{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4SGCX2J5SD2TFSZANM5FJ4WKHE","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":"06ecd6c13631396e806f38b56d0c9594ec324bb19bd220f31ba179420dbb2c4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-01T03:27:41Z","title_canon_sha256":"bbf995eaef2f4fa6d7d538f0babf4c400b4abbf9611d6d1f576cf0aaaca5ac0b"},"schema_version":"1.0","source":{"id":"1305.0078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0078","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0078v1","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0078","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"4SGCX2J5SD2T","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4SGCX2J5SD2TFSZA","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4SGCX2J5","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:67c32ba1726a9a9515346150629db9104eab985e574a7b4ff88419a48eee0d54","target":"graph","created_at":"2026-05-18T03:26:42Z","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":"Let $ \\ti \\Om $ be a bounded convex domain in Euclidean $ n $ space, $ \\hat x \\in \\ar \\ti \\Om, $ and $ r > 0. $ Let $ \\ti u = (\\ti u^1, \\ti u^2, \\dots, \\ti u^N) $ be a weak solution to \\[\\nabla \\cdot \\left (|\\nabla \\ti u |^{p-2} \\nabla \\ti u \\right) = 0 \\mbox{in} \\ti \\Om \\cap B (\\hat x, 4 r) \\mbox{with} |\\nabla \\ti u|^{p-2} \\, \\ti u_\\nu = 0 \\mbox{on} \\ar \\ti \\Om \\cap B (\\hat x, 4 r). \\] We show that sub solution type arguments for certain uniformly elliptic systems can be used to deduce that $ | \\nabla \\ti u | $ is bounded in $ \\ti \\Om \\cap B (\\hat x, r)$ with constants depending only on $ n, ","authors_text":"Agnid Banerjee, John L. Lewis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-01T03:27:41Z","title":"Gradient bounds for p-harmonic systems with vanishing neumann data in a convex domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0078","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":"sha256:3fd0468530ef8cb638e8214c317bdae50f3cb27b11dbd4103ef530870490c7ca","target":"record","created_at":"2026-05-18T03:26:42Z","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":"06ecd6c13631396e806f38b56d0c9594ec324bb19bd220f31ba179420dbb2c4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-01T03:27:41Z","title_canon_sha256":"bbf995eaef2f4fa6d7d538f0babf4c400b4abbf9611d6d1f576cf0aaaca5ac0b"},"schema_version":"1.0","source":{"id":"1305.0078","kind":"arxiv","version":1}},"canonical_sha256":"e48c2be93d90f532cb206b3a54f2ca393f784565376cd15b72a09d7920bbc4db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e48c2be93d90f532cb206b3a54f2ca393f784565376cd15b72a09d7920bbc4db","first_computed_at":"2026-05-18T03:26:42.080089Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:42.080089Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jJpIjSopD6BsNzNpYxnbqy7A5lGO5f39wL43XIUOuNPWFfw5aRwzFKIY9Gpt4hx8GQ/y9RprcJMUuwU5/g8HAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:42.080892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fd0468530ef8cb638e8214c317bdae50f3cb27b11dbd4103ef530870490c7ca","sha256:67c32ba1726a9a9515346150629db9104eab985e574a7b4ff88419a48eee0d54"],"state_sha256":"3f21396771348f955bcac46fc238191f73b637eb36cde7be76cbedd8fd26c483"}