{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RNKJNRH65XMSSDGVSEUPWGPLPI","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":"2c1feb35930e8bd158e4e70ab71612e2ea1fdf1503c6c596bea4d6ddeb9b1610","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-23T09:49:56Z","title_canon_sha256":"a9b517b43886ab5b7b5e9e10199797e98f4a22b94c50c47979725510b9ca63b3"},"schema_version":"1.0","source":{"id":"1606.07248","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07248","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07248v3","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07248","created_at":"2026-05-18T00:37:54Z"},{"alias_kind":"pith_short_12","alias_value":"RNKJNRH65XMS","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RNKJNRH65XMSSDGV","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RNKJNRH6","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:b7b607e48bdc4c44584ec5f059d0f29c78af16f6da0fe1069eddbc982ee9bdb4","target":"graph","created_at":"2026-05-18T00:37:54Z","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 give an algorithm for finding a solution to the Carath\\'{e}odory-Fej\\'{e}r interpolation problem on the polydisc $\\mathbb D^n,$ whenever it exists. A necessary condition for the existence of a solution becomes apparent from this algorithm. A generalization of the well-known theorem due to Nehari has been obtained. A proof of the Kor\\'{a}nyi--Puk\\'{a}nszky theorem is given using the spectral theorem.","authors_text":"Gadadhar Misra, Rajeev Gupta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-23T09:49:56Z","title":"The Carath\\'eodory-Fej\\'er interpolation problem for the polydisc"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07248","kind":"arxiv","version":3},"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:d145cea69296ec6728d4957f708c43347d63f9b600bc80896f89fd1f11182855","target":"record","created_at":"2026-05-18T00:37:54Z","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":"2c1feb35930e8bd158e4e70ab71612e2ea1fdf1503c6c596bea4d6ddeb9b1610","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-06-23T09:49:56Z","title_canon_sha256":"a9b517b43886ab5b7b5e9e10199797e98f4a22b94c50c47979725510b9ca63b3"},"schema_version":"1.0","source":{"id":"1606.07248","kind":"arxiv","version":3}},"canonical_sha256":"8b5496c4feedd9290cd59128fb19eb7a005e58b27f97a96be6b45e0a4cad65ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b5496c4feedd9290cd59128fb19eb7a005e58b27f97a96be6b45e0a4cad65ce","first_computed_at":"2026-05-18T00:37:54.862539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:54.862539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xIw2IyxjkJdg4/1jifX0x5ceQdt53Mlu7qJF5J7bGrOKe2x/hhRQ5mUOHSiOw2LFeamIuJiLvESr6eWEh2b0BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:54.863211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07248","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d145cea69296ec6728d4957f708c43347d63f9b600bc80896f89fd1f11182855","sha256:b7b607e48bdc4c44584ec5f059d0f29c78af16f6da0fe1069eddbc982ee9bdb4"],"state_sha256":"c4eccb7db65c1b4d1876097efabfc21f18cb6b47c8632697ca4e745de6e250c1"}