{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:HIHI565ODEF774AEFGL6777HKF","short_pith_number":"pith:HIHI565O","schema_version":"1.0","canonical_sha256":"3a0e8efbae190bfff0042997efffe75159aacc7bff670b44fae6a9c2acd42a01","source":{"kind":"arxiv","id":"2406.05864","version":1},"attestation_state":"computed","paper":{"title":"Dilation distance and the stability of ergodic commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Malte Gerhold, Orr Shalit","submitted_at":"2024-06-09T17:38:35Z","abstract_excerpt":"We revisit and generalize the notion of dilation distance ${\\rm d_{D}}(u,v)$ between unitary tuples and study its relation to the natural Haagerup-R{\\o}rdam distance ${\\rm d_{HR}}(u,v) = \\inf\\{\\|\\pi(u) - \\rho(v)\\|\\}$, where the infimum is taken over all pairs of faithful representations $\\pi \\colon C^*(u) \\to B(\\mathcal{H})$, $\\rho \\colon C^*(v) \\to B(\\mathcal{H})$. We show that ${\\rm d_{HR}}(u,v)\\leq 10\\operatorname{d_{rD}}(u,v)^{1/2}$, where ${\\rm d_{rD}}(u,v)$ is a relaxed dilation distance, improving and extending earlier results. For an antisymmetric matrix $\\Theta$, we show via a concret"},"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":"2406.05864","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-06-09T17:38:35Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"20a50451193a9c47127969a974b4a3e6e1a1ca15c576eb896509adbacf83e78a","abstract_canon_sha256":"2d437705490880b7e345572cba3f5406f1142aef643e7df719bf9078cf48806b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:29:34.565754Z","signature_b64":"zCtp7ka3n7NPacWeCCfy6QPnhbBESBAjbuwARgy+btKucsAJaLB+PgCmTakvCzJb09Yo6aVhfT6Z1ysWHv28Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0e8efbae190bfff0042997efffe75159aacc7bff670b44fae6a9c2acd42a01","last_reissued_at":"2026-07-05T08:29:34.565202Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:29:34.565202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dilation distance and the stability of ergodic commutation relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Malte Gerhold, Orr Shalit","submitted_at":"2024-06-09T17:38:35Z","abstract_excerpt":"We revisit and generalize the notion of dilation distance ${\\rm d_{D}}(u,v)$ between unitary tuples and study its relation to the natural Haagerup-R{\\o}rdam distance ${\\rm d_{HR}}(u,v) = \\inf\\{\\|\\pi(u) - \\rho(v)\\|\\}$, where the infimum is taken over all pairs of faithful representations $\\pi \\colon C^*(u) \\to B(\\mathcal{H})$, $\\rho \\colon C^*(v) \\to B(\\mathcal{H})$. We show that ${\\rm d_{HR}}(u,v)\\leq 10\\operatorname{d_{rD}}(u,v)^{1/2}$, where ${\\rm d_{rD}}(u,v)$ is a relaxed dilation distance, improving and extending earlier results. For an antisymmetric matrix $\\Theta$, we show via a concret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.05864","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.05864/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2406.05864","created_at":"2026-07-05T08:29:34.565272+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.05864v1","created_at":"2026-07-05T08:29:34.565272+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.05864","created_at":"2026-07-05T08:29:34.565272+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIHI565ODEF7","created_at":"2026-07-05T08:29:34.565272+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIHI565ODEF774AE","created_at":"2026-07-05T08:29:34.565272+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIHI565O","created_at":"2026-07-05T08:29:34.565272+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12506","citing_title":"On the universal commuting dilation constant","ref_index":17,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF","json":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF.json","graph_json":"https://pith.science/api/pith-number/HIHI565ODEF774AEFGL6777HKF/graph.json","events_json":"https://pith.science/api/pith-number/HIHI565ODEF774AEFGL6777HKF/events.json","paper":"https://pith.science/paper/HIHI565O"},"agent_actions":{"view_html":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF","download_json":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF.json","view_paper":"https://pith.science/paper/HIHI565O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.05864&json=true","fetch_graph":"https://pith.science/api/pith-number/HIHI565ODEF774AEFGL6777HKF/graph.json","fetch_events":"https://pith.science/api/pith-number/HIHI565ODEF774AEFGL6777HKF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF/action/storage_attestation","attest_author":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF/action/author_attestation","sign_citation":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF/action/citation_signature","submit_replication":"https://pith.science/pith/HIHI565ODEF774AEFGL6777HKF/action/replication_record"}},"created_at":"2026-07-05T08:29:34.565272+00:00","updated_at":"2026-07-05T08:29:34.565272+00:00"}