{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N5M7AJ2QCNP72XPX7KWMOM7DH5","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":"bd21de14afd141122e9165f91e934067d5b8d6ca4efd771f7d2773c37e1c37f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T22:53:47Z","title_canon_sha256":"0db55c11971d68f958124636380cc04e67eab6201f15d7c7c2a226b68092b13e"},"schema_version":"1.0","source":{"id":"1502.02719","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.02719","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1502.02719v2","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.02719","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"N5M7AJ2QCNP7","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N5M7AJ2QCNP72XPX","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N5M7AJ2Q","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:411be8b176667cac874a7b1571f76bf68e6c80ebf26e5561fe3141fb9874780d","target":"graph","created_at":"2026-05-18T01:04:50Z","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 characterize metric spaces whose Lipschitz free space is isometric to $\\ell_1$. In particular, the Lipschitz free space over an ultrametric space is not isometric to $\\ell_1(\\Gamma)$ for any set $\\Gamma$. We give a lower bound for the Banach-Mazur distance in the finite case.","authors_text":"Anton\\'in Proch\\'azka, Aude Dalet, Pedro L. Kaufmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T22:53:47Z","title":"Characterization of metric spaces whose free space is isometric to $\\ell_1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02719","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":"sha256:0dd495cbd82d9ca397a9d920478e7a96daf27758b37b376069b0193a34e5f0dd","target":"record","created_at":"2026-05-18T01:04:50Z","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":"bd21de14afd141122e9165f91e934067d5b8d6ca4efd771f7d2773c37e1c37f2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-02-09T22:53:47Z","title_canon_sha256":"0db55c11971d68f958124636380cc04e67eab6201f15d7c7c2a226b68092b13e"},"schema_version":"1.0","source":{"id":"1502.02719","kind":"arxiv","version":2}},"canonical_sha256":"6f59f02750135ffd5df7faacc733e33f71d2c9a6bff761723a0c847dbabae2a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f59f02750135ffd5df7faacc733e33f71d2c9a6bff761723a0c847dbabae2a9","first_computed_at":"2026-05-18T01:04:50.660894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.660894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L852OOMDpDRH5uenj69tNBtz4/2onpAFha3409ptRDHjmPcpl4ussF2TpI1iKaAg+9lFhyJGiYHoLyK8FsliDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.661287Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.02719","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0dd495cbd82d9ca397a9d920478e7a96daf27758b37b376069b0193a34e5f0dd","sha256:411be8b176667cac874a7b1571f76bf68e6c80ebf26e5561fe3141fb9874780d"],"state_sha256":"4cc2fe2a593edd8e3015abb6572da86200d06b3fd135fa9c9ed415f97934729c"}