{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:KOYTY5NCZSPV4BVGRAUN3LYYGF","short_pith_number":"pith:KOYTY5NC","schema_version":"1.0","canonical_sha256":"53b13c75a2cc9f5e06a68828ddaf1831689ed88aaa100cf0c498b8397e8a420f","source":{"kind":"arxiv","id":"1410.5570","version":2},"attestation_state":"computed","paper":{"title":"Two refinements of the Bishop-Phelps-Bollob\\'as modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javier Meri, Mariia Soloviova, Mario Chica, Miguel Martin, Vladimir Kadets","submitted_at":"2014-10-21T08:18:09Z","abstract_excerpt":"Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\\'as proved the nowadays known as the Bishop-Phelps-Bollob\\'as theorem, which allows to approximate at the same time a functional and a vector in which it almost attains the norm. Very recently, two Bishop-Phelps-Bollob\\'as moduli of a Banach space have been introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\\'as theorem in this space. In this paper"},"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":"1410.5570","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-21T08:18:09Z","cross_cats_sorted":[],"title_canon_sha256":"389dbb8c43ccf515a2abc485f9b91b81326165118b280dfcda89c8794f19cd5c","abstract_canon_sha256":"7cb98c23ddacb9e47545a20bbfb7b72c3454773608dc577d09f8a4b1da12fe13"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:54.664510Z","signature_b64":"XLqN/aG3/rqMdHFvIkwAk7FcI2r99GZSKrghGzZecamdxHHzCTuBRoBWdfdZXZrTlDM3z0xr6UopcpWFF5IyBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53b13c75a2cc9f5e06a68828ddaf1831689ed88aaa100cf0c498b8397e8a420f","last_reissued_at":"2026-05-18T00:45:54.663902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:54.663902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Two refinements of the Bishop-Phelps-Bollob\\'as modulus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Javier Meri, Mariia Soloviova, Mario Chica, Miguel Martin, Vladimir Kadets","submitted_at":"2014-10-21T08:18:09Z","abstract_excerpt":"Extending the celebrated result by Bishop and Phelps that the set of norm attaining functionals is always dense in the topological dual of a Banach space, Bollob\\'as proved the nowadays known as the Bishop-Phelps-Bollob\\'as theorem, which allows to approximate at the same time a functional and a vector in which it almost attains the norm. Very recently, two Bishop-Phelps-Bollob\\'as moduli of a Banach space have been introduced [J. Math. Anal. Appl. 412 (2014), 697--719] to measure, for a given Banach space, what is the best possible Bishop-Phelps-Bollob\\'as theorem in this space. In this paper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5570","kind":"arxiv","version":2},"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":"1410.5570","created_at":"2026-05-18T00:45:54.663983+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.5570v2","created_at":"2026-05-18T00:45:54.663983+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5570","created_at":"2026-05-18T00:45:54.663983+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOYTY5NCZSPV","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOYTY5NCZSPV4BVG","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOYTY5NC","created_at":"2026-05-18T12:28:35.611951+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/KOYTY5NCZSPV4BVGRAUN3LYYGF","json":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF.json","graph_json":"https://pith.science/api/pith-number/KOYTY5NCZSPV4BVGRAUN3LYYGF/graph.json","events_json":"https://pith.science/api/pith-number/KOYTY5NCZSPV4BVGRAUN3LYYGF/events.json","paper":"https://pith.science/paper/KOYTY5NC"},"agent_actions":{"view_html":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF","download_json":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF.json","view_paper":"https://pith.science/paper/KOYTY5NC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.5570&json=true","fetch_graph":"https://pith.science/api/pith-number/KOYTY5NCZSPV4BVGRAUN3LYYGF/graph.json","fetch_events":"https://pith.science/api/pith-number/KOYTY5NCZSPV4BVGRAUN3LYYGF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF/action/storage_attestation","attest_author":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF/action/author_attestation","sign_citation":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF/action/citation_signature","submit_replication":"https://pith.science/pith/KOYTY5NCZSPV4BVGRAUN3LYYGF/action/replication_record"}},"created_at":"2026-05-18T00:45:54.663983+00:00","updated_at":"2026-05-18T00:45:54.663983+00:00"}