{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:BO6BBZWXQ4QWHOR2545KR6NNMR","short_pith_number":"pith:BO6BBZWX","schema_version":"1.0","canonical_sha256":"0bbc10e6d7872163ba3aef3aa8f9ad6455010413282e0577842371e1ae07bedc","source":{"kind":"arxiv","id":"1608.00495","version":2},"attestation_state":"computed","paper":{"title":"On the Pelczynski conjecture on Auerbach Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.FA","authors_text":"Andrzej Weber, Micha{\\l} Wojciechowski","submitted_at":"2016-08-01T17:04:53Z","abstract_excerpt":"We consider Auerbach bases in Banach spaces of dimension n>2. We show that there exists at least (n-1)n/2+1 such bases. This estimate follows from the calculation of the Lusternik-Schnirelmann category of the flag variety. A better estimate is obtained for generic Banach spaces by the Morse theory."},"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":"1608.00495","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-01T17:04:53Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"fa45c013608cac59d7f09ca41ff30b5323a79704dac266fd0968cdab0cc69a2f","abstract_canon_sha256":"169b693ddfc6f26d8bdba864b755325e3837a7388ebc3004cee7bf67d5ca1475"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:00.114864Z","signature_b64":"dbr7BpQNMLuq9xNnAAhurrT7SvjwHdaD8EXWk+bGWvgbv9HtjTNdlbi0dHAN2E3Fo9/wr/YZ6qyTXzcgeCCdDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bbc10e6d7872163ba3aef3aa8f9ad6455010413282e0577842371e1ae07bedc","last_reissued_at":"2026-05-18T01:02:00.114435Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:00.114435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Pelczynski conjecture on Auerbach Bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.FA","authors_text":"Andrzej Weber, Micha{\\l} Wojciechowski","submitted_at":"2016-08-01T17:04:53Z","abstract_excerpt":"We consider Auerbach bases in Banach spaces of dimension n>2. We show that there exists at least (n-1)n/2+1 such bases. This estimate follows from the calculation of the Lusternik-Schnirelmann category of the flag variety. A better estimate is obtained for generic Banach spaces by the Morse theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00495","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":"1608.00495","created_at":"2026-05-18T01:02:00.114507+00:00"},{"alias_kind":"arxiv_version","alias_value":"1608.00495v2","created_at":"2026-05-18T01:02:00.114507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.00495","created_at":"2026-05-18T01:02:00.114507+00:00"},{"alias_kind":"pith_short_12","alias_value":"BO6BBZWXQ4QW","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"BO6BBZWXQ4QWHOR2","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"BO6BBZWX","created_at":"2026-05-18T12:30:07.202191+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/BO6BBZWXQ4QWHOR2545KR6NNMR","json":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR.json","graph_json":"https://pith.science/api/pith-number/BO6BBZWXQ4QWHOR2545KR6NNMR/graph.json","events_json":"https://pith.science/api/pith-number/BO6BBZWXQ4QWHOR2545KR6NNMR/events.json","paper":"https://pith.science/paper/BO6BBZWX"},"agent_actions":{"view_html":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR","download_json":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR.json","view_paper":"https://pith.science/paper/BO6BBZWX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1608.00495&json=true","fetch_graph":"https://pith.science/api/pith-number/BO6BBZWXQ4QWHOR2545KR6NNMR/graph.json","fetch_events":"https://pith.science/api/pith-number/BO6BBZWXQ4QWHOR2545KR6NNMR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR/action/storage_attestation","attest_author":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR/action/author_attestation","sign_citation":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR/action/citation_signature","submit_replication":"https://pith.science/pith/BO6BBZWXQ4QWHOR2545KR6NNMR/action/replication_record"}},"created_at":"2026-05-18T01:02:00.114507+00:00","updated_at":"2026-05-18T01:02:00.114507+00:00"}