{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6GW5HDAIRFCMLBIS6JX7IYCKKH","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":"dfa881ac5ec4e39ce04748ebd294ffd0d500ce15aa3c66948b79ec6fda4a7d3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-07T14:37:47Z","title_canon_sha256":"d104fe70b41dad64b0b6f492669af6fc14e9522c1fd2b16d220d0458a9a346a7"},"schema_version":"1.0","source":{"id":"1211.1559","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1559","created_at":"2026-05-18T02:32:39Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1559v1","created_at":"2026-05-18T02:32:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1559","created_at":"2026-05-18T02:32:39Z"},{"alias_kind":"pith_short_12","alias_value":"6GW5HDAIRFCM","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6GW5HDAIRFCMLBIS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6GW5HDAI","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:9226dc8ff5946edb5c18034703199d7b0a5849a28e2ce8344482f52275410b0d","target":"graph","created_at":"2026-05-18T02:32:39Z","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"},"paper":{"abstract_excerpt":"Entropy numbers and Kolmogorov numbers of convex hulls in Banach spaces are studied. Applications are given.","authors_text":"Aicke Hinrichs, Bernd Carl, Philipp Rudolph","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-07T14:37:47Z","title":"Entropy numbers of convex hulls in Banach spaces and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1559","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:fab8e34af8e8614eed120555d9ccc4fc829d3d9d828769d4972a019d3807e1e2","target":"record","created_at":"2026-05-18T02:32:39Z","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":"dfa881ac5ec4e39ce04748ebd294ffd0d500ce15aa3c66948b79ec6fda4a7d3a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-11-07T14:37:47Z","title_canon_sha256":"d104fe70b41dad64b0b6f492669af6fc14e9522c1fd2b16d220d0458a9a346a7"},"schema_version":"1.0","source":{"id":"1211.1559","kind":"arxiv","version":1}},"canonical_sha256":"f1add38c088944c58512f26ff4604a51e12b07ad6884d55725850c02ce5e84e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1add38c088944c58512f26ff4604a51e12b07ad6884d55725850c02ce5e84e0","first_computed_at":"2026-05-18T02:32:39.214605Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:39.214605Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jRkwTOzLBDcqZdZ587sgXLWz6PHL0dprDmnWfLRI2zz4fUeSCFCM+xi0CE0UdFKajlAWhyCMS8XHuD0mrFXyCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:39.214987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1559","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fab8e34af8e8614eed120555d9ccc4fc829d3d9d828769d4972a019d3807e1e2","sha256:9226dc8ff5946edb5c18034703199d7b0a5849a28e2ce8344482f52275410b0d"],"state_sha256":"9bb43cfe378bea481165616ce763ce0c60d24e51f43d97147a3924cad0ad0106"}