{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JTFPDCWDEDNNSRW4KBKNL2JV7B","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":"f9e9fc7324870bd510a3824e59db78b837a3104b84361b58229b7ed54d731787","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T15:03:15Z","title_canon_sha256":"f87695d60532422626f6953c2c7a59b2185c141ddf9b7b73d895437b29cdc179"},"schema_version":"1.0","source":{"id":"1407.5518","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5518","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5518v1","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5518","created_at":"2026-05-18T02:47:13Z"},{"alias_kind":"pith_short_12","alias_value":"JTFPDCWDEDNN","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"JTFPDCWDEDNNSRW4","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"JTFPDCWD","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:84799977aae00963d86c0ef25898947413d6f542c9706a66b12760379e13c63f","target":"graph","created_at":"2026-05-18T02:47:13Z","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 study the best constant in a Hardy inequality for the p-Laplace operator on convex domains with Robin boundary conditions. We show, in particular, that the best constant equals $((p-1)/p)^p$ whenever Dirichlet boundary conditions are imposed on a subset of the boundary of non-zero measure. We also discuss some generalizations to non-convex domains.","authors_text":"Ari Laptev, Hynek Kovarik, Tomas Ekholm","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T15:03:15Z","title":"Hardy inequalities for p-Laplacians with Robin boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5518","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":"sha256:6035ef0bc8b989d0ec8c67594b3542d51a8acc42c9b00c3979d14067a629c41c","target":"record","created_at":"2026-05-18T02:47:13Z","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":"f9e9fc7324870bd510a3824e59db78b837a3104b84361b58229b7ed54d731787","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-21T15:03:15Z","title_canon_sha256":"f87695d60532422626f6953c2c7a59b2185c141ddf9b7b73d895437b29cdc179"},"schema_version":"1.0","source":{"id":"1407.5518","kind":"arxiv","version":1}},"canonical_sha256":"4ccaf18ac320dad946dc5054d5e935f87739ca96d4f65ae4d5606d89de6dadbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ccaf18ac320dad946dc5054d5e935f87739ca96d4f65ae4d5606d89de6dadbc","first_computed_at":"2026-05-18T02:47:13.867519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:13.867519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PQjCDZwEQE160bN5PeoEVPOWrGcFwnjm4YwFPZVB7o70aW0mE5V+KMXgAfRKwi7HYnQTMsACYHqIsVEGyjIRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:13.868140Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5518","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6035ef0bc8b989d0ec8c67594b3542d51a8acc42c9b00c3979d14067a629c41c","sha256:84799977aae00963d86c0ef25898947413d6f542c9706a66b12760379e13c63f"],"state_sha256":"8adc2eed17c9f9ccccbc070201a21966a7a878a7c7e94355d801a27d0955960c"}