{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:HYCJLV4WTUEYPM7YD3TCRXVVPS","short_pith_number":"pith:HYCJLV4W","canonical_record":{"source":{"id":"1108.5092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e1aa096e4ca41213440a13e9a052bce00a324c13489891eefe424bc600abe762","abstract_canon_sha256":"656b7c8a20dbb66ec43a2d8bfefe733443d614226293cceb3850d12dc765e0ac"},"schema_version":"1.0"},"canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","source":{"kind":"arxiv","id":"1108.5092","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5092","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5092v1","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5092","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"HYCJLV4WTUEY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HYCJLV4WTUEYPM7Y","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HYCJLV4W","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:HYCJLV4WTUEYPM7YD3TCRXVVPS","target":"record","payload":{"canonical_record":{"source":{"id":"1108.5092","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e1aa096e4ca41213440a13e9a052bce00a324c13489891eefe424bc600abe762","abstract_canon_sha256":"656b7c8a20dbb66ec43a2d8bfefe733443d614226293cceb3850d12dc765e0ac"},"schema_version":"1.0"},"canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:45.445924Z","signature_b64":"tUxLYcduRp5DQYLZFkfEMtk8fUcxKghUpUg9qEwkxXPCAqnt8JvNK5Qb6nVPCD2fMRLI0N1cvnNAaNyzCmcPAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","last_reissued_at":"2026-05-18T04:14:45.445236Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:45.445236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1108.5092","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"svIJ9UvwOiEthblXLIvrkT2ac9RR+A+vp6LG3QeGIj5jLtdyUsBispy2rJLFvlUbhf2CePAA9Gv6Se9c2hAZAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T05:13:59.329640Z"},"content_sha256":"c4b18e03fea4398c34a8a05f09b56dc165f84e9b1fc92e1d45e06ba9b43dab76","schema_version":"1.0","event_id":"sha256:c4b18e03fea4398c34a8a05f09b56dc165f84e9b1fc92e1d45e06ba9b43dab76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:HYCJLV4WTUEYPM7YD3TCRXVVPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large deviations in Selberg's central limit theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Maksym Radziwill","submitted_at":"2011-08-25T13:57:37Z","abstract_excerpt":"Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \\epsilon} the measure of those t \\in [T;2T] for which log |\\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard Gaussian random variable takes on values greater than V. We extend the range of V to V << (loglog T)^{1/10 - \\epsilon}. We also speculate on the size of the largest V for which this normal approximation can hold and on the correct approximation beyond that point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5092","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WjWMx+pBiHjqrZ2wTzvfQm+p7xJNTLt9DvKSexkjT7rTSFhG4UY8tUlXsn0OF9czd/CCro0EGJlaUIlSLdvlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T05:13:59.330247Z"},"content_sha256":"2a041fe0c85309cfbdf5d79080dbfb1b1dc94e6a69b7f6a2fccd8c2727e8c407","schema_version":"1.0","event_id":"sha256:2a041fe0c85309cfbdf5d79080dbfb1b1dc94e6a69b7f6a2fccd8c2727e8c407"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/bundle.json","state_url":"https://pith.science/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-24T05:13:59Z","links":{"resolver":"https://pith.science/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS","bundle":"https://pith.science/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/bundle.json","state":"https://pith.science/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYCJLV4WTUEYPM7YD3TCRXVVPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:HYCJLV4WTUEYPM7YD3TCRXVVPS","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":"656b7c8a20dbb66ec43a2d8bfefe733443d614226293cceb3850d12dc765e0ac","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","title_canon_sha256":"e1aa096e4ca41213440a13e9a052bce00a324c13489891eefe424bc600abe762"},"schema_version":"1.0","source":{"id":"1108.5092","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.5092","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1108.5092v1","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5092","created_at":"2026-05-18T04:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"HYCJLV4WTUEY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"HYCJLV4WTUEYPM7Y","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"HYCJLV4W","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:2a041fe0c85309cfbdf5d79080dbfb1b1dc94e6a69b7f6a2fccd8c2727e8c407","target":"graph","created_at":"2026-05-18T04:14:45Z","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":"Following Selberg it is known that uniformly for V << (logloglog T)^{1/2 - \\epsilon} the measure of those t \\in [T;2T] for which log |\\zeta(1/2 + it)| > V*((1/2)loglog T)^{1/2} is approximately T times the probability that a standard Gaussian random variable takes on values greater than V. We extend the range of V to V << (loglog T)^{1/10 - \\epsilon}. We also speculate on the size of the largest V for which this normal approximation can hold and on the correct approximation beyond that point.","authors_text":"Maksym Radziwill","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","title":"Large deviations in Selberg's central limit theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5092","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:c4b18e03fea4398c34a8a05f09b56dc165f84e9b1fc92e1d45e06ba9b43dab76","target":"record","created_at":"2026-05-18T04:14:45Z","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":"656b7c8a20dbb66ec43a2d8bfefe733443d614226293cceb3850d12dc765e0ac","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-08-25T13:57:37Z","title_canon_sha256":"e1aa096e4ca41213440a13e9a052bce00a324c13489891eefe424bc600abe762"},"schema_version":"1.0","source":{"id":"1108.5092","kind":"arxiv","version":1}},"canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0495d7969d0987b3f81ee628deb57c82fb7fdf068d1e0d9e495eb56e599d2e","first_computed_at":"2026-05-18T04:14:45.445236Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:14:45.445236Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tUxLYcduRp5DQYLZFkfEMtk8fUcxKghUpUg9qEwkxXPCAqnt8JvNK5Qb6nVPCD2fMRLI0N1cvnNAaNyzCmcPAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:14:45.445924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.5092","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b18e03fea4398c34a8a05f09b56dc165f84e9b1fc92e1d45e06ba9b43dab76","sha256:2a041fe0c85309cfbdf5d79080dbfb1b1dc94e6a69b7f6a2fccd8c2727e8c407"],"state_sha256":"3aaf903aa5712fe257a574b08225b2e6cb0c51f024fa6366919a1029627a041c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T3RvpPh4s7GaH7BGE4+6DTqVIlP7aIicnmdqHNnK/A9glydF11X3rM0s3U7CrxrEy7Gi4Lm+sP0grxFpySmaAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T05:13:59.333784Z","bundle_sha256":"1b52039d74ee6e93adbb61eb52e01e19fd98bc3e7358d6a55e24f3924708b9ed"}}