{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:DKYDJL6RBGJC6YKDFKZO5GOAGT","short_pith_number":"pith:DKYDJL6R","canonical_record":{"source":{"id":"1901.04061","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-13T21:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"3c229bb35f122e48f79d7d58682bf5c04c55590abddfbb19764253c5bccc8d3c","abstract_canon_sha256":"b7ba92cffe06066442c1500baf7f2932e4f150bae2aaaaafb439416e71c22728"},"schema_version":"1.0"},"canonical_sha256":"1ab034afd109922f61432ab2ee99c034c69cab39481c2f1a70c7fbf0c8255f89","source":{"kind":"arxiv","id":"1901.04061","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04061","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04061v4","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04061","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKYDJL6RBGJC","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_16","alias_value":"DKYDJL6RBGJC6YKD","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_8","alias_value":"DKYDJL6R","created_at":"2026-07-05T04:25:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:DKYDJL6RBGJC6YKDFKZO5GOAGT","target":"record","payload":{"canonical_record":{"source":{"id":"1901.04061","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-13T21:04:02Z","cross_cats_sorted":[],"title_canon_sha256":"3c229bb35f122e48f79d7d58682bf5c04c55590abddfbb19764253c5bccc8d3c","abstract_canon_sha256":"b7ba92cffe06066442c1500baf7f2932e4f150bae2aaaaafb439416e71c22728"},"schema_version":"1.0"},"canonical_sha256":"1ab034afd109922f61432ab2ee99c034c69cab39481c2f1a70c7fbf0c8255f89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:25:38.420184Z","signature_b64":"uF2SjcVFGfYpZEQh7CTo10TOQydVLGQ04W621AnN+j2Oh/JGqB4MJTPp+Nm5lN6yO8+/1cnAi3ozeSK8C5SUAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ab034afd109922f61432ab2ee99c034c69cab39481c2f1a70c7fbf0c8255f89","last_reissued_at":"2026-07-05T04:25:38.419719Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:25:38.419719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.04061","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfBV96lIk2zCRpVlgJA5mzGOYFa6KQgRxe/Y5FmG0Xg7t9Di7JFvzNFmLLUR0ZcJ7Q/jQqvPgrru84jvSonWAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:55:48.263223Z"},"content_sha256":"f3e449a1aca3a8140479e4f1d70386fe6fd89dd22c8fedd2115188ce3ef96815","schema_version":"1.0","event_id":"sha256:f3e449a1aca3a8140479e4f1d70386fe6fd89dd22c8fedd2115188ce3ef96815"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:DKYDJL6RBGJC6YKDFKZO5GOAGT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of the Riemann zeta function on short intervals of the critical line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fr\\'ed\\'eric Ouimet, Louis-Pierre Arguin, Maksym Radziwi\\l\\l","submitted_at":"2019-01-13T21:04:02Z","abstract_excerpt":"We show that as $T\\to \\infty$, for all $t\\in [T,2T]$ outside of a set of measure $\\mathrm{o}(T)$, $$ \\int_{-(\\log T)^{\\theta}}^{(\\log T)^{\\theta}} |\\zeta(\\tfrac 12 + \\mathrm{i} t + \\mathrm{i} h)|^{\\beta} \\mathrm{d} h = (\\log T)^{f_{\\theta}(\\beta) + \\mathrm{o}(1)}, $$ for some explicit exponent $f_{\\theta}(\\beta)$, where $\\theta > -1$ and $\\beta > 0$. This proves an extended version of a conjecture of Fyodorov and Keating (2014). In particular, it shows that, for all $\\theta > -1$, the moments exhibit a phase transition at a critical exponent $\\beta_c(\\theta)$, below which $f_\\theta(\\beta)$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04061","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1901.04061/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:25:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tEkLSwEJ/f8+/eg7SrVO8OnH52GZz2IzI0M+kWbExaK6/rSsyy0y4eIki0Z9mEQeIUOIpr7F3/YdXoGYFrxNDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T11:55:48.263607Z"},"content_sha256":"300b836f80bed8f986f484bf075e670421a3d738395eaa72bd463416392dca15","schema_version":"1.0","event_id":"sha256:300b836f80bed8f986f484bf075e670421a3d738395eaa72bd463416392dca15"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/bundle.json","state_url":"https://pith.science/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/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":"2026-07-05T11:55:48Z","links":{"resolver":"https://pith.science/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT","bundle":"https://pith.science/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/bundle.json","state":"https://pith.science/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DKYDJL6RBGJC6YKDFKZO5GOAGT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:DKYDJL6RBGJC6YKDFKZO5GOAGT","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":"b7ba92cffe06066442c1500baf7f2932e4f150bae2aaaaafb439416e71c22728","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-13T21:04:02Z","title_canon_sha256":"3c229bb35f122e48f79d7d58682bf5c04c55590abddfbb19764253c5bccc8d3c"},"schema_version":"1.0","source":{"id":"1901.04061","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.04061","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"arxiv_version","alias_value":"1901.04061v4","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.04061","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_12","alias_value":"DKYDJL6RBGJC","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_16","alias_value":"DKYDJL6RBGJC6YKD","created_at":"2026-07-05T04:25:38Z"},{"alias_kind":"pith_short_8","alias_value":"DKYDJL6R","created_at":"2026-07-05T04:25:38Z"}],"graph_snapshots":[{"event_id":"sha256:300b836f80bed8f986f484bf075e670421a3d738395eaa72bd463416392dca15","target":"graph","created_at":"2026-07-05T04:25:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1901.04061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that as $T\\to \\infty$, for all $t\\in [T,2T]$ outside of a set of measure $\\mathrm{o}(T)$, $$ \\int_{-(\\log T)^{\\theta}}^{(\\log T)^{\\theta}} |\\zeta(\\tfrac 12 + \\mathrm{i} t + \\mathrm{i} h)|^{\\beta} \\mathrm{d} h = (\\log T)^{f_{\\theta}(\\beta) + \\mathrm{o}(1)}, $$ for some explicit exponent $f_{\\theta}(\\beta)$, where $\\theta > -1$ and $\\beta > 0$. This proves an extended version of a conjecture of Fyodorov and Keating (2014). In particular, it shows that, for all $\\theta > -1$, the moments exhibit a phase transition at a critical exponent $\\beta_c(\\theta)$, below which $f_\\theta(\\beta)$ is ","authors_text":"Fr\\'ed\\'eric Ouimet, Louis-Pierre Arguin, Maksym Radziwi\\l\\l","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-13T21:04:02Z","title":"Moments of the Riemann zeta function on short intervals of the critical line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.04061","kind":"arxiv","version":4},"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:f3e449a1aca3a8140479e4f1d70386fe6fd89dd22c8fedd2115188ce3ef96815","target":"record","created_at":"2026-07-05T04:25:38Z","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":"b7ba92cffe06066442c1500baf7f2932e4f150bae2aaaaafb439416e71c22728","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-01-13T21:04:02Z","title_canon_sha256":"3c229bb35f122e48f79d7d58682bf5c04c55590abddfbb19764253c5bccc8d3c"},"schema_version":"1.0","source":{"id":"1901.04061","kind":"arxiv","version":4}},"canonical_sha256":"1ab034afd109922f61432ab2ee99c034c69cab39481c2f1a70c7fbf0c8255f89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ab034afd109922f61432ab2ee99c034c69cab39481c2f1a70c7fbf0c8255f89","first_computed_at":"2026-07-05T04:25:38.419719Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:25:38.419719Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uF2SjcVFGfYpZEQh7CTo10TOQydVLGQ04W621AnN+j2Oh/JGqB4MJTPp+Nm5lN6yO8+/1cnAi3ozeSK8C5SUAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:25:38.420184Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.04061","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3e449a1aca3a8140479e4f1d70386fe6fd89dd22c8fedd2115188ce3ef96815","sha256:300b836f80bed8f986f484bf075e670421a3d738395eaa72bd463416392dca15"],"state_sha256":"12892cacf53b9e981d221e6f2dca3f8690ca5504dd62429dd33990fbb8253a44"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHusiJlVWqo1SsM8/xFBmf9dEd7yLcsCClaLeXfAyA17qE4u2pV8ZK+lND3gME19WA/CW9fUuMqhOoj6sejLAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T11:55:48.265551Z","bundle_sha256":"7070ae78f96363dff463836300c319349f28bbdc9d2464337da62949d2feb237"}}