{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:YFJACO7MQVXCKCJ5RGIL2UKH4H","short_pith_number":"pith:YFJACO7M","schema_version":"1.0","canonical_sha256":"c152013bec856e25093d8990bd5147e1c1f98b1e5a89ed3e4505d500de2aa3e6","source":{"kind":"arxiv","id":"1408.2389","version":1},"attestation_state":"computed","paper":{"title":"Contractivity, Complete Contractivity and Curvature inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal","submitted_at":"2014-08-11T12:49:14Z","abstract_excerpt":"Let $\\|\\cdot\\|_{\\mathbf A}$ be a norm on $\\mathbb C^m$ given by the formula $\\|(z_1,\\ldots,z_m)\\|_{\\mathbf A}=\\|z_1A_1+\\cdots+z_mA_m\\|_{\\rm op}$ for some choice of an $m$-tuple of $n\\times n$ linearly independent matrices $\\mathbf A=(A_1, \\ldots, A_m).$ Let $\\Omega_\\mathbf A\\subset \\mathbb C^m$ be the unit ball with respect to the norm $\\|\\cdot\\|_{\\mathbf A}.$ %For a holomorphic function $f$ on $\\Omega_\\mathbf A,$ let %$\\rho_{V}(f):=\\left ( %\\begin{smallmatrix} %f(w)I_p& \\sum_{i=1}^{m} \\partial_if(w)V_{i} \\\\ %0 & f(w)I_q %\\end{smallmatrix}\\right ),$ where $V_1, \\ldots, V_m$ are $p\\times q$ %ma"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1408.2389","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-08-11T12:49:14Z","cross_cats_sorted":[],"title_canon_sha256":"b76b33057bb6791015d27dce96b75b6d448b321af148950a9f6eb5216fe11641","abstract_canon_sha256":"43c8e1a18fd1b65106f4b9ed2952360fb0be12ddb5e04672b4377e5f9e6be86a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:29.541373Z","signature_b64":"GydAzJe9y7YPcLezBOZqq+t/J29gh5sFqJrmzCB9CCn3aYk5W7N0pMLoaHr+mmioXU0oJVO5TfyKyfrKuN70Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c152013bec856e25093d8990bd5147e1c1f98b1e5a89ed3e4505d500de2aa3e6","last_reissued_at":"2026-05-18T02:45:29.540841Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:29.540841Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contractivity, Complete Contractivity and Curvature inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Avijit Pal","submitted_at":"2014-08-11T12:49:14Z","abstract_excerpt":"Let $\\|\\cdot\\|_{\\mathbf A}$ be a norm on $\\mathbb C^m$ given by the formula $\\|(z_1,\\ldots,z_m)\\|_{\\mathbf A}=\\|z_1A_1+\\cdots+z_mA_m\\|_{\\rm op}$ for some choice of an $m$-tuple of $n\\times n$ linearly independent matrices $\\mathbf A=(A_1, \\ldots, A_m).$ Let $\\Omega_\\mathbf A\\subset \\mathbb C^m$ be the unit ball with respect to the norm $\\|\\cdot\\|_{\\mathbf A}.$ %For a holomorphic function $f$ on $\\Omega_\\mathbf A,$ let %$\\rho_{V}(f):=\\left ( %\\begin{smallmatrix} %f(w)I_p& \\sum_{i=1}^{m} \\partial_if(w)V_{i} \\\\ %0 & f(w)I_q %\\end{smallmatrix}\\right ),$ where $V_1, \\ldots, V_m$ are $p\\times q$ %ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2389","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1408.2389","created_at":"2026-05-18T02:45:29.540924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1408.2389v1","created_at":"2026-05-18T02:45:29.540924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2389","created_at":"2026-05-18T02:45:29.540924+00:00"},{"alias_kind":"pith_short_12","alias_value":"YFJACO7MQVXC","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"YFJACO7MQVXCKCJ5","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"YFJACO7M","created_at":"2026-05-18T12:28:57.508820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H","json":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H.json","graph_json":"https://pith.science/api/pith-number/YFJACO7MQVXCKCJ5RGIL2UKH4H/graph.json","events_json":"https://pith.science/api/pith-number/YFJACO7MQVXCKCJ5RGIL2UKH4H/events.json","paper":"https://pith.science/paper/YFJACO7M"},"agent_actions":{"view_html":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H","download_json":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H.json","view_paper":"https://pith.science/paper/YFJACO7M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1408.2389&json=true","fetch_graph":"https://pith.science/api/pith-number/YFJACO7MQVXCKCJ5RGIL2UKH4H/graph.json","fetch_events":"https://pith.science/api/pith-number/YFJACO7MQVXCKCJ5RGIL2UKH4H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H/action/storage_attestation","attest_author":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H/action/author_attestation","sign_citation":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H/action/citation_signature","submit_replication":"https://pith.science/pith/YFJACO7MQVXCKCJ5RGIL2UKH4H/action/replication_record"}},"created_at":"2026-05-18T02:45:29.540924+00:00","updated_at":"2026-05-18T02:45:29.540924+00:00"}