{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ZP53K32GETTMOOYCN7UXFTYRUN","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":"add182031647ea8c722bd94a15f6b9c6c209ba08b7e9942e5f4cd48e3ca80b37","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T15:31:14Z","title_canon_sha256":"4136debcd3e20a3ed3686ac780ff2b2ae952d8590881762f5823ba79b4b0186f"},"schema_version":"1.0","source":{"id":"2608.13366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13366","created_at":"2026-08-14T01:04:18Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13366v1","created_at":"2026-08-14T01:04:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13366","created_at":"2026-08-14T01:04:18Z"},{"alias_kind":"pith_short_12","alias_value":"ZP53K32GETTM","created_at":"2026-08-14T01:04:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZP53K32GETTMOOYC","created_at":"2026-08-14T01:04:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZP53K32G","created_at":"2026-08-14T01:04:18Z"}],"graph_snapshots":[{"event_id":"sha256:de140e1df731afbd0848bf4d20e4cfd6e5783dce19a1c359eae3961637571e84","target":"graph","created_at":"2026-08-14T01:04:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2608.13366/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we introduce the notion of a distinguished variety in the domain $\\mathbf{\\Theta}_n$. One of the main results of the paper is a determinantal representation for every distinguished variety in $\\mathbf{\\Theta}_n$. We also show that the closure of every distinguished variety is polynomially convex. Furthermore, we obtain a dilation and a functional model for a class of pure $\\mathbf{\\Theta}_n$-contractions. Finally, we show that for a $\\mathbf{\\Theta}_n$-contraction $\\mathbf{T}=(T_1,\\dots,T_n)$ such that $T_n^*$ is a pure contraction, there exists an algebraic variety in $\\mathbf{","authors_text":"Aparna Gupta, Bhaskar Paul, Shubhankar Mandal Avijit Pal","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T15:31:14Z","title":"Dilation and Functional Models for Pure $\\mathbf{\\Theta}_n$-Contractions and the von Neumann Inequality on Distinguished Varieties in $\\mathbf{\\Theta}_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13366","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:df42cb645b1ab9f8c05c52a7de07db2e867e235ec5fcbeb8b2a86f9087f67bad","target":"record","created_at":"2026-08-14T01:04:18Z","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":"add182031647ea8c722bd94a15f6b9c6c209ba08b7e9942e5f4cd48e3ca80b37","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T15:31:14Z","title_canon_sha256":"4136debcd3e20a3ed3686ac780ff2b2ae952d8590881762f5823ba79b4b0186f"},"schema_version":"1.0","source":{"id":"2608.13366","kind":"arxiv","version":1}},"canonical_sha256":"cbfbb56f4624e6c73b026fe972cf11a37b342c76038db6ff29b2e097620b6ade","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cbfbb56f4624e6c73b026fe972cf11a37b342c76038db6ff29b2e097620b6ade","first_computed_at":"2026-08-14T01:04:18.271666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:04:18.271666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"thtSaXAM77V1qL7N93v04ZFTx2U61mYwN1WgAD+9ajgSViXg9Te8zHWroGA08lKeTXlPZ9JO5Wyoqvs/Ud2uAw==","signature_status":"signed_v1","signed_at":"2026-08-14T01:04:18.273306Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:df42cb645b1ab9f8c05c52a7de07db2e867e235ec5fcbeb8b2a86f9087f67bad","sha256:de140e1df731afbd0848bf4d20e4cfd6e5783dce19a1c359eae3961637571e84"],"state_sha256":"7b487f7a8953bbc4eaba6010e49b7e83866a16d7d35c2e6092f6eb6149b1cab1"}