{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:AKS3UJM7RER3BXX2VFEK3OJ7D2","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f070ed9d646fd9834bd4675a5c927991b6cc409eafb122595a3ae047463770d1","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-01T18:50:20Z","title_canon_sha256":"4f8aac848df8fc175c09121bc730ec381808828769d623eaff443c7007a0a1b5"},"schema_version":"1.0","source":{"id":"2302.00664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.00664","created_at":"2026-07-05T05:38:05Z"},{"alias_kind":"arxiv_version","alias_value":"2302.00664v1","created_at":"2026-07-05T05:38:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.00664","created_at":"2026-07-05T05:38:05Z"},{"alias_kind":"pith_short_12","alias_value":"AKS3UJM7RER3","created_at":"2026-07-05T05:38:05Z"},{"alias_kind":"pith_short_16","alias_value":"AKS3UJM7RER3BXX2","created_at":"2026-07-05T05:38:05Z"},{"alias_kind":"pith_short_8","alias_value":"AKS3UJM7","created_at":"2026-07-05T05:38:05Z"}],"graph_snapshots":[{"event_id":"sha256:e6af3945c1dc03e6e799fe20a0723243be2f2d099e16e637fc609b288995c389","target":"graph","created_at":"2026-07-05T05:38:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.00664/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study Auerbach basis of the Banach spaces $l^n_p$. We provide a complete classification of the spaces in terms of the cardinality of their bases. We also give a complete description of these bases for $l^3_p$ ($l^2_p$ is easy).","authors_text":"Arun Maiti, Debmalya Sain","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-01T18:50:20Z","title":"On the Auerbach bases of $l^{n}_p$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.00664","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5dc236228c25fa15d48532b30ca2bab39baac3329c7a6b9cd0ddb65aa662a42e","target":"record","created_at":"2026-07-05T05:38:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f070ed9d646fd9834bd4675a5c927991b6cc409eafb122595a3ae047463770d1","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-01T18:50:20Z","title_canon_sha256":"4f8aac848df8fc175c09121bc730ec381808828769d623eaff443c7007a0a1b5"},"schema_version":"1.0","source":{"id":"2302.00664","kind":"arxiv","version":1}},"canonical_sha256":"02a5ba259f8923b0defaa948adb93f1ebc80f03a811f0ecf928c09e0e9e8c00c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02a5ba259f8923b0defaa948adb93f1ebc80f03a811f0ecf928c09e0e9e8c00c","first_computed_at":"2026-07-05T05:38:05.749273Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:38:05.749273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RXBv1QRIXr+CuWE85O6ug1sC2YobzpK1CgmlhmRwYhepzWsrAJ6yCN7KlsYM8HPwepBrEgkIH5ywzflnDp80AQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:38:05.749661Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.00664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5dc236228c25fa15d48532b30ca2bab39baac3329c7a6b9cd0ddb65aa662a42e","sha256:e6af3945c1dc03e6e799fe20a0723243be2f2d099e16e637fc609b288995c389"],"state_sha256":"4fff6edc6af7ca9233cfa379c65f66b30029165164940a69031351a723def1ca"}