{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RKD7S3JN7JZEERWVS2SU2JMYL5","short_pith_number":"pith:RKD7S3JN","schema_version":"1.0","canonical_sha256":"8a87f96d2dfa724246d596a54d25985f5d55d64f688e6610ec8a04e66abac290","source":{"kind":"arxiv","id":"1808.00715","version":1},"attestation_state":"computed","paper":{"title":"Complete metric spaces with property (Z) are length metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes","submitted_at":"2018-08-02T09:04:55Z","abstract_excerpt":"We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\\'{i}a-Lirola, Proch\\'{a}zka and Rueda Zoca, and by Becerra Guerrero, L\\'{o}pez-P\\'{e}rez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces."},"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":"1808.00715","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-02T09:04:55Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"f7d0faecd4381470df1c6d4b8a3dfb96d60da4d6eea0803f7f3eb1c7c5568515","abstract_canon_sha256":"10e24a1e83067dfc3f424967359274c6fbc8ebee4366dac6ab047c4c94f21593"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:03.584491Z","signature_b64":"zrqXDuQ9bK/bGp8NRfNbJlQNjmQBPRtoh+Ae+vQe/zDspU2q+2AeExKyRjhh5f7XJqyLNCugP7K0lxSxeKrXAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8a87f96d2dfa724246d596a54d25985f5d55d64f688e6610ec8a04e66abac290","last_reissued_at":"2026-05-18T00:09:03.583825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:03.583825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete metric spaces with property (Z) are length metric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes","submitted_at":"2018-08-02T09:04:55Z","abstract_excerpt":"We prove that every complete metric space with property (Z) is a length space. These answers questions posed by Garc\\'{i}a-Lirola, Proch\\'{a}zka and Rueda Zoca, and by Becerra Guerrero, L\\'{o}pez-P\\'{e}rez and Rueda Zoca, related to the structure of Lipschitz-free Banach spaces of metric spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00715","kind":"arxiv","version":1},"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":"1808.00715","created_at":"2026-05-18T00:09:03.583903+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.00715v1","created_at":"2026-05-18T00:09:03.583903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.00715","created_at":"2026-05-18T00:09:03.583903+00:00"},{"alias_kind":"pith_short_12","alias_value":"RKD7S3JN7JZE","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RKD7S3JN7JZEERWV","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RKD7S3JN","created_at":"2026-05-18T12:32:50.500415+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/RKD7S3JN7JZEERWVS2SU2JMYL5","json":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5.json","graph_json":"https://pith.science/api/pith-number/RKD7S3JN7JZEERWVS2SU2JMYL5/graph.json","events_json":"https://pith.science/api/pith-number/RKD7S3JN7JZEERWVS2SU2JMYL5/events.json","paper":"https://pith.science/paper/RKD7S3JN"},"agent_actions":{"view_html":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5","download_json":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5.json","view_paper":"https://pith.science/paper/RKD7S3JN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.00715&json=true","fetch_graph":"https://pith.science/api/pith-number/RKD7S3JN7JZEERWVS2SU2JMYL5/graph.json","fetch_events":"https://pith.science/api/pith-number/RKD7S3JN7JZEERWVS2SU2JMYL5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5/action/storage_attestation","attest_author":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5/action/author_attestation","sign_citation":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5/action/citation_signature","submit_replication":"https://pith.science/pith/RKD7S3JN7JZEERWVS2SU2JMYL5/action/replication_record"}},"created_at":"2026-05-18T00:09:03.583903+00:00","updated_at":"2026-05-18T00:09:03.583903+00:00"}