{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:OHMUDS3CAHSNL52V2VQZ6FCJNI","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":"3bd395092b7d468d9151baae1dbe96d0f82c1ca487b7e3539edcd5137a510994","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-01T18:20:49Z","title_canon_sha256":"b624e4bf451052b6a52d92db8a24f0398776834a2cd4197fe43796ee30cbcd2a"},"schema_version":"1.0","source":{"id":"1311.0245","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0245","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0245v2","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0245","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"OHMUDS3CAHSN","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"OHMUDS3CAHSNL52V","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"OHMUDS3C","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:341674bd51fc33f416b8a3dd25da151db5a1b50b853b81a2ec2cdca835538c67","target":"graph","created_at":"2026-05-18T02:31:36Z","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 study the phenomena that arise when we combine the standard pseudodifferential operators with those operators that appear in the study of some sub-elliptic estimates, and on strongly pseudoconvex domains. The algebra of operators we introduce is geometrically invariant, and is adapted to a smooth distribution of tangent subspaces of constant rank. We isolate certain ideals in the algebra whose analysis is of particular interest.","authors_text":"Elias M. Stein, Po-Lam Yung","cross_cats":["math.AP","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-01T18:20:49Z","title":"Pseudodifferential operators of mixed type adapted to distributions of $k$-planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0245","kind":"arxiv","version":2},"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":"sha256:736126874770fcecafc5d84124819e866a7b6458ab8a65e123c21f5eb56daeea","target":"record","created_at":"2026-05-18T02:31:36Z","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":"3bd395092b7d468d9151baae1dbe96d0f82c1ca487b7e3539edcd5137a510994","cross_cats_sorted":["math.AP","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-11-01T18:20:49Z","title_canon_sha256":"b624e4bf451052b6a52d92db8a24f0398776834a2cd4197fe43796ee30cbcd2a"},"schema_version":"1.0","source":{"id":"1311.0245","kind":"arxiv","version":2}},"canonical_sha256":"71d941cb6201e4d5f755d5619f14496a0acea3e80d72e4f4a5680c704f4be407","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71d941cb6201e4d5f755d5619f14496a0acea3e80d72e4f4a5680c704f4be407","first_computed_at":"2026-05-18T02:31:36.124987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:36.124987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fmx2dNsAmTmm6QBiMXKchion2nzey0+bEBxq0aLpZHzrqvQTixfxGemqS8x9NQmVNSbGIuX8Z0z+JMKkLTRBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:36.125688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0245","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:736126874770fcecafc5d84124819e866a7b6458ab8a65e123c21f5eb56daeea","sha256:341674bd51fc33f416b8a3dd25da151db5a1b50b853b81a2ec2cdca835538c67"],"state_sha256":"d6301fd6a0026db5bb034faf76c159ed82a2f87214b0e5ab05b92bf5b5c3a2b2"}