{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SG7VEC5PWXCBKRLCK4VRATVRGJ","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":"d81d379e39c9cdec286b71cd3fc13503e523bb326f81c0199ce84748481d3187","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T09:32:38Z","title_canon_sha256":"b3abc319681809cbfa00a297de482011ecb819788516bd251dd014728b5e31b2"},"schema_version":"1.0","source":{"id":"1503.03234","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.03234","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1503.03234v1","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.03234","created_at":"2026-05-18T01:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"SG7VEC5PWXCB","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SG7VEC5PWXCBKRLC","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SG7VEC5P","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:6dc415d845c3e60e99697cb52c425e366022080e308c1e25b45360cd08007402","target":"graph","created_at":"2026-05-18T01:06:41Z","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":"By using a nonassociative algebra argument, we prove that $u\\equiv0$ is the only cubic homogeneous polynomial solution to the $p$-Laplace equation $\\mathrm{div} |Du|^{p-2}Du(x)=0 $ in $\\mathbb{R}^n$ for any $n\\ge2$ and $p\\not\\in\\{0,2\\}$.","authors_text":"Vladimir G. Tkachev","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T09:32:38Z","title":"On the non-vanishing property for real analytic solutions of the $p$-Laplace equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.03234","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:d19e75a72a98e9ab459a6cc057b7d0988e308b70f84271fe7840cbe93ba3a878","target":"record","created_at":"2026-05-18T01:06:41Z","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":"d81d379e39c9cdec286b71cd3fc13503e523bb326f81c0199ce84748481d3187","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-11T09:32:38Z","title_canon_sha256":"b3abc319681809cbfa00a297de482011ecb819788516bd251dd014728b5e31b2"},"schema_version":"1.0","source":{"id":"1503.03234","kind":"arxiv","version":1}},"canonical_sha256":"91bf520bafb5c4154562572b104eb13250adeefc9dd737eb6d377500319a3076","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91bf520bafb5c4154562572b104eb13250adeefc9dd737eb6d377500319a3076","first_computed_at":"2026-05-18T01:06:41.134456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:41.134456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5YYr9p5e71w5lnAW8ukC2xXIJH5y1XOT6mEZO+K2Yioc6JmfLHFNJaiuxLYf6BfHFc3sjYW00JZw+PqZHIOlBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:41.135088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.03234","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d19e75a72a98e9ab459a6cc057b7d0988e308b70f84271fe7840cbe93ba3a878","sha256:6dc415d845c3e60e99697cb52c425e366022080e308c1e25b45360cd08007402"],"state_sha256":"e50f4a8921da4c2ac3dc86ef80ce1e2551ce9fd132b0d14f840a1d995bdf7547"}