{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7MGGNFPCY5UHZT3UHUJF5FAC4E","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":"260edbcfafd565d69eaf6d236ef2709e57129a0793c585b47e9800186e42e7f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T10:08:13Z","title_canon_sha256":"5fe05fafc2bf4e5580eed4039070726a82fdfcf99536e9366635aa174b65d174"},"schema_version":"1.0","source":{"id":"1906.01313","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.01313","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"arxiv_version","alias_value":"1906.01313v1","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.01313","created_at":"2026-05-17T23:44:17Z"},{"alias_kind":"pith_short_12","alias_value":"7MGGNFPCY5UH","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7MGGNFPCY5UHZT3U","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7MGGNFPC","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:7d0622b1afa3de0d93c0bdacdd143f29bd6e60fccd6018c0ebc69bd2e8291dc4","target":"graph","created_at":"2026-05-17T23:44:17Z","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":"There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to possess a non-zero Toeplitz operator. This condition is just that the adjoint of the product of the contractions is not pure. On one hand this brings out the importance of the product of the contractions and on the other hand, the non-pureness turns out to be equivalent to the existence of a pseudo-extension to a tuple of commuting unitaries. The second main result is a commutant pseudo-extension theorem obtained by stud","authors_text":"B. Krishna Das, Haripada Sau, Tirthankar Bhattacharyya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T10:08:13Z","title":"Toeplitz operators and pseudo-extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.01313","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:bef49a2503878817bdc8c11b28a70023195e0cf04cd28ecda5d2eef459933465","target":"record","created_at":"2026-05-17T23:44:17Z","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":"260edbcfafd565d69eaf6d236ef2709e57129a0793c585b47e9800186e42e7f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-06-04T10:08:13Z","title_canon_sha256":"5fe05fafc2bf4e5580eed4039070726a82fdfcf99536e9366635aa174b65d174"},"schema_version":"1.0","source":{"id":"1906.01313","kind":"arxiv","version":1}},"canonical_sha256":"fb0c6695e2c7687ccf743d125e9402e13353e527aa0e3e1d514af2ebdc87820a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb0c6695e2c7687ccf743d125e9402e13353e527aa0e3e1d514af2ebdc87820a","first_computed_at":"2026-05-17T23:44:17.034456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:17.034456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5V1ZnMqTSWerRwxTsG1SNDFIVGQz3IWrXbFgSMU29wd7nOlTLHJDjdZCqh1JULtSRHkfAUCk1YjXjK/ttanZAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:17.035218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.01313","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bef49a2503878817bdc8c11b28a70023195e0cf04cd28ecda5d2eef459933465","sha256:7d0622b1afa3de0d93c0bdacdd143f29bd6e60fccd6018c0ebc69bd2e8291dc4"],"state_sha256":"f3a616feb97e2188ef79401b6d999bce7570a1302d8471f9a7395a60d1c7256c"}