{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HGJIWFYJM5STLEBUM3Z72IIXFL","short_pith_number":"pith:HGJIWFYJ","canonical_record":{"source":{"id":"2407.13124","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-07-18T03:25:55Z","cross_cats_sorted":["math.MP","math.NT"],"title_canon_sha256":"49782d9392540349870167428a0a9291ce9b5def85e41a2519a45f7345c533c6","abstract_canon_sha256":"ad5b8e88a043f6fce2c60db488cb3fe5b1ca5624e17e5aa2307dc8bb6f9aa122"},"schema_version":"1.0"},"canonical_sha256":"39928b1709676535903466f3fd21172ac5645492e4bc77568050e4c803e43018","source":{"kind":"arxiv","id":"2407.13124","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.13124","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"2407.13124v3","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.13124","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"HGJIWFYJM5ST","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_16","alias_value":"HGJIWFYJM5STLEBU","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_8","alias_value":"HGJIWFYJ","created_at":"2026-07-05T10:43:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HGJIWFYJM5STLEBUM3Z72IIXFL","target":"record","payload":{"canonical_record":{"source":{"id":"2407.13124","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-07-18T03:25:55Z","cross_cats_sorted":["math.MP","math.NT"],"title_canon_sha256":"49782d9392540349870167428a0a9291ce9b5def85e41a2519a45f7345c533c6","abstract_canon_sha256":"ad5b8e88a043f6fce2c60db488cb3fe5b1ca5624e17e5aa2307dc8bb6f9aa122"},"schema_version":"1.0"},"canonical_sha256":"39928b1709676535903466f3fd21172ac5645492e4bc77568050e4c803e43018","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:43:36.960439Z","signature_b64":"AemNtmEHDy+uCtujqZghuuV4mKwfe7XRG9yZDK4qiMYweCJiriOwGDQRQEXYXhy8jUEp5U1XD4v/A+uuDxdKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39928b1709676535903466f3fd21172ac5645492e4bc77568050e4c803e43018","last_reissued_at":"2026-07-05T10:43:36.959910Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:43:36.959910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.13124","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJbuN7RNC8LsTXR0a0RoOk5b9vS18nfi1UlMLkYDeyQXjV5q+rUKtLQWPCTMLtPIqYIKwChakOp5bKBDB54gBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:05:11.583888Z"},"content_sha256":"0d5e64ade40bb7893d49ebf6ec8187c4fd2198870413d19d7615706258cb3b1f","schema_version":"1.0","event_id":"sha256:0d5e64ade40bb7893d49ebf6ec8187c4fd2198870413d19d7615706258cb3b1f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HGJIWFYJM5STLEBUM3Z72IIXFL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Moments of the derivative of the characteristic polynomial of unitary matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NT"],"primary_cat":"math-ph","authors_text":"Brian Conrey, Emilia Alvarez, Michael O. Rubinstein, Nina C. Snaith","submitted_at":"2024-07-18T03:25:55Z","abstract_excerpt":"Let $\\Lambda_X(s)=\\det(I-sX^{\\dagger})$ be the characteristic polynomial of a Haar distributed unitary matrix $X$. It is believed that the distribution of values of $\\Lambda_X(s)$ model the distribution of values of the Riemann zeta-function $\\zeta(s)$. This principle motivates many avenues of study. Of particular interest is the behavior of $\\Lambda_X'(s)$ and the distribution of its zeros (all of which lie inside or on the unit circle). In this article we present several identities for the moments of $\\Lambda_X'(s)$ averaged over $U(N)$, for $s \\in \\mathbb{C}$ as well as specialized to $|s|="},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13124","kind":"arxiv","version":3},"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/2407.13124/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":"2026-07-05T10:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OfIQGTz2xshWb6lBoHGw+pnfr5e1orBjOrlxcqremCQy5+SznkjbfJMfOlPDIlVzX2BCYk8Q9n1iV8YtQrnaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:05:11.584480Z"},"content_sha256":"f992714cb2b302c33422b2f0e0a9dcf32605602521ae91b87b5ff10e43f9a167","schema_version":"1.0","event_id":"sha256:f992714cb2b302c33422b2f0e0a9dcf32605602521ae91b87b5ff10e43f9a167"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/bundle.json","state_url":"https://pith.science/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/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":"2026-08-03T22:05:11Z","links":{"resolver":"https://pith.science/pith/HGJIWFYJM5STLEBUM3Z72IIXFL","bundle":"https://pith.science/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/bundle.json","state":"https://pith.science/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGJIWFYJM5STLEBUM3Z72IIXFL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HGJIWFYJM5STLEBUM3Z72IIXFL","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":"ad5b8e88a043f6fce2c60db488cb3fe5b1ca5624e17e5aa2307dc8bb6f9aa122","cross_cats_sorted":["math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-07-18T03:25:55Z","title_canon_sha256":"49782d9392540349870167428a0a9291ce9b5def85e41a2519a45f7345c533c6"},"schema_version":"1.0","source":{"id":"2407.13124","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.13124","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"2407.13124v3","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.13124","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"HGJIWFYJM5ST","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_16","alias_value":"HGJIWFYJM5STLEBU","created_at":"2026-07-05T10:43:36Z"},{"alias_kind":"pith_short_8","alias_value":"HGJIWFYJ","created_at":"2026-07-05T10:43:36Z"}],"graph_snapshots":[{"event_id":"sha256:f992714cb2b302c33422b2f0e0a9dcf32605602521ae91b87b5ff10e43f9a167","target":"graph","created_at":"2026-07-05T10:43:36Z","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/2407.13124/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\Lambda_X(s)=\\det(I-sX^{\\dagger})$ be the characteristic polynomial of a Haar distributed unitary matrix $X$. It is believed that the distribution of values of $\\Lambda_X(s)$ model the distribution of values of the Riemann zeta-function $\\zeta(s)$. This principle motivates many avenues of study. Of particular interest is the behavior of $\\Lambda_X'(s)$ and the distribution of its zeros (all of which lie inside or on the unit circle). In this article we present several identities for the moments of $\\Lambda_X'(s)$ averaged over $U(N)$, for $s \\in \\mathbb{C}$ as well as specialized to $|s|=","authors_text":"Brian Conrey, Emilia Alvarez, Michael O. Rubinstein, Nina C. Snaith","cross_cats":["math.MP","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-07-18T03:25:55Z","title":"Moments of the derivative of the characteristic polynomial of unitary matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.13124","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":"sha256:0d5e64ade40bb7893d49ebf6ec8187c4fd2198870413d19d7615706258cb3b1f","target":"record","created_at":"2026-07-05T10:43:36Z","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":"ad5b8e88a043f6fce2c60db488cb3fe5b1ca5624e17e5aa2307dc8bb6f9aa122","cross_cats_sorted":["math.MP","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-07-18T03:25:55Z","title_canon_sha256":"49782d9392540349870167428a0a9291ce9b5def85e41a2519a45f7345c533c6"},"schema_version":"1.0","source":{"id":"2407.13124","kind":"arxiv","version":3}},"canonical_sha256":"39928b1709676535903466f3fd21172ac5645492e4bc77568050e4c803e43018","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39928b1709676535903466f3fd21172ac5645492e4bc77568050e4c803e43018","first_computed_at":"2026-07-05T10:43:36.959910Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:43:36.959910Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AemNtmEHDy+uCtujqZghuuV4mKwfe7XRG9yZDK4qiMYweCJiriOwGDQRQEXYXhy8jUEp5U1XD4v/A+uuDxdKBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:43:36.960439Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.13124","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d5e64ade40bb7893d49ebf6ec8187c4fd2198870413d19d7615706258cb3b1f","sha256:f992714cb2b302c33422b2f0e0a9dcf32605602521ae91b87b5ff10e43f9a167"],"state_sha256":"3fb7d4da54066298758646d0cfb38345767e377fa8c53835c79637f07da516d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"disq/APmfe71Ou8hRYWaBXnbYvTdNOpRR7FwzpDvjlqm5RE/DjeCvFsGbGcUCWp+s0m1QbitIMpuX64no5GCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:05:11.587850Z","bundle_sha256":"cb8cf31d6a75e7b3b321846e6ffe0d4ac459323df1ab56805c1f13d3e4b73ab6"}}