{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:ND5ZMXA5RBGBSXPRCVQZQZU4W5","short_pith_number":"pith:ND5ZMXA5","canonical_record":{"source":{"id":"2304.14202","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-04-27T14:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"2d38245e433e1e9222f61b9753d6f0f56ac8c685a74ca0fe822a53bab64f7e03","abstract_canon_sha256":"cf697477af4b10b94d008690ead6c861e735b715bf4d6641c58fe788ee3db702"},"schema_version":"1.0"},"canonical_sha256":"68fb965c1d884c195df1156198669cb74b2af9e50f2244aa66822a6bd6a6576e","source":{"kind":"arxiv","id":"2304.14202","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.14202","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"2304.14202v3","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.14202","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"ND5ZMXA5RBGB","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_16","alias_value":"ND5ZMXA5RBGBSXPR","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_8","alias_value":"ND5ZMXA5","created_at":"2026-06-19T16:09:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:ND5ZMXA5RBGBSXPRCVQZQZU4W5","target":"record","payload":{"canonical_record":{"source":{"id":"2304.14202","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-04-27T14:07:22Z","cross_cats_sorted":[],"title_canon_sha256":"2d38245e433e1e9222f61b9753d6f0f56ac8c685a74ca0fe822a53bab64f7e03","abstract_canon_sha256":"cf697477af4b10b94d008690ead6c861e735b715bf4d6641c58fe788ee3db702"},"schema_version":"1.0"},"canonical_sha256":"68fb965c1d884c195df1156198669cb74b2af9e50f2244aa66822a6bd6a6576e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:09:45.199857Z","signature_b64":"qU9l5t9fFSYUKWSL6LhaZmkrO8mnmKIkCOyQMiG9bOTdxYuLil8vnG/VNAkbUg0pZyxDnwIyvWAaEAEEdz0kDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68fb965c1d884c195df1156198669cb74b2af9e50f2244aa66822a6bd6a6576e","last_reissued_at":"2026-06-19T16:09:45.199433Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:09:45.199433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2304.14202","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":"2026-06-19T16:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eWRu3qnvQQpVWin38wmD+MlnB6sXJ/6PLdF+6AGX311d10qW3b6va5/mMHgjuaL0Td/2rv2x/aQbRiKOyMOgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:15:44.935098Z"},"content_sha256":"5d14c3c578e66d48849bd5f2d456195d7cc01c5fffa7e6abca16f255195706cd","schema_version":"1.0","event_id":"sha256:5d14c3c578e66d48849bd5f2d456195d7cc01c5fffa7e6abca16f255195706cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:ND5ZMXA5RBGBSXPRCVQZQZU4W5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Explicit non-Poissonian Pair Correlation Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christian Wei{\\ss}","submitted_at":"2023-04-27T14:07:22Z","abstract_excerpt":"A generic uniformly distributed random sequence on the unit interval has Poissonian pair correlations. Usually, the pair correlations statistic is therefore studied for equidistributed sequences. At the same time, there are only very few explicitly known examples of sequences with this property and many types of deterministic sequences have been proven to fail having the Poissonian pair correlation property. In this paper we study the pair correlation statistic in the non-uniform case and analyze the first elementary example of such a sequence, namely $x_n := \\left\\{ \\frac{\\log(2n-1)}{\\log(2)}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.14202","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/2304.14202/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":"2026-06-19T16:09:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7xGUoB6qY+BBp7qTyud2WWBoWWFy5TR7Jftcz5L90uq845wwkaIlKpXrSyL+Wj3ZOWilje3cuUw4mGC/Gf+5Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T23:15:44.935479Z"},"content_sha256":"a0817b718f107950ed01cc0f27e14443c3762f7545d8f556179d70c14a089ed4","schema_version":"1.0","event_id":"sha256:a0817b718f107950ed01cc0f27e14443c3762f7545d8f556179d70c14a089ed4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/bundle.json","state_url":"https://pith.science/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/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":"2026-07-04T23:15:44Z","links":{"resolver":"https://pith.science/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5","bundle":"https://pith.science/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/bundle.json","state":"https://pith.science/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ND5ZMXA5RBGBSXPRCVQZQZU4W5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:ND5ZMXA5RBGBSXPRCVQZQZU4W5","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":"cf697477af4b10b94d008690ead6c861e735b715bf4d6641c58fe788ee3db702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-04-27T14:07:22Z","title_canon_sha256":"2d38245e433e1e9222f61b9753d6f0f56ac8c685a74ca0fe822a53bab64f7e03"},"schema_version":"1.0","source":{"id":"2304.14202","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2304.14202","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"2304.14202v3","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2304.14202","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"ND5ZMXA5RBGB","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_16","alias_value":"ND5ZMXA5RBGBSXPR","created_at":"2026-06-19T16:09:45Z"},{"alias_kind":"pith_short_8","alias_value":"ND5ZMXA5","created_at":"2026-06-19T16:09:45Z"}],"graph_snapshots":[{"event_id":"sha256:a0817b718f107950ed01cc0f27e14443c3762f7545d8f556179d70c14a089ed4","target":"graph","created_at":"2026-06-19T16:09:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2304.14202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A generic uniformly distributed random sequence on the unit interval has Poissonian pair correlations. Usually, the pair correlations statistic is therefore studied for equidistributed sequences. At the same time, there are only very few explicitly known examples of sequences with this property and many types of deterministic sequences have been proven to fail having the Poissonian pair correlation property. In this paper we study the pair correlation statistic in the non-uniform case and analyze the first elementary example of such a sequence, namely $x_n := \\left\\{ \\frac{\\log(2n-1)}{\\log(2)}","authors_text":"Christian Wei{\\ss}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-04-27T14:07:22Z","title":"An Explicit non-Poissonian Pair Correlation Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2304.14202","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":"sha256:5d14c3c578e66d48849bd5f2d456195d7cc01c5fffa7e6abca16f255195706cd","target":"record","created_at":"2026-06-19T16:09:45Z","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":"cf697477af4b10b94d008690ead6c861e735b715bf4d6641c58fe788ee3db702","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2023-04-27T14:07:22Z","title_canon_sha256":"2d38245e433e1e9222f61b9753d6f0f56ac8c685a74ca0fe822a53bab64f7e03"},"schema_version":"1.0","source":{"id":"2304.14202","kind":"arxiv","version":3}},"canonical_sha256":"68fb965c1d884c195df1156198669cb74b2af9e50f2244aa66822a6bd6a6576e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68fb965c1d884c195df1156198669cb74b2af9e50f2244aa66822a6bd6a6576e","first_computed_at":"2026-06-19T16:09:45.199433Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:09:45.199433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qU9l5t9fFSYUKWSL6LhaZmkrO8mnmKIkCOyQMiG9bOTdxYuLil8vnG/VNAkbUg0pZyxDnwIyvWAaEAEEdz0kDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:09:45.199857Z","signed_message":"canonical_sha256_bytes"},"source_id":"2304.14202","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d14c3c578e66d48849bd5f2d456195d7cc01c5fffa7e6abca16f255195706cd","sha256:a0817b718f107950ed01cc0f27e14443c3762f7545d8f556179d70c14a089ed4"],"state_sha256":"d8dd0ef5a260eae87d0f93509e77df337e014781177a2bddf60d4eaf179b06dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2D2uRVZ+9tPkZYiqKhs4RbJ7XB4kxGTeE6fYsZEbw3Rkyu6qKKzkOyq59weIHIkxh+YeDz8N/IiR+liEpJIeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T23:15:44.937512Z","bundle_sha256":"caaf54ddf21351ba2056c93f3087df1f15fb953ac726a68c068f406ef57b2af5"}}