{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:52VUVEB3ZNO7ABNKJ2KO7XTWYR","short_pith_number":"pith:52VUVEB3","schema_version":"1.0","canonical_sha256":"eeab4a903bcb5df005aa4e94efde76c4740478566cf57a802849144aff2c2794","source":{"kind":"arxiv","id":"2607.23592","version":1},"attestation_state":"computed","paper":{"title":"Some counterexamples for the special lagrangian curvature equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Guanyu Tao, Guohuan Qiu","submitted_at":"2026-07-26T10:42:01Z","abstract_excerpt":"We construct three counterexamples for the special Lagrangian curvature equation (SLCE). First, in dimension two, we use a post-focal branch of a parallel surface with constant positive Gauss curvature to construct an explicit Lipschitz viscosity solution which is not $C^1$. Second, still in dimension two, we construct a sequence of smooth admissible solutions on a fixed rectangle with uniformly bounded $C^1$-norm but unbounded curvature at one point; furthermore, we show that any uniform $C^{1,\\beta}$ estimate fails for $\\beta > 1/3$. Third, in dimension three and in the subcritical phase, we"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.23592","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-26T10:42:01Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"6bcfeb07bdc30283dfa4e658fcac436ed6124ce87358940462b61aea638dbfa5","abstract_canon_sha256":"5acdbf6154e8ca11bb093c89ea5d0582e940e2ff69f7b9c6558cdc6a93ba6b30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:23:01.017459Z","signature_b64":"szB7ed1ppDfeN/F1KWTKnxXalYr1f3TVQBr9XiyqacKsfniiWXuNUfxolrY6TfdG1fK52ScXYlhxyvS13MhzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eeab4a903bcb5df005aa4e94efde76c4740478566cf57a802849144aff2c2794","last_reissued_at":"2026-07-28T01:23:01.016610Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:23:01.016610Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some counterexamples for the special lagrangian curvature equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Guanyu Tao, Guohuan Qiu","submitted_at":"2026-07-26T10:42:01Z","abstract_excerpt":"We construct three counterexamples for the special Lagrangian curvature equation (SLCE). First, in dimension two, we use a post-focal branch of a parallel surface with constant positive Gauss curvature to construct an explicit Lipschitz viscosity solution which is not $C^1$. Second, still in dimension two, we construct a sequence of smooth admissible solutions on a fixed rectangle with uniformly bounded $C^1$-norm but unbounded curvature at one point; furthermore, we show that any uniform $C^{1,\\beta}$ estimate fails for $\\beta > 1/3$. Third, in dimension three and in the subcritical phase, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23592","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.23592","created_at":"2026-07-28T01:23:01.017046+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.23592v1","created_at":"2026-07-28T01:23:01.017046+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23592","created_at":"2026-07-28T01:23:01.017046+00:00"},{"alias_kind":"pith_short_12","alias_value":"52VUVEB3ZNO7","created_at":"2026-07-28T01:23:01.017046+00:00"},{"alias_kind":"pith_short_16","alias_value":"52VUVEB3ZNO7ABNK","created_at":"2026-07-28T01:23:01.017046+00:00"},{"alias_kind":"pith_short_8","alias_value":"52VUVEB3","created_at":"2026-07-28T01:23:01.017046+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR","json":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR.json","graph_json":"https://pith.science/api/pith-number/52VUVEB3ZNO7ABNKJ2KO7XTWYR/graph.json","events_json":"https://pith.science/api/pith-number/52VUVEB3ZNO7ABNKJ2KO7XTWYR/events.json","paper":"https://pith.science/paper/52VUVEB3"},"agent_actions":{"view_html":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR","download_json":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR.json","view_paper":"https://pith.science/paper/52VUVEB3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.23592&json=true","fetch_graph":"https://pith.science/api/pith-number/52VUVEB3ZNO7ABNKJ2KO7XTWYR/graph.json","fetch_events":"https://pith.science/api/pith-number/52VUVEB3ZNO7ABNKJ2KO7XTWYR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR/action/storage_attestation","attest_author":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR/action/author_attestation","sign_citation":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR/action/citation_signature","submit_replication":"https://pith.science/pith/52VUVEB3ZNO7ABNKJ2KO7XTWYR/action/replication_record"}},"created_at":"2026-07-28T01:23:01.017046+00:00","updated_at":"2026-07-28T01:23:01.017046+00:00"}