{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QQXQYS2OEFQ4LQYLNHIO3PLLZ4","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":"daf1237797145794571bb6019c4f5a53ee604f07ca762d482120747dfebe47ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T16:08:57Z","title_canon_sha256":"6eac44f9a21fa9e0d51e3b3a28671aa83d185410914fe23ae194c25856623a1d"},"schema_version":"1.0","source":{"id":"2607.12935","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.12935","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.12935v1","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12935","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_12","alias_value":"QQXQYS2OEFQ4","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_16","alias_value":"QQXQYS2OEFQ4LQYL","created_at":"2026-07-15T01:22:26Z"},{"alias_kind":"pith_short_8","alias_value":"QQXQYS2O","created_at":"2026-07-15T01:22:26Z"}],"graph_snapshots":[{"event_id":"sha256:936177d0e06ad95d8ba8273178c8fd6d803bdb718d79a895626df91a0bda9dce","target":"graph","created_at":"2026-07-15T01:22:26Z","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/2607.12935/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a separable Banach space $X$ with a Schauder basis such that $B_X$ is not a uniformly continuous retract of $B_{X^{**}}$. Consequently, $X$ is not a uniformly continuous retract of $X^{**}$ and hence is not a Lipschitz retract of $X^{**}$.","authors_text":"Antonio Acuaviva","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T16:08:57Z","title":"A Separable Banach Space with a Schauder Basis Which Is Not a Lipschitz Retract of Its Bidual"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12935","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:c56536c0a800608ddd160fae892f47b219df5d71f0288d18b1f7c1038332e20b","target":"record","created_at":"2026-07-15T01:22:26Z","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":"daf1237797145794571bb6019c4f5a53ee604f07ca762d482120747dfebe47ec","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.FA","submitted_at":"2026-07-14T16:08:57Z","title_canon_sha256":"6eac44f9a21fa9e0d51e3b3a28671aa83d185410914fe23ae194c25856623a1d"},"schema_version":"1.0","source":{"id":"2607.12935","kind":"arxiv","version":1}},"canonical_sha256":"842f0c4b4e2161c5c30b69d0edbd6bcf2db7d724c92e5731187f673f628207de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"842f0c4b4e2161c5c30b69d0edbd6bcf2db7d724c92e5731187f673f628207de","first_computed_at":"2026-07-15T01:22:26.069179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-15T01:22:26.069179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uxawm+1GD1nCO4MVPj0XxxbzfmHT5AwA/L9BrRHPj//m4dBvAP9LAxiZw6lA/2mdj8rrgIvqCUE56L6Q/UGYDA==","signature_status":"signed_v1","signed_at":"2026-07-15T01:22:26.070010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.12935","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c56536c0a800608ddd160fae892f47b219df5d71f0288d18b1f7c1038332e20b","sha256:936177d0e06ad95d8ba8273178c8fd6d803bdb718d79a895626df91a0bda9dce"],"state_sha256":"7cf9f83760da08594ad61e4df6bf439032451c69f5f603e38c1b5b8aaaa289ca"}