1.0","source":{"id":"2604.09929","kind":"arxiv","version":2}},"canonical_sha256":"43e584a7cd7e7f4e2d5e0ec36c85ef03504d17dcc57f7be9aa9d442c45b27c2c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43e584a7cd7e7f4e2d5e0ec36c85ef03504d17dcc57f7be9aa9d442c45b27c2c","first_computed_at":"2026-06-03T01:05:12.797425Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T01:05:12.797425Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"njaXdtdMxh7hVu1TQf2A7+9+yjBuHFdj4dnVPqrfsY84rJyrjXBsPra5Mr28zNIfLSyz7lCItTREsQW4u0C1DA==","signature_status":"signed_v1","signed_at":"2026-06-03T01:05:12.797880Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.09929","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b59b4d4d6f14e079041f21bef98f38019c9198a90e674bab13cb79aea08940e","sha256:9d48fcbe3d176ff4a60e52311df47f2127a129f64d84496b2a09f2ca1184a29f"],"state_sha256":"7efea196da43604ca65a7696f1bbc08762e727088268e17ba55f729970499bdf"}