{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:46R7PGAZP3OMSG5A4O3HBALEKD","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":"b727bb8173ed1a3098720da98bb7ecfc7bec397d34060f35720062e482e5af69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-10T08:40:30Z","title_canon_sha256":"6e38007a16efb00e2033b12cbb72dac4a4146e48d0b52ba77cb34b8fe372a035"},"schema_version":"1.0","source":{"id":"1701.02474","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02474","created_at":"2026-05-18T00:42:17Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02474v2","created_at":"2026-05-18T00:42:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02474","created_at":"2026-05-18T00:42:17Z"},{"alias_kind":"pith_short_12","alias_value":"46R7PGAZP3OM","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"46R7PGAZP3OMSG5A","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"46R7PGAZ","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:36fbec15102072fa4a573e10938678ebd6db012135742abb2f4d77ba57d0d9dd","target":"graph","created_at":"2026-05-18T00:42:17Z","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":"In this paper, we consider the question of contractivity vs. complete contractivity for domains in $\\mathbb{C}^2$, which are unit balls with respect to some norm. We show that for a large class of Reinhardt domains, the corresponding Banach spaces do not have Property P, which implies that there exists contractive homomorphisms on these domains which are not completely contractive. At the end, we present a simple proof of the fact that the complex Banach spaces $(\\mathbb{C}^2,\\|\\cdot\\|_{\\infty})$ and $(\\mathbb{C}^3,\\|\\cdot\\|_{\\infty})$ have Property P.","authors_text":"Samya Kumar Ray","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-10T08:40:30Z","title":"Contractivity vs. Complete Contractivity via property P"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02474","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":"sha256:2f782c42fb0da8b12813ae0c26c789452ba5d050909635f4c997946ab2fabd7f","target":"record","created_at":"2026-05-18T00:42:17Z","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":"b727bb8173ed1a3098720da98bb7ecfc7bec397d34060f35720062e482e5af69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-01-10T08:40:30Z","title_canon_sha256":"6e38007a16efb00e2033b12cbb72dac4a4146e48d0b52ba77cb34b8fe372a035"},"schema_version":"1.0","source":{"id":"1701.02474","kind":"arxiv","version":2}},"canonical_sha256":"e7a3f798197edcc91ba0e3b670816450d9f46c9d7f8f4fd5abbac7eef0b40e58","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7a3f798197edcc91ba0e3b670816450d9f46c9d7f8f4fd5abbac7eef0b40e58","first_computed_at":"2026-05-18T00:42:17.504369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:17.504369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eM7sQQwUGaKF6z1JOeNe4G6o1rMphUew7Rs/6GC52fAdat5gHqpfmTzqHgUiviC5KB9iNYIPiLvq9GecbVtfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:17.504985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02474","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f782c42fb0da8b12813ae0c26c789452ba5d050909635f4c997946ab2fabd7f","sha256:36fbec15102072fa4a573e10938678ebd6db012135742abb2f4d77ba57d0d9dd"],"state_sha256":"acc0c6e0ff2b20e1f86bcbc2eef770dc5bdf05de0a0a2daded9a6880ab576a9f"}