{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RY3KG5UBEZDZNSB2DTKKN5SUE3","short_pith_number":"pith:RY3KG5UB","schema_version":"1.0","canonical_sha256":"8e36a37681264796c83a1cd4a6f65426d4e750b69318e7626edb81c79d0a75cf","source":{"kind":"arxiv","id":"1401.4095","version":2},"attestation_state":"computed","paper":{"title":"A direct proof that $\\ell_\\infty^{(3)}$ has generalized roundness zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anthony Weston, Ian Doust, Stephen S\\'anchez","submitted_at":"2014-01-16T17:19:40Z","abstract_excerpt":"Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p \\leq 2$. Lennard, Tonge and Weston gave an indirect proof that $\\ell_{\\infty}^{(3)}$ has generalized roundness zero by appealing to highly non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this paper we give a direct proof that $\\ell_{\\infty}^{(3)}$ has generalized roundness zero. This provides insight into the"},"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":"1401.4095","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-16T17:19:40Z","cross_cats_sorted":[],"title_canon_sha256":"0d3809ee63aea89f10d135034d0e908c43d1d8ff6dc36f0ea1b39c6becfd0020","abstract_canon_sha256":"07b0b2e89c1502a4b1bebb41fa7d0e19ebc5c09e6bd2806cf20251c014c02add"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:36.058830Z","signature_b64":"5qVNRu0b4MhYNKdqbdFb81RCaXeBMxFkUUQe56kV89AlNBA9Vnag9Z6G4KjvpbN0f6qPW6mZwcT99eXYo5EBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e36a37681264796c83a1cd4a6f65426d4e750b69318e7626edb81c79d0a75cf","last_reissued_at":"2026-05-18T01:08:36.058241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:36.058241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A direct proof that $\\ell_\\infty^{(3)}$ has generalized roundness zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Anthony Weston, Ian Doust, Stephen S\\'anchez","submitted_at":"2014-01-16T17:19:40Z","abstract_excerpt":"Metric spaces of generalized roundness zero have interesting non-embedding properties. For instance, we note that no metric space of generalized roundness zero is isometric to any metric subspace of any $L_{p}$-space for which $0 < p \\leq 2$. Lennard, Tonge and Weston gave an indirect proof that $\\ell_{\\infty}^{(3)}$ has generalized roundness zero by appealing to highly non-trivial isometric embedding theorems of Bretagnolle Dacunha-Castelle and Krivine, and Misiewicz. In this paper we give a direct proof that $\\ell_{\\infty}^{(3)}$ has generalized roundness zero. This provides insight into the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4095","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1401.4095","created_at":"2026-05-18T01:08:36.058353+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.4095v2","created_at":"2026-05-18T01:08:36.058353+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4095","created_at":"2026-05-18T01:08:36.058353+00:00"},{"alias_kind":"pith_short_12","alias_value":"RY3KG5UBEZDZ","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RY3KG5UBEZDZNSB2","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RY3KG5UB","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3","json":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3.json","graph_json":"https://pith.science/api/pith-number/RY3KG5UBEZDZNSB2DTKKN5SUE3/graph.json","events_json":"https://pith.science/api/pith-number/RY3KG5UBEZDZNSB2DTKKN5SUE3/events.json","paper":"https://pith.science/paper/RY3KG5UB"},"agent_actions":{"view_html":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3","download_json":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3.json","view_paper":"https://pith.science/paper/RY3KG5UB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.4095&json=true","fetch_graph":"https://pith.science/api/pith-number/RY3KG5UBEZDZNSB2DTKKN5SUE3/graph.json","fetch_events":"https://pith.science/api/pith-number/RY3KG5UBEZDZNSB2DTKKN5SUE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3/action/storage_attestation","attest_author":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3/action/author_attestation","sign_citation":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3/action/citation_signature","submit_replication":"https://pith.science/pith/RY3KG5UBEZDZNSB2DTKKN5SUE3/action/replication_record"}},"created_at":"2026-05-18T01:08:36.058353+00:00","updated_at":"2026-05-18T01:08:36.058353+00:00"}