{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NROZ62DVHZN6DMVMLBCYNGR6RN","short_pith_number":"pith:NROZ62DV","schema_version":"1.0","canonical_sha256":"6c5d9f68753e5be1b2ac5845869a3e8b7d346938118a069d272ad88b8bcd2c49","source":{"kind":"arxiv","id":"1308.4429","version":1},"attestation_state":"computed","paper":{"title":"On explicit constructions of auerbach bases in separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Robert Bogucki","submitted_at":"2013-08-20T20:47:40Z","abstract_excerpt":"This paper considers explicit constructions of Auerbach bases in separable Banach spaces. Answering the question of A. Pe{\\l}czy{\\'n}ski, we prove by construction the existence of Auerbach basis in arbitrary subspace of $c_0$ of finite codimension and in the space $C(K)$ for $K$ compact countable metric space."},"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":"1308.4429","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-08-20T20:47:40Z","cross_cats_sorted":[],"title_canon_sha256":"fdcd915fedd5f2c29787050c6a99037af2c91370097e114d86176eff8abbdcd7","abstract_canon_sha256":"2cc89bf182aa7a3b08689cd9f5fba7fdf0dd245fb76eea58fdf8504b75123c69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:31.860394Z","signature_b64":"LE1d+LuGiNNhgDaq8L871Sp8c6y1pSfFWLZTGtpusXOvLNYHFhvBYJ4cFt8HhIf/S+EUVoLWJgWy8c9YhwySDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c5d9f68753e5be1b2ac5845869a3e8b7d346938118a069d272ad88b8bcd2c49","last_reissued_at":"2026-05-18T03:15:31.859685Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:31.859685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On explicit constructions of auerbach bases in separable Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Robert Bogucki","submitted_at":"2013-08-20T20:47:40Z","abstract_excerpt":"This paper considers explicit constructions of Auerbach bases in separable Banach spaces. Answering the question of A. Pe{\\l}czy{\\'n}ski, we prove by construction the existence of Auerbach basis in arbitrary subspace of $c_0$ of finite codimension and in the space $C(K)$ for $K$ compact countable metric space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4429","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":"1308.4429","created_at":"2026-05-18T03:15:31.859829+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.4429v1","created_at":"2026-05-18T03:15:31.859829+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4429","created_at":"2026-05-18T03:15:31.859829+00:00"},{"alias_kind":"pith_short_12","alias_value":"NROZ62DVHZN6","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NROZ62DVHZN6DMVM","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NROZ62DV","created_at":"2026-05-18T12:27:52.871228+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/NROZ62DVHZN6DMVMLBCYNGR6RN","json":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN.json","graph_json":"https://pith.science/api/pith-number/NROZ62DVHZN6DMVMLBCYNGR6RN/graph.json","events_json":"https://pith.science/api/pith-number/NROZ62DVHZN6DMVMLBCYNGR6RN/events.json","paper":"https://pith.science/paper/NROZ62DV"},"agent_actions":{"view_html":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN","download_json":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN.json","view_paper":"https://pith.science/paper/NROZ62DV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.4429&json=true","fetch_graph":"https://pith.science/api/pith-number/NROZ62DVHZN6DMVMLBCYNGR6RN/graph.json","fetch_events":"https://pith.science/api/pith-number/NROZ62DVHZN6DMVMLBCYNGR6RN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN/action/storage_attestation","attest_author":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN/action/author_attestation","sign_citation":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN/action/citation_signature","submit_replication":"https://pith.science/pith/NROZ62DVHZN6DMVMLBCYNGR6RN/action/replication_record"}},"created_at":"2026-05-18T03:15:31.859829+00:00","updated_at":"2026-05-18T03:15:31.859829+00:00"}