{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6Y37RZTD5E3Q6TZZAYCOOB3OOO","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":"dd724243c0fe8aadde6472c351b044b035b5c51a44c2b45c0985b2f8c17f91f6","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-08-15T08:56:45Z","title_canon_sha256":"ffe4e3ba53e69f636ac6398c2c2050a04b4d72aea1f6b2b439f0791b1b96d1b9"},"schema_version":"1.0","source":{"id":"1608.04210","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.04210","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"1608.04210v1","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.04210","created_at":"2026-05-18T01:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"6Y37RZTD5E3Q","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"6Y37RZTD5E3Q6TZZ","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"6Y37RZTD","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:6436478706c30156eb1c59769052e00aaaa5ad180ffc3e52a6c7d78ceb5f54d8","target":"graph","created_at":"2026-05-18T01:09:04Z","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":"The Bernoulli convolution with parameter $\\lambda\\in(0,1)$ is the measure on $\\bf R$ that is the distribution of the random power series $\\sum\\pm\\lambda^n$, where $\\pm$ are independent fair coin-tosses. This paper surveys recent progress on our understanding of the regularity properties of these measures.","authors_text":"P\\'eter P. Varj\\'u","cross_cats":["math.DS","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-08-15T08:56:45Z","title":"Recent progress on Bernoulli convolutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04210","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":"sha256:91b22a47c1371908554f7459f57af1a0d889b02a18f057bcc1c5fe20c9b1b758","target":"record","created_at":"2026-05-18T01:09:04Z","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":"dd724243c0fe8aadde6472c351b044b035b5c51a44c2b45c0985b2f8c17f91f6","cross_cats_sorted":["math.DS","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-08-15T08:56:45Z","title_canon_sha256":"ffe4e3ba53e69f636ac6398c2c2050a04b4d72aea1f6b2b439f0791b1b96d1b9"},"schema_version":"1.0","source":{"id":"1608.04210","kind":"arxiv","version":1}},"canonical_sha256":"f637f8e663e9370f4f390604e7076e73a1df92d13b362d2f1d87e6b3847822e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f637f8e663e9370f4f390604e7076e73a1df92d13b362d2f1d87e6b3847822e4","first_computed_at":"2026-05-18T01:09:04.058297Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:04.058297Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PDjtcj6ZEOQ+sXO3OmqaogLazHbhYqthKn7iNyfeEOwDFvzjUO7g72E1QiML1sgFufTkp17/iC/2tBCBCw8KCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:04.058833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.04210","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91b22a47c1371908554f7459f57af1a0d889b02a18f057bcc1c5fe20c9b1b758","sha256:6436478706c30156eb1c59769052e00aaaa5ad180ffc3e52a6c7d78ceb5f54d8"],"state_sha256":"ec53cf474a98ceae345dbaaf5d2c7208ec4d43055c0de7694acf90b5c2b64704"}