{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VPSFWZPMGRTXA5YSSXNU4G7K4Q","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":"9129ac93dc8ebac460d2581952abe101e1ede798b360638ebd9d682bda03adb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-19T19:20:02Z","title_canon_sha256":"53232793e02d846a2083870a40036cb76a66c84bff48bd3da97f5054fe563415"},"schema_version":"1.0","source":{"id":"1910.08824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1910.08824","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"1910.08824v1","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1910.08824","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"VPSFWZPMGRTX","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"VPSFWZPMGRTXA5YS","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"VPSFWZPM","created_at":"2026-06-23T02:13:11Z"}],"graph_snapshots":[{"event_id":"sha256:783717a311d4959d85358b9f36f3d53317505dd61f792067004b6ad4d5ef9b88","target":"graph","created_at":"2026-06-23T02:13:11Z","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/1910.08824/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mathbf{T} \\equiv (T_1,\\cdots,T_n)$ be a commuting $n$-tuple of operators on a Hilbert space $\\mathcal{H}$, and let $T_i \\equiv V_i P \\; (1 \\le i \\le n)$ be its canonical joint polar decomposition (i.e., $P:=\\sqrt{T_1^*T_1+\\cdots+T_n^*T_n}$, $(V_1,\\cdots,V_n)$ a joint partial isometry, and $\\bigcap_{i=1}^n \\ker T_i = \\bigcap_{i=1}^n \\ker V_i = \\ker P)$. \\ The spherical Aluthge transform of $\\mathbf{T}$ is the (necessarily commuting) $n$-tuple $\\hat{\\mathbf{T}}:=(\\sqrt{P}V_1\\sqrt{P},\\cdots,\\sqrt{P}V_n\\sqrt{P})$. \\ We prove that $\\sigma_T(\\hat{\\mathbf{T}})=\\sigma_T(\\mathbf{T})$, where $\\sig","authors_text":"Chafiq Benhida, Jasang Yoon, Raul E. Curto, Sang Hoon Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-19T19:20:02Z","title":"Joint spectra of spherical Aluthge transforms of commuting n-tuples of Hilbert space operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1910.08824","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":"sha256:0f37b8ca24a90d8a8c05158316d068e40bf5924b4bf39fa9955db0f64e562334","target":"record","created_at":"2026-06-23T02:13:11Z","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":"9129ac93dc8ebac460d2581952abe101e1ede798b360638ebd9d682bda03adb0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-10-19T19:20:02Z","title_canon_sha256":"53232793e02d846a2083870a40036cb76a66c84bff48bd3da97f5054fe563415"},"schema_version":"1.0","source":{"id":"1910.08824","kind":"arxiv","version":1}},"canonical_sha256":"abe45b65ec346770771295db4e1beae43d59e8cc555ff0210883676e8ae8f04e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abe45b65ec346770771295db4e1beae43d59e8cc555ff0210883676e8ae8f04e","first_computed_at":"2026-06-23T02:13:11.097832Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:11.097832Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4h0EJNvKlIEDWb0UZ2by7ItDArju0K5KhV3SAgHydQgqPO9gPcPdIiU9/wAPxu0DmvqRehVqUtrUTVymLAODw==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:11.098344Z","signed_message":"canonical_sha256_bytes"},"source_id":"1910.08824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f37b8ca24a90d8a8c05158316d068e40bf5924b4bf39fa9955db0f64e562334","sha256:783717a311d4959d85358b9f36f3d53317505dd61f792067004b6ad4d5ef9b88"],"state_sha256":"beb092de9fea52160f53b61bd7d594810e84e36a7c15ecd89080dd714e5f189d"}