{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:J2BPT46IRGTUIF6S4BF34VWEEN","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":"2aa763d47e2295c8cde5282cdf6fcb6fff204e0b85c22b279b1ae68cdcd658c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-28T10:28:00Z","title_canon_sha256":"3d01192e30d1394e107691ea0f29357a2d2a759e071378537ae0d7c601121a62"},"schema_version":"1.0","source":{"id":"1712.09808","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.09808","created_at":"2026-05-18T00:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1712.09808v1","created_at":"2026-05-18T00:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09808","created_at":"2026-05-18T00:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"J2BPT46IRGTU","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"J2BPT46IRGTUIF6S","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"J2BPT46I","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:5cc49191109b48721e3d75f42807a90f9967fc50ab9a4a56109fd07a74f91e54","target":"graph","created_at":"2026-05-18T00:27:05Z","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 prove the Kato conjecture for elliptic operators, $L=-\\nabla\\cdot\\left((\\mathbf A+\\mathbf D)\\nabla\\ \\right)$, with $\\mathbf A$ a complex measurable bounded coercive matrix and $\\mathbf D$ a measurable real-valued skew-symmetric matrix in $\\mathbb{R}^n$ with entries in $BMO(\\mathbb{R}^n)$;\\, i.e., the domain of $\\sqrt{L}\\,$ is the Sobolev space $\\dot H^1(\\mathbb{R}^n)$ in any dimension, with the estimate $\\|\\sqrt{L}\\, f\\|_2\\lesssim \\| \\nabla f\\|_2$.","authors_text":"Luis Escauriaza, Steve Hofmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-28T10:28:00Z","title":"Kato square root problem with unbounded leading coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09808","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:fb873946730030bb935c48d1ae6cce13ff692a12070e7095445127bcd9b0678a","target":"record","created_at":"2026-05-18T00:27:05Z","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":"2aa763d47e2295c8cde5282cdf6fcb6fff204e0b85c22b279b1ae68cdcd658c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-28T10:28:00Z","title_canon_sha256":"3d01192e30d1394e107691ea0f29357a2d2a759e071378537ae0d7c601121a62"},"schema_version":"1.0","source":{"id":"1712.09808","kind":"arxiv","version":1}},"canonical_sha256":"4e82f9f3c889a74417d2e04bbe56c423442a17654390874407f0d4fbc2bd8301","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e82f9f3c889a74417d2e04bbe56c423442a17654390874407f0d4fbc2bd8301","first_computed_at":"2026-05-18T00:27:05.499150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:05.499150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PRNYf1V+5Y0F0bH130mQwbm8hixAxe5m9kytH2EmS3jEN0sA8aUpLsqHh6j7cgsoNwK1exbmXZsEba3TtLxGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:05.499638Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.09808","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb873946730030bb935c48d1ae6cce13ff692a12070e7095445127bcd9b0678a","sha256:5cc49191109b48721e3d75f42807a90f9967fc50ab9a4a56109fd07a74f91e54"],"state_sha256":"22822fe34f19931614025ed3a9a3c5833071ffa123bb04a70dac9fcf92298610"}