{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VN3FUUXTJCQEOO6RPAPC7RDDKH","short_pith_number":"pith:VN3FUUXT","schema_version":"1.0","canonical_sha256":"ab765a52f348a0473bd1781e2fc46351e122c8da579868cd3f6db174e8e2be4b","source":{"kind":"arxiv","id":"1908.07786","version":1},"attestation_state":"computed","paper":{"title":"On the Banach lattice c_0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Jos\\'e David Rodr\\'iguez Abell\\'an","submitted_at":"2019-08-21T10:47:53Z","abstract_excerpt":"We show that $c_0$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_0$ is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, the free Banach lattice generated by $c_0$ is not projective."},"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":"1908.07786","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-08-21T10:47:53Z","cross_cats_sorted":[],"title_canon_sha256":"5cb216a7576cab05a62415e72fca355da6bf78babac91a558c973ce6fe84e988","abstract_canon_sha256":"46b9de60f2abed7f521945c3eb74ba73b4b278474ca6358f7e59daaea5573385"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:44:26.412907Z","signature_b64":"niJ39uaAtdnmIYzM0qYQ56Rx37m8G/Fr51YSwZvnAuN9WGjZr2TQ9nEjp7OhP+8JVZmM+afGPgBJ3xkYaDXUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab765a52f348a0473bd1781e2fc46351e122c8da579868cd3f6db174e8e2be4b","last_reissued_at":"2026-07-05T00:44:26.412480Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:44:26.412480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Banach lattice c_0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio Avil\\'es, Gonzalo Mart\\'inez-Cervantes, Jos\\'e David Rodr\\'iguez Abell\\'an","submitted_at":"2019-08-21T10:47:53Z","abstract_excerpt":"We show that $c_0$ is not a projective Banach lattice, answering a question of B. de Pagter and A. Wickstead. On the other hand, we show that $c_0$ is complemented in the free Banach lattice generated by itself (seen as a Banach space). As a consequence, the free Banach lattice generated by $c_0$ is not projective."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.07786","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.07786/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.07786","created_at":"2026-07-05T00:44:26.412536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.07786v1","created_at":"2026-07-05T00:44:26.412536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.07786","created_at":"2026-07-05T00:44:26.412536+00:00"},{"alias_kind":"pith_short_12","alias_value":"VN3FUUXTJCQE","created_at":"2026-07-05T00:44:26.412536+00:00"},{"alias_kind":"pith_short_16","alias_value":"VN3FUUXTJCQEOO6R","created_at":"2026-07-05T00:44:26.412536+00:00"},{"alias_kind":"pith_short_8","alias_value":"VN3FUUXT","created_at":"2026-07-05T00:44:26.412536+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/VN3FUUXTJCQEOO6RPAPC7RDDKH","json":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH.json","graph_json":"https://pith.science/api/pith-number/VN3FUUXTJCQEOO6RPAPC7RDDKH/graph.json","events_json":"https://pith.science/api/pith-number/VN3FUUXTJCQEOO6RPAPC7RDDKH/events.json","paper":"https://pith.science/paper/VN3FUUXT"},"agent_actions":{"view_html":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH","download_json":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH.json","view_paper":"https://pith.science/paper/VN3FUUXT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.07786&json=true","fetch_graph":"https://pith.science/api/pith-number/VN3FUUXTJCQEOO6RPAPC7RDDKH/graph.json","fetch_events":"https://pith.science/api/pith-number/VN3FUUXTJCQEOO6RPAPC7RDDKH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH/action/storage_attestation","attest_author":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH/action/author_attestation","sign_citation":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH/action/citation_signature","submit_replication":"https://pith.science/pith/VN3FUUXTJCQEOO6RPAPC7RDDKH/action/replication_record"}},"created_at":"2026-07-05T00:44:26.412536+00:00","updated_at":"2026-07-05T00:44:26.412536+00:00"}