{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NXLH5A6LMI2Q7J6ZMIP4IOWE7R","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":"fb46d48ee11db3e8682b45c4c19946d302021bb903a8aacb8ef98062b52a7976","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-04T15:18:38Z","title_canon_sha256":"10e207e4632313a2ce0df35ed1e0cb5a5ad19c65459085a63fc29d388ee1b40b"},"schema_version":"1.0","source":{"id":"1504.01016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.01016","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"arxiv_version","alias_value":"1504.01016v2","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.01016","created_at":"2026-05-18T01:23:29Z"},{"alias_kind":"pith_short_12","alias_value":"NXLH5A6LMI2Q","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NXLH5A6LMI2Q7J6Z","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NXLH5A6L","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:8ca1bc813bad582f7ab6c27cdf2bd18a70038f39a5671c7d58d89f2338e3493c","target":"graph","created_at":"2026-05-18T01:23:29Z","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":"We identify the exposed points of the unit ball of the dual space of the ball algebra. As a corollary, we show that the predual of $H^\\infty(\\mathbb{B}_d)$ has no extreme points in its unit ball.","authors_text":"Kenneth R. Davidson, Rapha\\\"el Clou\\^atre","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-04T15:18:38Z","title":"The unit ball of the predual of $H^\\infty(\\mathbb{B}_d)$ has no extreme points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.01016","kind":"arxiv","version":2},"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":"sha256:58de5251980930d82b69527056592db0e5d7b4c314af3cfb586a3402c9719e28","target":"record","created_at":"2026-05-18T01:23:29Z","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":"fb46d48ee11db3e8682b45c4c19946d302021bb903a8aacb8ef98062b52a7976","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-04T15:18:38Z","title_canon_sha256":"10e207e4632313a2ce0df35ed1e0cb5a5ad19c65459085a63fc29d388ee1b40b"},"schema_version":"1.0","source":{"id":"1504.01016","kind":"arxiv","version":2}},"canonical_sha256":"6dd67e83cb62350fa7d9621fc43ac4fc4af2942db7bbb4b5c1e8045294f6bc5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dd67e83cb62350fa7d9621fc43ac4fc4af2942db7bbb4b5c1e8045294f6bc5c","first_computed_at":"2026-05-18T01:23:29.380336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:29.380336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W2rearmW/kx2JrEqnt2wS6OB5HMcGRGJU8Aic2gXMNnCX/ZE0YRB9poVWhfNe1J+IEMBFoPyEfkT1bnhlsVtBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:29.380997Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.01016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58de5251980930d82b69527056592db0e5d7b4c314af3cfb586a3402c9719e28","sha256:8ca1bc813bad582f7ab6c27cdf2bd18a70038f39a5671c7d58d89f2338e3493c"],"state_sha256":"dc6ecddcf871277544478bc799acf5d26526dbe6fbd45418717c2a67a6bb2c4f"}