{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:XSTWK5LZO6A6I3MTVSJJY2B3JC","short_pith_number":"pith:XSTWK5LZ","canonical_record":{"source":{"id":"1005.4640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-25T17:30:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e4e27140689e106bdcf6d64c3235a30438f730a3219bcdcfe2afe130d20c5ce9","abstract_canon_sha256":"f8a3746a94d92dc2d4c1500d164e82f47918a8a1082bcadacd85cf563153d1cf"},"schema_version":"1.0"},"canonical_sha256":"bca76575797781e46d93ac929c683b48b5917af66449da80102a58fbb3f63a03","source":{"kind":"arxiv","id":"1005.4640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4640","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4640v2","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4640","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"XSTWK5LZO6A6","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XSTWK5LZO6A6I3MT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XSTWK5LZ","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:XSTWK5LZO6A6I3MTVSJJY2B3JC","target":"record","payload":{"canonical_record":{"source":{"id":"1005.4640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-25T17:30:51Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"e4e27140689e106bdcf6d64c3235a30438f730a3219bcdcfe2afe130d20c5ce9","abstract_canon_sha256":"f8a3746a94d92dc2d4c1500d164e82f47918a8a1082bcadacd85cf563153d1cf"},"schema_version":"1.0"},"canonical_sha256":"bca76575797781e46d93ac929c683b48b5917af66449da80102a58fbb3f63a03","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:52.363300Z","signature_b64":"vCR0661znRymwIvmtkAW23Tp/Lx5/EIFaoU/ys5Jjq3mhhMZ/3zgfTnzy1cCfj2oTyDlBPnQkZ8ICZh1o3ucCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bca76575797781e46d93ac929c683b48b5917af66449da80102a58fbb3f63a03","last_reissued_at":"2026-05-18T04:31:52.362837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:52.362837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.4640","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvOGhWtmxWCDEM/JexEQFYXMqOd7UqvHjlZEpWAwKjQ44NaC7QXmf+PQnczWJBhrrIipz7ggaBxlq2CK11/GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:59:34.149498Z"},"content_sha256":"893634bf39d2491b414680d2d8198263691c84f045254530cef5c7fe02f9cc11","schema_version":"1.0","event_id":"sha256:893634bf39d2491b414680d2d8198263691c84f045254530cef5c7fe02f9cc11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:XSTWK5LZO6A6I3MTVSJJY2B3JC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the distribution of extreme values of zeta and $L$-functions in the strip $1/2<\\sigma<1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.NT","authors_text":"Youness Lamzouri","submitted_at":"2010-05-25T17:30:51Z","abstract_excerpt":"We study the distribution of large (and small) values of several families of $L$-functions on a line $\\text{Re(s)}=\\sigma$ where $1/2<\\sigma<1$. We consider the Riemann zeta function $\\zeta(s)$ in the $t$-aspect, Dirichlet $L$-functions in the $q$-aspect, and $L$-functions attached to primitive holomorphic cusp forms of weight $2$ in the level aspect. For each family we show that the $L$-values can be very well modeled by an adequate random Euler product, uniformly in a wide range. We also prove new $\\Omega$-results for quadratic Dirichlet $L$-functions (predicted to be best possible by the pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4640","kind":"arxiv","version":2},"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":"2026-05-18T04:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TB7/NDEvxiAbBSe3xVFq/gz0LLaZiUQdPVbJQXmbGiHQw5VrreSq9ln0inqq33HwEySFi2TYNJa8x9LEZgf7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T17:59:34.149877Z"},"content_sha256":"fea35ff3d17561a4fe78fb19f08ce9e2c727a3022148dfe9a1bb09736c8c168d","schema_version":"1.0","event_id":"sha256:fea35ff3d17561a4fe78fb19f08ce9e2c727a3022148dfe9a1bb09736c8c168d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/bundle.json","state_url":"https://pith.science/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/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":"2026-05-28T17:59:34Z","links":{"resolver":"https://pith.science/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC","bundle":"https://pith.science/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/bundle.json","state":"https://pith.science/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSTWK5LZO6A6I3MTVSJJY2B3JC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:XSTWK5LZO6A6I3MTVSJJY2B3JC","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":"f8a3746a94d92dc2d4c1500d164e82f47918a8a1082bcadacd85cf563153d1cf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-25T17:30:51Z","title_canon_sha256":"e4e27140689e106bdcf6d64c3235a30438f730a3219bcdcfe2afe130d20c5ce9"},"schema_version":"1.0","source":{"id":"1005.4640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4640","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4640v2","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4640","created_at":"2026-05-18T04:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"XSTWK5LZO6A6","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"XSTWK5LZO6A6I3MT","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"XSTWK5LZ","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:fea35ff3d17561a4fe78fb19f08ce9e2c727a3022148dfe9a1bb09736c8c168d","target":"graph","created_at":"2026-05-18T04:31:52Z","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 study the distribution of large (and small) values of several families of $L$-functions on a line $\\text{Re(s)}=\\sigma$ where $1/2<\\sigma<1$. We consider the Riemann zeta function $\\zeta(s)$ in the $t$-aspect, Dirichlet $L$-functions in the $q$-aspect, and $L$-functions attached to primitive holomorphic cusp forms of weight $2$ in the level aspect. For each family we show that the $L$-values can be very well modeled by an adequate random Euler product, uniformly in a wide range. We also prove new $\\Omega$-results for quadratic Dirichlet $L$-functions (predicted to be best possible by the pr","authors_text":"Youness Lamzouri","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-25T17:30:51Z","title":"On the distribution of extreme values of zeta and $L$-functions in the strip $1/2<\\sigma<1$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4640","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":"sha256:893634bf39d2491b414680d2d8198263691c84f045254530cef5c7fe02f9cc11","target":"record","created_at":"2026-05-18T04:31:52Z","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":"f8a3746a94d92dc2d4c1500d164e82f47918a8a1082bcadacd85cf563153d1cf","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-25T17:30:51Z","title_canon_sha256":"e4e27140689e106bdcf6d64c3235a30438f730a3219bcdcfe2afe130d20c5ce9"},"schema_version":"1.0","source":{"id":"1005.4640","kind":"arxiv","version":2}},"canonical_sha256":"bca76575797781e46d93ac929c683b48b5917af66449da80102a58fbb3f63a03","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bca76575797781e46d93ac929c683b48b5917af66449da80102a58fbb3f63a03","first_computed_at":"2026-05-18T04:31:52.362837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:52.362837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCR0661znRymwIvmtkAW23Tp/Lx5/EIFaoU/ys5Jjq3mhhMZ/3zgfTnzy1cCfj2oTyDlBPnQkZ8ICZh1o3ucCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:52.363300Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:893634bf39d2491b414680d2d8198263691c84f045254530cef5c7fe02f9cc11","sha256:fea35ff3d17561a4fe78fb19f08ce9e2c727a3022148dfe9a1bb09736c8c168d"],"state_sha256":"be9e30204a0d34e69b51384c9af6c33fabb5af1b79faa29b3c99973083a83230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2CjqTHYaEXX6u3A/BaU63MuuZS8PZi+uDohwgTMmYI73FL+U8GVQocUbU7YnyvwpJJ2Xj3HoYtv5iIqgAiY/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T17:59:34.152333Z","bundle_sha256":"9d34e8e0cb56454d92afb765dabebe0a9b5ed576bfe544184a58c47d27d97b77"}}