{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:X73FO7K3QDAZJZISM2SK2GRCB7","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":"51ce9d7392369d796f0c89379c2137228a298e415de480e14bd64a9715560d69","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-12-11T20:54:08Z","title_canon_sha256":"7740351a6c4f5e4c4b59cc214f7fd597bc0999277d41b7f92f423c8dbca87514"},"schema_version":"1.0","source":{"id":"0912.2340","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2340","created_at":"2026-05-18T04:27:18Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2340v2","created_at":"2026-05-18T04:27:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2340","created_at":"2026-05-18T04:27:18Z"},{"alias_kind":"pith_short_12","alias_value":"X73FO7K3QDAZ","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"X73FO7K3QDAZJZIS","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"X73FO7K3","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:910a6da326b10d5294bfbd4b02d467df693f791a1cc9acd13777776f9a2ccae1","target":"graph","created_at":"2026-05-18T04:27:18Z","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":"In this paper we extend a method of Arveson and McCullough to prove a tangential interpolation theorem for subalgebras of $H^\\infty$. This tangential interpolation result implies a Toelitz corona theorem. In particular, it is shown that the set of matrix positivity conditions is indexed by cyclic subspaces, which is analogous to the results obtained for the ball and the polydisk algebra by Trent-Wick and Douglas-Sarkar.","authors_text":"Brett D. Wick, Mrinal Raghupathi","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-12-11T20:54:08Z","title":"Duality, Tangential Interpolation, and Toeplitz Corona Problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2340","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:ac509005826aa2032e568a354315ad6b9babc3607166ce5bf74c1f1335a67b1d","target":"record","created_at":"2026-05-18T04:27:18Z","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":"51ce9d7392369d796f0c89379c2137228a298e415de480e14bd64a9715560d69","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2009-12-11T20:54:08Z","title_canon_sha256":"7740351a6c4f5e4c4b59cc214f7fd597bc0999277d41b7f92f423c8dbca87514"},"schema_version":"1.0","source":{"id":"0912.2340","kind":"arxiv","version":2}},"canonical_sha256":"bff6577d5b80c194e51266a4ad1a220fc081ef424cfb13090f6dc1e0af6aaefa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bff6577d5b80c194e51266a4ad1a220fc081ef424cfb13090f6dc1e0af6aaefa","first_computed_at":"2026-05-18T04:27:18.002106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:18.002106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5rxUGeEl1NWGpmaf9eOUbxY+HLddT/mIXItz126zRFSrB6EDtfJAIG7nDIU7m4niccPg3WAZy2FbUnG5wDOsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:18.002626Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2340","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac509005826aa2032e568a354315ad6b9babc3607166ce5bf74c1f1335a67b1d","sha256:910a6da326b10d5294bfbd4b02d467df693f791a1cc9acd13777776f9a2ccae1"],"state_sha256":"3de27f4efe94972f01cb3d3a93d135a7fe205f5232ff83cd43b71b36eeef211b"}