{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SHRCO6ZXU6PBUUTC32I2NLHAF6","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":"ae527de4942fc8521ce10a3abe6f4a7c64bdb3a169b1822fea5487f15af97eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-28T09:16:39Z","title_canon_sha256":"2fc0841db602b91cd13ba3985edd8952c9de7c4d89f36da3d2eeec062bd6c926"},"schema_version":"1.0","source":{"id":"1305.6420","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.6420","created_at":"2026-05-18T00:45:54Z"},{"alias_kind":"arxiv_version","alias_value":"1305.6420v2","created_at":"2026-05-18T00:45:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.6420","created_at":"2026-05-18T00:45:54Z"},{"alias_kind":"pith_short_12","alias_value":"SHRCO6ZXU6PB","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SHRCO6ZXU6PBUUTC","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SHRCO6ZX","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:53d02fb59be67347940824f58068faef0e8b618e96a8fd7467ed6e8292204e8f","target":"graph","created_at":"2026-05-18T00:45:54Z","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"},"paper":{"abstract_excerpt":"We study a Bishop-Phelps-Bollob\\'as version of Lindenstrauss properties A and B. For domain spaces, we study Banach spaces $X$ such that $(X,Y)$ has the Bishop-Phelps-Bollob\\'as property (BPBp) for every Banach space $Y$. We show that in this case, there exists a universal function $\\eta_X(\\varepsilon)$ such that for every $Y$, the pair $(X,Y)$ has the BPBp with this function. This allows us to prove some necessary isometric conditions for $X$ to have the property. We also prove that if $X$ has this property in every equivalent norm, then $X$ is one-dimensional. For range spaces, we study Bana","authors_text":"Han Ju Lee, Miguel Martin, Richard Aron, Sun Kwang Kim, Yun Sung Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-28T09:16:39Z","title":"The Bishop-Phelps-Bollob\\'as version of Lindenstrauss properties A and B"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.6420","kind":"arxiv","version":2},"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:ca05fe00244af953052a61c21fa00ec2f75360b848ac9c5fff099624f6a7343d","target":"record","created_at":"2026-05-18T00:45:54Z","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":"ae527de4942fc8521ce10a3abe6f4a7c64bdb3a169b1822fea5487f15af97eb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-05-28T09:16:39Z","title_canon_sha256":"2fc0841db602b91cd13ba3985edd8952c9de7c4d89f36da3d2eeec062bd6c926"},"schema_version":"1.0","source":{"id":"1305.6420","kind":"arxiv","version":2}},"canonical_sha256":"91e2277b37a79e1a5262de91a6ace02f86710bc6c3bbf97630c8477818ee82c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91e2277b37a79e1a5262de91a6ace02f86710bc6c3bbf97630c8477818ee82c4","first_computed_at":"2026-05-18T00:45:54.800444Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:54.800444Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EessszvqfnBd/zMpZlT4ugxLp/1PtzQCzU2fk7LNehQaUIsBrah2nDH+KcMJxg1osFAEm7gbIZQPwjdphh0aCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:54.801143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.6420","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca05fe00244af953052a61c21fa00ec2f75360b848ac9c5fff099624f6a7343d","sha256:53d02fb59be67347940824f58068faef0e8b618e96a8fd7467ed6e8292204e8f"],"state_sha256":"1927c240e304c109e3ac068f7dda3e8d321b829901f3773e0b34002c89f53070"}