{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:W2RCNSNXOMY5C6BDI2X32TCADB","short_pith_number":"pith:W2RCNSNX","canonical_record":{"source":{"id":"1504.03444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-14T07:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"84ee438bcbad5a54da7a9ed0510b9535d120771333ba7b7dd56364443c829189","abstract_canon_sha256":"f4a437bf0ce4b80dead67e3c80c1d896d7f75513ea6497d358dc443bfb5f8a7f"},"schema_version":"1.0"},"canonical_sha256":"b6a226c9b77331d1782346afbd4c4018576023152bf6f04c73edf31eb09b6a56","source":{"kind":"arxiv","id":"1504.03444","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03444","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03444v2","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03444","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"W2RCNSNXOMY5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W2RCNSNXOMY5C6BD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W2RCNSNX","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:W2RCNSNXOMY5C6BDI2X32TCADB","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03444","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-14T07:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"84ee438bcbad5a54da7a9ed0510b9535d120771333ba7b7dd56364443c829189","abstract_canon_sha256":"f4a437bf0ce4b80dead67e3c80c1d896d7f75513ea6497d358dc443bfb5f8a7f"},"schema_version":"1.0"},"canonical_sha256":"b6a226c9b77331d1782346afbd4c4018576023152bf6f04c73edf31eb09b6a56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:09.902632Z","signature_b64":"PVVnu9qzq47z37BXziXQVJqWZxM7ugB4eZtnffVhOkZPZrp/5SwgoMsHfdk9Rmrcg1PiZ3Q/ekuqBOkmzXw5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6a226c9b77331d1782346afbd4c4018576023152bf6f04c73edf31eb09b6a56","last_reissued_at":"2026-05-18T01:18:09.902065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:09.902065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03444","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":"2026-05-18T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZzMU674e4Z39Ww3Cy1lnKhLmVKoAj1Rs5D4DOzkRTF9rQC9QocdQ6uiOTlnbFZrWs6XeGouad1znBhLjTgSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:15:42.199931Z"},"content_sha256":"fd96334f59cdecce2084ee0329ace1734cdcf905f2193804ddd0f47c2b151190","schema_version":"1.0","event_id":"sha256:fd96334f59cdecce2084ee0329ace1734cdcf905f2193804ddd0f47c2b151190"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:W2RCNSNXOMY5C6BDI2X32TCADB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Squarefree polynomials and Mobius values in short intervals and arithmetic progressions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"J.P. Keating, Z. Rudnick","submitted_at":"2015-04-14T07:49:51Z","abstract_excerpt":"We calculate the mean and variance of sums of the M\\\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$ elements, in the limit $q\\to \\infty$. We do this by relating the sums in question to certain matrix integrals over the unitary group, using recent equidistribution results due to N. Katz, and then by evaluating these integrals. In many cases our results mirror what is either known or conjectured for the corresponding problems involving sums over the integers, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03444","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":"2026-05-18T01:18:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hf9+n0jHWFGRlXU1iFJXZOImjsA/wwK+sqsJ69ubdFxeVbmMeChwmgCygBkm5lO9YQ2KE14zBfKD49wrIO21Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T17:15:42.200646Z"},"content_sha256":"650c07ad384c77c58b71c43b971ec5d3d974574dcdd942be206f5e8d8e8c4c4e","schema_version":"1.0","event_id":"sha256:650c07ad384c77c58b71c43b971ec5d3d974574dcdd942be206f5e8d8e8c4c4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2RCNSNXOMY5C6BDI2X32TCADB/bundle.json","state_url":"https://pith.science/pith/W2RCNSNXOMY5C6BDI2X32TCADB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2RCNSNXOMY5C6BDI2X32TCADB/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":"2026-06-09T17:15:42Z","links":{"resolver":"https://pith.science/pith/W2RCNSNXOMY5C6BDI2X32TCADB","bundle":"https://pith.science/pith/W2RCNSNXOMY5C6BDI2X32TCADB/bundle.json","state":"https://pith.science/pith/W2RCNSNXOMY5C6BDI2X32TCADB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2RCNSNXOMY5C6BDI2X32TCADB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W2RCNSNXOMY5C6BDI2X32TCADB","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":"f4a437bf0ce4b80dead67e3c80c1d896d7f75513ea6497d358dc443bfb5f8a7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-14T07:49:51Z","title_canon_sha256":"84ee438bcbad5a54da7a9ed0510b9535d120771333ba7b7dd56364443c829189"},"schema_version":"1.0","source":{"id":"1504.03444","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03444","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03444v2","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03444","created_at":"2026-05-18T01:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"W2RCNSNXOMY5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W2RCNSNXOMY5C6BD","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W2RCNSNX","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:650c07ad384c77c58b71c43b971ec5d3d974574dcdd942be206f5e8d8e8c4c4e","target":"graph","created_at":"2026-05-18T01:18:09Z","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 calculate the mean and variance of sums of the M\\\"obius function and the indicator function of the squarefrees, in both short intervals and arithmetic progressions, in the context of the ring of polynomials over a finite field of $q$ elements, in the limit $q\\to \\infty$. We do this by relating the sums in question to certain matrix integrals over the unitary group, using recent equidistribution results due to N. Katz, and then by evaluating these integrals. In many cases our results mirror what is either known or conjectured for the corresponding problems involving sums over the integers, w","authors_text":"J.P. Keating, Z. Rudnick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-14T07:49:51Z","title":"Squarefree polynomials and Mobius values in short intervals and arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03444","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:fd96334f59cdecce2084ee0329ace1734cdcf905f2193804ddd0f47c2b151190","target":"record","created_at":"2026-05-18T01:18:09Z","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":"f4a437bf0ce4b80dead67e3c80c1d896d7f75513ea6497d358dc443bfb5f8a7f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-14T07:49:51Z","title_canon_sha256":"84ee438bcbad5a54da7a9ed0510b9535d120771333ba7b7dd56364443c829189"},"schema_version":"1.0","source":{"id":"1504.03444","kind":"arxiv","version":2}},"canonical_sha256":"b6a226c9b77331d1782346afbd4c4018576023152bf6f04c73edf31eb09b6a56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6a226c9b77331d1782346afbd4c4018576023152bf6f04c73edf31eb09b6a56","first_computed_at":"2026-05-18T01:18:09.902065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:09.902065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PVVnu9qzq47z37BXziXQVJqWZxM7ugB4eZtnffVhOkZPZrp/5SwgoMsHfdk9Rmrcg1PiZ3Q/ekuqBOkmzXw5Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:09.902632Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03444","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd96334f59cdecce2084ee0329ace1734cdcf905f2193804ddd0f47c2b151190","sha256:650c07ad384c77c58b71c43b971ec5d3d974574dcdd942be206f5e8d8e8c4c4e"],"state_sha256":"27b08bc2e7490abe6857bbf4ba36b0468f0124abb08d9b444935e08a078e7c7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yNL381m/66GpApqqDDl3TZ1tuTdB5uVook9fFI9qtu0gRGZcMzkW3P5Rn1pqpNZaW63+SMgdyfUa45pyHhasBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T17:15:42.204657Z","bundle_sha256":"a2a7e01e957bf234ab706cb41f766db25911fe7d32deb14cc10812c2fc870ac9"}}