{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:6NFTPED2JUEI7LBVRX6TEBMBOM","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":"313e27893f958b0e643abc2b3e3c1859f2c95d42868d90fab4a51b73190b03e9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-24T15:07:56Z","title_canon_sha256":"ffc81e1defba1fa9ee10e788aa2d86c04ff378d76e51be1ada1dbbd811fec2ea"},"schema_version":"1.0","source":{"id":"1610.01441","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.01441","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.01441v3","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.01441","created_at":"2026-05-18T00:36:39Z"},{"alias_kind":"pith_short_12","alias_value":"6NFTPED2JUEI","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"6NFTPED2JUEI7LBV","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"6NFTPED2","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:9c193b7ff40e8aac31f20472aaf7cea4ef6d9566f85acf4dd859cd37d53967d1","target":"graph","created_at":"2026-05-18T00:36:39Z","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":"This paper discusses some infinite trigonometric products which are characteristic functions of simple random walks on the real line; in fact, these define \"random Riemann-$\\zeta$ functions,\" a notion which is explained. The concept of typicality for random Riemann $\\zeta$ functions is explained and connected to the Riemann hypothesis. Then it is shown that the distribution functions of these random walks are Schwarz functions. It is also shown that their characteristic function factors into the characteristic function of a Levy stable random variable and a subdominant fluctuating factor. As a","authors_text":"Leif Albert, Michael K.-H. Kiessling","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-24T15:07:56Z","title":"Order and Chaos in some deterministic infinite trigonometric products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.01441","kind":"arxiv","version":3},"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:c4bd0d983ac5e5689c47eb0d9bf090eb81575f6faf3f3bdcbcfa4e3ad0d58b7a","target":"record","created_at":"2026-05-18T00:36:39Z","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":"313e27893f958b0e643abc2b3e3c1859f2c95d42868d90fab4a51b73190b03e9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-09-24T15:07:56Z","title_canon_sha256":"ffc81e1defba1fa9ee10e788aa2d86c04ff378d76e51be1ada1dbbd811fec2ea"},"schema_version":"1.0","source":{"id":"1610.01441","kind":"arxiv","version":3}},"canonical_sha256":"f34b37907a4d088fac358dfd320581732617c49a772bb2c01283f22b1b80bac3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f34b37907a4d088fac358dfd320581732617c49a772bb2c01283f22b1b80bac3","first_computed_at":"2026-05-18T00:36:39.257616Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:39.257616Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XUDcYmgffXSC08e7r6UlTOXNr9hjtYyetsdECpOjOnxlKLHlYGqDa5RGcNBrS4b9d7n3t04IQBXO8fWjiPiFCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:39.258149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.01441","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4bd0d983ac5e5689c47eb0d9bf090eb81575f6faf3f3bdcbcfa4e3ad0d58b7a","sha256:9c193b7ff40e8aac31f20472aaf7cea4ef6d9566f85acf4dd859cd37d53967d1"],"state_sha256":"a7dd7c8884c88abcb5abcaf6f31b42ecb0bddbb61760438c548a0b9a71311907"}