{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IKQ5JIYM5FX66TOSH2IVKNT76E","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":"8cb7f96a33299386716462b3f424410a7e242526c66d652c09994943154c3235","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-13T01:59:31Z","title_canon_sha256":"9256e4b5cdeca0577398affe60fb28bb1fdd0ce577573330880f269228e087d5"},"schema_version":"1.0","source":{"id":"2607.11001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.11001","created_at":"2026-07-14T01:21:51Z"},{"alias_kind":"arxiv_version","alias_value":"2607.11001v1","created_at":"2026-07-14T01:21:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.11001","created_at":"2026-07-14T01:21:51Z"},{"alias_kind":"pith_short_12","alias_value":"IKQ5JIYM5FX6","created_at":"2026-07-14T01:21:51Z"},{"alias_kind":"pith_short_16","alias_value":"IKQ5JIYM5FX66TOS","created_at":"2026-07-14T01:21:51Z"},{"alias_kind":"pith_short_8","alias_value":"IKQ5JIYM","created_at":"2026-07-14T01:21:51Z"}],"graph_snapshots":[{"event_id":"sha256:36b2f9be6d6c966346d2557bab5117fbe9256cd8e490c2fd6227b4d4090a5acd","target":"graph","created_at":"2026-07-14T01:21:51Z","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/2607.11001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Smith-Ward problem about matrix ranges, posed in the 1980s, was recently resolved in the negative by Marcel Scherer (arXiv:2607.04274) by obtaining a three-dimensional operator system $\\mathcal{S} \\subseteq M_4(C_r^*(\\mathbb{F}_2))$ without the lifting property. However, this operator system must be exact. In this paper we show that, for every finitely generated $C^*$-algebra $\\mathcal{A}$ without the local lifting property (LLP), there exists a three-dimensional operator system $\\mathcal{S} \\subseteq M_{n+2}(\\mathcal{A})$ without the lifting property (LP), thus generalizing Scherer's resu","authors_text":"Samuel J. Harris","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-13T01:59:31Z","title":"Ubiquity of counterexamples to the Smith-Ward problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.11001","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":"sha256:2d61de11163dbdbc2f0869eb22d3e2e45b02fc5135d5cf2de8faad020b314388","target":"record","created_at":"2026-07-14T01:21:51Z","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":"8cb7f96a33299386716462b3f424410a7e242526c66d652c09994943154c3235","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2026-07-13T01:59:31Z","title_canon_sha256":"9256e4b5cdeca0577398affe60fb28bb1fdd0ce577573330880f269228e087d5"},"schema_version":"1.0","source":{"id":"2607.11001","kind":"arxiv","version":1}},"canonical_sha256":"42a1d4a30ce96fef4dd23e9155367ff129f932be00f37221a82d852d8b5897d5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42a1d4a30ce96fef4dd23e9155367ff129f932be00f37221a82d852d8b5897d5","first_computed_at":"2026-07-14T01:21:51.859433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-14T01:21:51.859433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y2sSyoEknI9n308zY55ut0EZi5XYhe07MJoTG3x4aE1RL0q75Sk0aYRtPUzh1YBtk3dQ/Mh/cgZYJThb5yI/Bw==","signature_status":"signed_v1","signed_at":"2026-07-14T01:21:51.860235Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.11001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d61de11163dbdbc2f0869eb22d3e2e45b02fc5135d5cf2de8faad020b314388","sha256:36b2f9be6d6c966346d2557bab5117fbe9256cd8e490c2fd6227b4d4090a5acd"],"state_sha256":"9d55803b854ead0e7015a110ba01917aa4efd376b6705f5afdc67aa8b431c63b"}