{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:3LI54RVY2HOTQOZWPN2CQYYNOG","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":"68c95b4e888572f3afade30398045d88129c920f38398eb958256dc13d4bf414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-27T20:35:58Z","title_canon_sha256":"207852e803be01eaa9b612ddebc1a3c2fd780e967eaa54a40d60886e220b4911"},"schema_version":"1.0","source":{"id":"2212.13606","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.13606","created_at":"2026-07-05T05:28:53Z"},{"alias_kind":"arxiv_version","alias_value":"2212.13606v1","created_at":"2026-07-05T05:28:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.13606","created_at":"2026-07-05T05:28:53Z"},{"alias_kind":"pith_short_12","alias_value":"3LI54RVY2HOT","created_at":"2026-07-05T05:28:53Z"},{"alias_kind":"pith_short_16","alias_value":"3LI54RVY2HOTQOZW","created_at":"2026-07-05T05:28:53Z"},{"alias_kind":"pith_short_8","alias_value":"3LI54RVY","created_at":"2026-07-05T05:28:53Z"}],"graph_snapshots":[{"event_id":"sha256:6a97a467edd7a1d7cb583e65c350e456272a57dd181d3c6feb0718494b7166fc","target":"graph","created_at":"2026-07-05T05:28:53Z","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/2212.13606/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A Banach space (or its norm) is said to have the diameter $2$ property (D$2$P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter $2$. We construct an equivalent norm on $L_1[0,1]$ which is weakly midpoint locally uniformly rotund and has the D$2$P. We also prove that for Banach spaces admitting a norm-one finite-co-dimensional projection it is impossible to be uniformly rotund in every direction and at the same time have the D$2$P.","authors_text":"M\\\"art P\\~oldvere, Olav Nygaard, Stanimir Troyansky, Tauri Viil","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-27T20:35:58Z","title":"Strictly convex renormings and the diameter 2 property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.13606","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":"sha256:46632b826006e27577523639e7167b63fd0e5b42a182409dc9fa398b7a2ce314","target":"record","created_at":"2026-07-05T05:28:53Z","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":"68c95b4e888572f3afade30398045d88129c920f38398eb958256dc13d4bf414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2022-12-27T20:35:58Z","title_canon_sha256":"207852e803be01eaa9b612ddebc1a3c2fd780e967eaa54a40d60886e220b4911"},"schema_version":"1.0","source":{"id":"2212.13606","kind":"arxiv","version":1}},"canonical_sha256":"dad1de46b8d1dd383b367b7428630d71a0ddc7c64ca7112ff5a3f574d7a5c1f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dad1de46b8d1dd383b367b7428630d71a0ddc7c64ca7112ff5a3f574d7a5c1f3","first_computed_at":"2026-07-05T05:28:53.247447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:53.247447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TUjEs0rqc6CRDa1bqNy3HO1hIH4B2kk2CW3V3ycx88LZt9p+s9KyULiNK0Frk7euDRqh/fzjqakDIsOCdrhGBg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:53.247797Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.13606","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46632b826006e27577523639e7167b63fd0e5b42a182409dc9fa398b7a2ce314","sha256:6a97a467edd7a1d7cb583e65c350e456272a57dd181d3c6feb0718494b7166fc"],"state_sha256":"25f3729959cd7f6ac68fd0239b1248cb248df100bab345f95fdffa1b1a5f4653"}