{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4IHC6JANLXCMCN77FCQVUPOOW6","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":"26ae3d59adbd477b599996150bb5449d5b4fd5cb459f9458105e9b44a766abba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T04:44:11Z","title_canon_sha256":"23ca1afde64ab5193ec2ad3c6be0aa4e041db3e05539a90b5919c91168d4e361"},"schema_version":"1.0","source":{"id":"1305.7002","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.7002","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1305.7002v1","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.7002","created_at":"2026-05-18T03:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"4IHC6JANLXCM","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4IHC6JANLXCMCN77","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4IHC6JAN","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:c5be74496b2c0287413099be336f30d57d361c04058618b065dfba90e8e68228","target":"graph","created_at":"2026-05-18T03:03:32Z","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":"We analyze degenerate, second-order, elliptic operators $H$ in divergence form on $L_2(\\Ri^{n}\\times\\Ri^{m})$. We assume the coefficients are real symmetric and $a_1H_\\delta\\geq H\\geq a_2H_\\delta$ for some $a_1,a_2>0$ where \\[ H_\\delta=-{\\nabla}_{x_1}\\cdot(c_{\\delta_1, \\delta'_1}(x_1)\\,\\nabla_{x_1})-c_{\\delta_2, \\delta'_2}(x_1)\\,\\nabla_{x_2}^2 \\;. \\] Here $x_1\\in\\Ri^n$, $x_2\\in\\Ri^m$ and $c_{\\delta_i, \\delta'_i}$ are positive measurable functions such that $c_{\\delta_i, \\delta'_i}(x)$ behaves like $|x|^{\\delta_i}$ as $x\\to0$ and $|x|^{\\delta_i'}$ as $x\\to\\infty$ with $\\delta_1,\\delta_1'\\in[0,1","authors_text":"Adam Sikora, Derek W. Robinson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T04:44:11Z","title":"Analysis of degenerate elliptic operators of Gru\\v{s}in type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.7002","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":"sha256:5e5dc45661cd4281299f41415cbee55457bced1ebfddd44c7dfd7359def0c6d9","target":"record","created_at":"2026-05-18T03:03:32Z","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":"26ae3d59adbd477b599996150bb5449d5b4fd5cb459f9458105e9b44a766abba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-05-30T04:44:11Z","title_canon_sha256":"23ca1afde64ab5193ec2ad3c6be0aa4e041db3e05539a90b5919c91168d4e361"},"schema_version":"1.0","source":{"id":"1305.7002","kind":"arxiv","version":1}},"canonical_sha256":"e20e2f240d5dc4c137ff28a15a3dceb79742a3f5aaf060a2a072a10cfa0b20da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e20e2f240d5dc4c137ff28a15a3dceb79742a3f5aaf060a2a072a10cfa0b20da","first_computed_at":"2026-05-18T03:03:32.154951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:32.154951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pGiiAS7gXFoXa8yg6R7KGEt2v+ubsAD7ZztGPELRJKa7OGKyfZ3ZBvZ9cf0Rgp8wQ2bSVcKSc5T2DtDAyn+qDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:32.155564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.7002","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e5dc45661cd4281299f41415cbee55457bced1ebfddd44c7dfd7359def0c6d9","sha256:c5be74496b2c0287413099be336f30d57d361c04058618b065dfba90e8e68228"],"state_sha256":"dbc7e53da8d2eb6dbfc86d83af861fec4da45a821d17097766b428fb04f753cb"}