{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:SZLA72XZY6WFRM6MLQCF6NTFD5","short_pith_number":"pith:SZLA72XZ","canonical_record":{"source":{"id":"1008.2173","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T17:40:20Z","cross_cats_sorted":[],"title_canon_sha256":"a6fbd3cff5a69053d94b5607cbf07c4d4801e7ccf6b416c72d367b2cbcf28698","abstract_canon_sha256":"932a5bd1a822149abd1daec7d377da91b472ead259ed839495f5b3ee7c5f8462"},"schema_version":"1.0"},"canonical_sha256":"96560feaf9c7ac58b3cc5c045f36651f43928596486b84445606b6ebaaff40f3","source":{"kind":"arxiv","id":"1008.2173","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2173","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2173v2","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2173","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"pith_short_12","alias_value":"SZLA72XZY6WF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SZLA72XZY6WFRM6M","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SZLA72XZ","created_at":"2026-05-18T12:26:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:SZLA72XZY6WFRM6MLQCF6NTFD5","target":"record","payload":{"canonical_record":{"source":{"id":"1008.2173","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T17:40:20Z","cross_cats_sorted":[],"title_canon_sha256":"a6fbd3cff5a69053d94b5607cbf07c4d4801e7ccf6b416c72d367b2cbcf28698","abstract_canon_sha256":"932a5bd1a822149abd1daec7d377da91b472ead259ed839495f5b3ee7c5f8462"},"schema_version":"1.0"},"canonical_sha256":"96560feaf9c7ac58b3cc5c045f36651f43928596486b84445606b6ebaaff40f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:54.283763Z","signature_b64":"Vz7c9cB3n10Ra27rAtr5FoLNhNrKKxy0JCO5WBb7/0NqTehGbPws27VzAiTXBbbZAeRNQRXoDPHzYu0VvEHGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96560feaf9c7ac58b3cc5c045f36651f43928596486b84445606b6ebaaff40f3","last_reissued_at":"2026-05-18T04:07:54.283124Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:54.283124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.2173","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":"2026-05-18T04:07:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aMC0xHHFWM20L26qe0HAZTVaE/xQu/LgmmuzHhGH7oo6Yck/7BLZ3uDNQkZdCbCnQpUDFUEKWCUbIIFYD/yyDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:22:46.833404Z"},"content_sha256":"65d0807f537c34ec92ab1d64c945a009fac2d3cb3b602b7d2c65dda74265028b","schema_version":"1.0","event_id":"sha256:65d0807f537c34ec92ab1d64c945a009fac2d3cb3b602b7d2c65dda74265028b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:SZLA72XZY6WFRM6MLQCF6NTFD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The zeta function on the critical line: Numerical evidence for moments and random matrix theory models","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andrew M. Odlyzko, Ghaith A. Hiary","submitted_at":"2010-08-12T17:40:20Z","abstract_excerpt":"Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those and competing predictions. It is shown that for high moments and at large heights, the variability of moment values over adjacent intervals is substantial, even when those intervals are long, as long as a block containing 10^9 zeros near zero number 10^23. More than anything else, the variability illustrates the limits of what one can learn about the zeta fu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2173","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":"2026-05-18T04:07:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vxkICY8hQLeqNZFsl6fSsUW+dScs0jOcgfu2MtY3mnWq30y8uwdXFbDtjBTBv729FxjK1I4xDGUYXqEYwo7mCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T11:22:46.833754Z"},"content_sha256":"1ec89b7aaf84061ff4343bb6ecab4b4673da08c96dab07360eaaa6e64f0214b3","schema_version":"1.0","event_id":"sha256:1ec89b7aaf84061ff4343bb6ecab4b4673da08c96dab07360eaaa6e64f0214b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/bundle.json","state_url":"https://pith.science/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/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":"2026-06-27T11:22:46Z","links":{"resolver":"https://pith.science/pith/SZLA72XZY6WFRM6MLQCF6NTFD5","bundle":"https://pith.science/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/bundle.json","state":"https://pith.science/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZLA72XZY6WFRM6MLQCF6NTFD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SZLA72XZY6WFRM6MLQCF6NTFD5","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":"932a5bd1a822149abd1daec7d377da91b472ead259ed839495f5b3ee7c5f8462","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T17:40:20Z","title_canon_sha256":"a6fbd3cff5a69053d94b5607cbf07c4d4801e7ccf6b416c72d367b2cbcf28698"},"schema_version":"1.0","source":{"id":"1008.2173","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.2173","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"arxiv_version","alias_value":"1008.2173v2","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.2173","created_at":"2026-05-18T04:07:54Z"},{"alias_kind":"pith_short_12","alias_value":"SZLA72XZY6WF","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SZLA72XZY6WFRM6M","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SZLA72XZ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:1ec89b7aaf84061ff4343bb6ecab4b4673da08c96dab07360eaaa6e64f0214b3","target":"graph","created_at":"2026-05-18T04:07:54Z","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":"Results of extensive computations of moments of the Riemann zeta function on the critical line are presented. Calculated values are compared with predictions motivated by random matrix theory. The results can help in deciding between those and competing predictions. It is shown that for high moments and at large heights, the variability of moment values over adjacent intervals is substantial, even when those intervals are long, as long as a block containing 10^9 zeros near zero number 10^23. More than anything else, the variability illustrates the limits of what one can learn about the zeta fu","authors_text":"Andrew M. Odlyzko, Ghaith A. Hiary","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T17:40:20Z","title":"The zeta function on the critical line: Numerical evidence for moments and random matrix theory models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2173","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":"sha256:65d0807f537c34ec92ab1d64c945a009fac2d3cb3b602b7d2c65dda74265028b","target":"record","created_at":"2026-05-18T04:07:54Z","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":"932a5bd1a822149abd1daec7d377da91b472ead259ed839495f5b3ee7c5f8462","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.NT","submitted_at":"2010-08-12T17:40:20Z","title_canon_sha256":"a6fbd3cff5a69053d94b5607cbf07c4d4801e7ccf6b416c72d367b2cbcf28698"},"schema_version":"1.0","source":{"id":"1008.2173","kind":"arxiv","version":2}},"canonical_sha256":"96560feaf9c7ac58b3cc5c045f36651f43928596486b84445606b6ebaaff40f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96560feaf9c7ac58b3cc5c045f36651f43928596486b84445606b6ebaaff40f3","first_computed_at":"2026-05-18T04:07:54.283124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:54.283124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vz7c9cB3n10Ra27rAtr5FoLNhNrKKxy0JCO5WBb7/0NqTehGbPws27VzAiTXBbbZAeRNQRXoDPHzYu0VvEHGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:54.283763Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.2173","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65d0807f537c34ec92ab1d64c945a009fac2d3cb3b602b7d2c65dda74265028b","sha256:1ec89b7aaf84061ff4343bb6ecab4b4673da08c96dab07360eaaa6e64f0214b3"],"state_sha256":"b742db615fc9b2adb4350f54e2b158c4a5a15be72312eb5b39ab0b57e4a8343a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQ1veNRhTyOSh13edVGROaVD2vtlMsTPK6AxEm1jrX9+3AHTIIL8sP8OFNofJdvh6eTkzQavYwWtFzE2WDS/CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T11:22:46.835645Z","bundle_sha256":"eb7a00297fbfacaafd71b7dd66002995f18133e594c42ed822b3e9db9d45d3f6"}}