{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:JMNNNOQK3SMXQOMDUQ4ZTRCMJG","short_pith_number":"pith:JMNNNOQK","schema_version":"1.0","canonical_sha256":"4b1ad6ba0adc99783983a43999c44c4980d1b65eb2f765edf75b21c89d23c637","source":{"kind":"arxiv","id":"1301.0749","version":1},"attestation_state":"computed","paper":{"title":"Fremlin Tensor Products of Concavifications of Banach Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Omid Zabeti, Vladimir G. Troitsky","submitted_at":"2013-01-04T15:46:03Z","abstract_excerpt":"Suppose that $E$ is a uniformly complete vector lattice and $p_1,..., p_n$ are positive reals. We prove that the diagonal of the Fremlin projective tensor product of $E_{(p_1)},..., E_{(p_n)}$ can be identified with $E_{(p)}$ where $p = p_1+...+p_n$ and $E_{(p)}$ stands for the $p$-concavification of $E$. We also provide a variant of this result for Banach lattices. This extends the main result of [BBPTT]."},"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":"1301.0749","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-01-04T15:46:03Z","cross_cats_sorted":[],"title_canon_sha256":"d7de01bdebea4a2b420656509c0c19bc95d2213740ccf44016b3f048cc68d6b8","abstract_canon_sha256":"48aaf2fd8fc64be0a9cd2cc5d60730878bff5dad2feb4b2e63768b058a9e72f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:17.716600Z","signature_b64":"beXi1gVLBp3kXETIdqNvbuu4lKpjZHVlXlJz1ugM4OgIik7kTuW10jJZjvmCANriuBKw4W0CY/CqTXl6G7+hCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b1ad6ba0adc99783983a43999c44c4980d1b65eb2f765edf75b21c89d23c637","last_reissued_at":"2026-05-18T03:37:17.715898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:17.715898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fremlin Tensor Products of Concavifications of Banach Lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Omid Zabeti, Vladimir G. Troitsky","submitted_at":"2013-01-04T15:46:03Z","abstract_excerpt":"Suppose that $E$ is a uniformly complete vector lattice and $p_1,..., p_n$ are positive reals. We prove that the diagonal of the Fremlin projective tensor product of $E_{(p_1)},..., E_{(p_n)}$ can be identified with $E_{(p)}$ where $p = p_1+...+p_n$ and $E_{(p)}$ stands for the $p$-concavification of $E$. We also provide a variant of this result for Banach lattices. This extends the main result of [BBPTT]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0749","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":"1301.0749","created_at":"2026-05-18T03:37:17.715997+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.0749v1","created_at":"2026-05-18T03:37:17.715997+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0749","created_at":"2026-05-18T03:37:17.715997+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMNNNOQK3SMX","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMNNNOQK3SMXQOMD","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMNNNOQK","created_at":"2026-05-18T12:27:49.015174+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/JMNNNOQK3SMXQOMDUQ4ZTRCMJG","json":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG.json","graph_json":"https://pith.science/api/pith-number/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/graph.json","events_json":"https://pith.science/api/pith-number/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/events.json","paper":"https://pith.science/paper/JMNNNOQK"},"agent_actions":{"view_html":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG","download_json":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG.json","view_paper":"https://pith.science/paper/JMNNNOQK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.0749&json=true","fetch_graph":"https://pith.science/api/pith-number/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/graph.json","fetch_events":"https://pith.science/api/pith-number/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/action/storage_attestation","attest_author":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/action/author_attestation","sign_citation":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/action/citation_signature","submit_replication":"https://pith.science/pith/JMNNNOQK3SMXQOMDUQ4ZTRCMJG/action/replication_record"}},"created_at":"2026-05-18T03:37:17.715997+00:00","updated_at":"2026-05-18T03:37:17.715997+00:00"}