{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DM2BH6FCHU2UCTHQNCWCI62HJ5","short_pith_number":"pith:DM2BH6FC","schema_version":"1.0","canonical_sha256":"1b3413f8a23d35414cf068ac247b474f7d0e519ab70b5a22d3a3d09c729d7284","source":{"kind":"arxiv","id":"1604.07587","version":4},"attestation_state":"computed","paper":{"title":"Weak$^*$ Fixed Point Property in $\\ell_1$ and Polyhedrality in Lindenstrauss Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emanuele Casini, Enrico Miglierina, {\\L}ukasz Piasecki, Roxana Popescu","submitted_at":"2016-04-26T09:42:03Z","abstract_excerpt":"The aim of this paper is to study the $w^*$-fixed point property for nonexpansive mappings in the duals of separable Lindenstrauss spaces by means of suitable geometrical properties of the dual ball. First we show that a property concerning the behaviour of a class of $w^*$-closed subsets of the dual sphere is equivalent to the $w^*$-fixed point property. Then, the main result of our paper shows an equivalence between another, stronger geometrical property of the dual ball and the stable $w^*$-fixed point property. The last geometrical notion was introduced by Fonf and Vesel\\'{y} as a strength"},"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":"1604.07587","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-04-26T09:42:03Z","cross_cats_sorted":[],"title_canon_sha256":"c9aa546fd1aa2b4374759dbce2752c08b38c27fa9075799c9d9912f1d59d5b26","abstract_canon_sha256":"0247887f74ae5cfd1c1570796e093265c82f5fc45f3eff6d68768037551a1373"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:12.409093Z","signature_b64":"8a7d6GJUKCJd0k8v0zqbM4DTdhzq65HshSp/ytUtdA/BiM8ssDfp2F4sp8/gAAtDCC1OzEpUXsIEy7WYf83wAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b3413f8a23d35414cf068ac247b474f7d0e519ab70b5a22d3a3d09c729d7284","last_reissued_at":"2026-05-18T01:00:12.408434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:12.408434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak$^*$ Fixed Point Property in $\\ell_1$ and Polyhedrality in Lindenstrauss Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Emanuele Casini, Enrico Miglierina, {\\L}ukasz Piasecki, Roxana Popescu","submitted_at":"2016-04-26T09:42:03Z","abstract_excerpt":"The aim of this paper is to study the $w^*$-fixed point property for nonexpansive mappings in the duals of separable Lindenstrauss spaces by means of suitable geometrical properties of the dual ball. First we show that a property concerning the behaviour of a class of $w^*$-closed subsets of the dual sphere is equivalent to the $w^*$-fixed point property. Then, the main result of our paper shows an equivalence between another, stronger geometrical property of the dual ball and the stable $w^*$-fixed point property. The last geometrical notion was introduced by Fonf and Vesel\\'{y} as a strength"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.07587","kind":"arxiv","version":4},"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":"1604.07587","created_at":"2026-05-18T01:00:12.408547+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.07587v4","created_at":"2026-05-18T01:00:12.408547+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.07587","created_at":"2026-05-18T01:00:12.408547+00:00"},{"alias_kind":"pith_short_12","alias_value":"DM2BH6FCHU2U","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DM2BH6FCHU2UCTHQ","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DM2BH6FC","created_at":"2026-05-18T12:30:12.583610+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/DM2BH6FCHU2UCTHQNCWCI62HJ5","json":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5.json","graph_json":"https://pith.science/api/pith-number/DM2BH6FCHU2UCTHQNCWCI62HJ5/graph.json","events_json":"https://pith.science/api/pith-number/DM2BH6FCHU2UCTHQNCWCI62HJ5/events.json","paper":"https://pith.science/paper/DM2BH6FC"},"agent_actions":{"view_html":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5","download_json":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5.json","view_paper":"https://pith.science/paper/DM2BH6FC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.07587&json=true","fetch_graph":"https://pith.science/api/pith-number/DM2BH6FCHU2UCTHQNCWCI62HJ5/graph.json","fetch_events":"https://pith.science/api/pith-number/DM2BH6FCHU2UCTHQNCWCI62HJ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5/action/storage_attestation","attest_author":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5/action/author_attestation","sign_citation":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5/action/citation_signature","submit_replication":"https://pith.science/pith/DM2BH6FCHU2UCTHQNCWCI62HJ5/action/replication_record"}},"created_at":"2026-05-18T01:00:12.408547+00:00","updated_at":"2026-05-18T01:00:12.408547+00:00"}