{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TSQUNZXJJBAKVJXDFKXBPCOL6M","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":"9d24b49fed8e8d4161676a7327895ba252eb522191d1600e99e4ab71fe18cf64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-02T08:16:54Z","title_canon_sha256":"7942e79c0a93afb743c1893ec06247bd41145ae3eb67e3467963540f1508c6be"},"schema_version":"1.0","source":{"id":"1610.00237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.00237","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"arxiv_version","alias_value":"1610.00237v1","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.00237","created_at":"2026-05-18T01:03:31Z"},{"alias_kind":"pith_short_12","alias_value":"TSQUNZXJJBAK","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TSQUNZXJJBAKVJXD","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TSQUNZXJ","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:e8c6ee624e03c730a1e19ad6e12dc40242a769f7d5f742019384f12b241822d9","target":"graph","created_at":"2026-05-18T01:03:31Z","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":"The Aviles-Giga functional $I_{\\epsilon}(u)=\\int_{\\Omega} \\frac{\\left|1-\\left|\\nabla u\\right|^2\\right|^2}{\\epsilon}+\\epsilon \\left|\\nabla^2 u\\right|^2 \\, dx$ is a well known second order functional that models phenomena from blistering to liquid crystals. The zero energy states of the Aviles-Giga functional have been characterized by Jabin, Otto, Perthame. Among other results they showed that if $\\lim_{n\\rightarrow \\infty} I_{\\epsilon_n}(u_n)=0$ for some sequence $u_n\\in W^{2,2}_0(\\Omega)$ and $u=\\lim_{n\\rightarrow \\infty} u_n$ then $\\nabla u$ is Lipschitz continuous outside a locally finite s","authors_text":"Andrew Lorent, Guanying Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-02T08:16:54Z","title":"Regularity of the Eikonal equation with two vanishing entropies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00237","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:ab988b12e0d50f4e082b92f7774f602d8585f87e7ab9b3107404f231ca67ee62","target":"record","created_at":"2026-05-18T01:03:31Z","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":"9d24b49fed8e8d4161676a7327895ba252eb522191d1600e99e4ab71fe18cf64","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-02T08:16:54Z","title_canon_sha256":"7942e79c0a93afb743c1893ec06247bd41145ae3eb67e3467963540f1508c6be"},"schema_version":"1.0","source":{"id":"1610.00237","kind":"arxiv","version":1}},"canonical_sha256":"9ca146e6e94840aaa6e32aae1789cbf30131e53c2c859354b543933782cbdee9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ca146e6e94840aaa6e32aae1789cbf30131e53c2c859354b543933782cbdee9","first_computed_at":"2026-05-18T01:03:31.557267Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:31.557267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/hMBfOi5jq/qEmNMUBACGBkej0ueD277jHTjczyZ36pK2eyHX9DmN39c1DIGzpQL45HyjGptuM3umNAMLmm9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:31.557767Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.00237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ab988b12e0d50f4e082b92f7774f602d8585f87e7ab9b3107404f231ca67ee62","sha256:e8c6ee624e03c730a1e19ad6e12dc40242a769f7d5f742019384f12b241822d9"],"state_sha256":"a4aa5bd35bfe9928a677911c05760d9cbf3b0b2ca6688dbbab940cdc1b81a5cd"}