{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DCJVZN6EWXB4E6U4LW35RPMMJQ","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":"365c324a25a5a31d002ac04f5d822aadf8847a1afeba6aadd518d94a81cc36d7","cross_cats_sorted":["math.FA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-21T20:41:46Z","title_canon_sha256":"01218446c801ec475d294c95e23b441b4b69bfb90cb6c62d5021ae938e0c2838"},"schema_version":"1.0","source":{"id":"1706.07115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07115","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07115v1","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07115","created_at":"2026-05-18T00:41:52Z"},{"alias_kind":"pith_short_12","alias_value":"DCJVZN6EWXB4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"DCJVZN6EWXB4E6U4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"DCJVZN6E","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:ede0dbed8ad014622c247babea1316c76fa16087d79cee5819e26ad189126373","target":"graph","created_at":"2026-05-18T00:41:52Z","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":"For a semi-finite von Neumann algebra $\\mathcal A$, we study the case of equality in Young's inequality of s-numbers for a pair of $\\tau$-measurable operators $a,b$, and we prove that equality is only possible if $|a|^p=|b|^q$. We also extend the result to unbounded operators affiliated with $\\mathcal A$, and relate this problem with other symmetric norm Young inequalities.","authors_text":"Gabriel Larotonda","cross_cats":["math.FA","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-21T20:41:46Z","title":"The case of equality in Young's inequality for the s-numbers in semi-finite von Neumann algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07115","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:b3b33f8c0210b23a63cf6a631a30e15146851ee40493454f26afb09be470bca0","target":"record","created_at":"2026-05-18T00:41:52Z","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":"365c324a25a5a31d002ac04f5d822aadf8847a1afeba6aadd518d94a81cc36d7","cross_cats_sorted":["math.FA","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-21T20:41:46Z","title_canon_sha256":"01218446c801ec475d294c95e23b441b4b69bfb90cb6c62d5021ae938e0c2838"},"schema_version":"1.0","source":{"id":"1706.07115","kind":"arxiv","version":1}},"canonical_sha256":"18935cb7c4b5c3c27a9c5db7d8bd8c4c0ef72d3f0d4928a6590004dae9b09169","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18935cb7c4b5c3c27a9c5db7d8bd8c4c0ef72d3f0d4928a6590004dae9b09169","first_computed_at":"2026-05-18T00:41:52.575761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:52.575761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9GxCVVuei66kfbcl3wgjJnfs106AEbeqokOALtDDWs9dtVpCXmTzFaQWvoff/cUvE/lUgsyh828deBZwAejtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:52.576386Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3b33f8c0210b23a63cf6a631a30e15146851ee40493454f26afb09be470bca0","sha256:ede0dbed8ad014622c247babea1316c76fa16087d79cee5819e26ad189126373"],"state_sha256":"0233229abf070d2d41209cf7836f236ef99d26058ea60934b1274335ba471baa"}