{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HK5CR5HCANMPMREATR37HSQPZG","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":"5a35c1ab44ac38a6e64173acafcb185ebf17ce54c07a42f4552124f7c9d046d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-13T20:40:08Z","title_canon_sha256":"90a5329d1e8c11c0dac53ed4b5e4316af43b2f7ed2e0d30c7b498432a063e4cb"},"schema_version":"1.0","source":{"id":"1509.03897","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.03897","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"arxiv_version","alias_value":"1509.03897v1","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.03897","created_at":"2026-05-18T01:33:08Z"},{"alias_kind":"pith_short_12","alias_value":"HK5CR5HCANMP","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HK5CR5HCANMPMREA","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HK5CR5HC","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:2d95576e544c8c7c957635fe75471d0a97c59d96a14243a232927474e3311dc3","target":"graph","created_at":"2026-05-18T01:33:08Z","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 consider weak distributional solutions to the equation $-\\Delta_pu=f(u)$ in half-spaces under zero Dirichlet boundary condition. We assume that the nonlinearity is positive and superlinear at zero. For $p>2$ (the case $1<p\\leq2$ is already known) we prove that any positive solution is strictly monotone increasing in the direction orthogonal to the boundary of the half-space. As a consequence we deduce some Liouville type theorems for the Lane-Emden type equation. Furthermore any nonnegative solution turns out to be $C^{2,\\alpha}$ smooth.","authors_text":"Alberto Farina, Berardino Sciunzi, Luigi Montoro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-13T20:40:08Z","title":"Monotonicity in half-spaces of positive solutions to $-\\Delta_p u=f(u)$ in the case $p>2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03897","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:d6cd06db0baa9c4ef716afe8034a5e8d8f1b3210d4a9b2ad64f1fe8cac34e386","target":"record","created_at":"2026-05-18T01:33:08Z","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":"5a35c1ab44ac38a6e64173acafcb185ebf17ce54c07a42f4552124f7c9d046d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-13T20:40:08Z","title_canon_sha256":"90a5329d1e8c11c0dac53ed4b5e4316af43b2f7ed2e0d30c7b498432a063e4cb"},"schema_version":"1.0","source":{"id":"1509.03897","kind":"arxiv","version":1}},"canonical_sha256":"3aba28f4e20358f644809c77f3ca0fc990a14b0da0fe2679116ad35ea75a2e6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3aba28f4e20358f644809c77f3ca0fc990a14b0da0fe2679116ad35ea75a2e6b","first_computed_at":"2026-05-18T01:33:08.785195Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:08.785195Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4FVCFhYGiC4iC3Ti8k2uo65JN896eoOqamTl/HKJ8He5g+OYanyMW44/25NKwEIUB/35n6bxacV8sNAVLhaODA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:08.785832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.03897","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6cd06db0baa9c4ef716afe8034a5e8d8f1b3210d4a9b2ad64f1fe8cac34e386","sha256:2d95576e544c8c7c957635fe75471d0a97c59d96a14243a232927474e3311dc3"],"state_sha256":"c4205b2bd16cce48a76f5a4183aa58644a459ec09e89e22724cb8faa38c99317"}