{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QABMF6MCWARYT3SGA2B6LAZR2P","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":"8dbebd85e557240c9846d5e13c989a17fdcfe45e1173ddc4ec58912f4b2f328f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-21T15:53:09Z","title_canon_sha256":"7b072fbd0845f79d31cc7f8085f3ca0686f02713699385eb4225ab27c660897b"},"schema_version":"1.0","source":{"id":"1604.06364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06364","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06364v2","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06364","created_at":"2026-05-18T01:16:23Z"},{"alias_kind":"pith_short_12","alias_value":"QABMF6MCWARY","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QABMF6MCWARYT3SG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QABMF6MC","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:3c7ecaf7bc67e79fc335935fec58f85eebc5ec72ae63c6cbc765670e9c1c3d48","target":"graph","created_at":"2026-05-18T01:16:23Z","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 extend some of the results of Agler, Knese, and McCarthy [1] to $n$-tuples of commuting isometries for $n>2$. Let $\\mathbb{V}=(V_1,\\dots,V_n)$ be an $n$-tuple of a commuting isometries on a Hilbert space and let Ann$(\\mathbb{V})$ denote the set of all $n$-variable polynomials $p$ such that $p(\\mathbb{V})=0$. When Ann$(\\mathbb{V})$ defines an affine algebraic variety of dimension 1 and $\\mathbb{V}$ is completely non-unitary, we show that $\\mathbb{V}$ decomposes as a direct sum of $n$-tuples $\\mathbb{W}=(W_1,\\dots,W_n)$ with the property that, for each $i=1,\\dots,n$, $W_i$ is either a shift o","authors_text":"Edward J. Timko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-21T15:53:09Z","title":"On polynomial $n$-tuples of commuting isometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06364","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":"sha256:77684213bd5a0aa7c4a3123b2771051a23db09a86842017f0d13324f87528f80","target":"record","created_at":"2026-05-18T01:16:23Z","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":"8dbebd85e557240c9846d5e13c989a17fdcfe45e1173ddc4ec58912f4b2f328f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-21T15:53:09Z","title_canon_sha256":"7b072fbd0845f79d31cc7f8085f3ca0686f02713699385eb4225ab27c660897b"},"schema_version":"1.0","source":{"id":"1604.06364","kind":"arxiv","version":2}},"canonical_sha256":"8002c2f982b02389ee460683e58331d3c91ed2950a7040c29367b8edb02dd6cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8002c2f982b02389ee460683e58331d3c91ed2950a7040c29367b8edb02dd6cb","first_computed_at":"2026-05-18T01:16:23.981931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:23.981931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lueexPfi6YqxxM4EI8lIG2DUgW3Tv90i/G9VvjK4xKJbjEzRE+nEyO2x5/B4h+7zDXgFSzW/uqPIZ0W1Oi7kBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:23.982474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77684213bd5a0aa7c4a3123b2771051a23db09a86842017f0d13324f87528f80","sha256:3c7ecaf7bc67e79fc335935fec58f85eebc5ec72ae63c6cbc765670e9c1c3d48"],"state_sha256":"b4d02cb1c4a391c87c56726baaa16b3bc418fd50fa45563ac757a61903f57cd5"}