{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:7UMMA3JBMMILLAIINEXT32MTB3","short_pith_number":"pith:7UMMA3JB","canonical_record":{"source":{"id":"2207.00047","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-06-30T18:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"3ee80b0ac330123ad62ea021bc343eee83ab57d5379a914f09511c788353d47e","abstract_canon_sha256":"911744d06927fe20e97b4cf0eaf5772fcb9d993176049c5d188175ea226ca45e"},"schema_version":"1.0"},"canonical_sha256":"fd18c06d216310b58108692f3de9930effb86f1c2488319bfdaef6064c27a57e","source":{"kind":"arxiv","id":"2207.00047","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.00047","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"2207.00047v3","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.00047","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"7UMMA3JBMMIL","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_16","alias_value":"7UMMA3JBMMILLAII","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_8","alias_value":"7UMMA3JB","created_at":"2026-07-05T06:34:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:7UMMA3JBMMILLAIINEXT32MTB3","target":"record","payload":{"canonical_record":{"source":{"id":"2207.00047","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-06-30T18:26:08Z","cross_cats_sorted":[],"title_canon_sha256":"3ee80b0ac330123ad62ea021bc343eee83ab57d5379a914f09511c788353d47e","abstract_canon_sha256":"911744d06927fe20e97b4cf0eaf5772fcb9d993176049c5d188175ea226ca45e"},"schema_version":"1.0"},"canonical_sha256":"fd18c06d216310b58108692f3de9930effb86f1c2488319bfdaef6064c27a57e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:34:45.245518Z","signature_b64":"lVd658l8a+7C6UsrxJPzJSMkxTZV9kk+nlu+dastHYmasLlO/pKGhJn34UkB3h9+vxHytT3ZUXxz4VTjjZvLCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd18c06d216310b58108692f3de9930effb86f1c2488319bfdaef6064c27a57e","last_reissued_at":"2026-07-05T06:34:45.244949Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:34:45.244949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.00047","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":"2026-07-05T06:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eX7FTB8t9N0I28sAe59AYmZORdE9bRtxg+ov8rijBC/0gD/fBNEVbMraco3z+8ZReDRR5Uyt1rEnm/bLybwMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:29:18.648841Z"},"content_sha256":"48060b2df6464fb5c7386031ffcc3048690e1a82e7c49a27b7c007f88d1deb14","schema_version":"1.0","event_id":"sha256:48060b2df6464fb5c7386031ffcc3048690e1a82e7c49a27b7c007f88d1deb14"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:7UMMA3JBMMILLAIINEXT32MTB3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Distribution of $k$-Free Effective Divisors and the Summatory Totient Function in Function Fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Hamilton Wan, Hannah Lang, Nancy Xu, Sanjana Das","submitted_at":"2022-06-30T18:26:08Z","abstract_excerpt":"Motivated by the study of the summatory $k$-free indicator and totient functions in the classical setting, we investigate their function field analogues. First, we derive an expression for the error terms of the summatory functions in terms of the zeros of the associated zeta function. Under the Linear Independence hypothesis, we explicitly construct the limiting distributions of these error terms and compute the frequency with which they occur in an interval $[-\\beta, \\beta]$ for a real $\\beta > 0$. We also show that these error terms are unbiased, that is, they are positive and negative equa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.00047","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/2207.00047/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":"2026-07-05T06:34:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rrAJUB+UiXVFNGRZF86WAiz/yCqkB9lLQXOuRQft/SPQrqX8DSbyL54+Jt2Bo0bWGSPta+xlGN3HtdoBchS8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T03:29:18.649230Z"},"content_sha256":"369851abd6c5b23d5b67e96c03baac81adee9c84afcaaa69bcb517a2b3dddde8","schema_version":"1.0","event_id":"sha256:369851abd6c5b23d5b67e96c03baac81adee9c84afcaaa69bcb517a2b3dddde8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UMMA3JBMMILLAIINEXT32MTB3/bundle.json","state_url":"https://pith.science/pith/7UMMA3JBMMILLAIINEXT32MTB3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UMMA3JBMMILLAIINEXT32MTB3/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":"2026-08-18T03:29:18Z","links":{"resolver":"https://pith.science/pith/7UMMA3JBMMILLAIINEXT32MTB3","bundle":"https://pith.science/pith/7UMMA3JBMMILLAIINEXT32MTB3/bundle.json","state":"https://pith.science/pith/7UMMA3JBMMILLAIINEXT32MTB3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UMMA3JBMMILLAIINEXT32MTB3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7UMMA3JBMMILLAIINEXT32MTB3","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":"911744d06927fe20e97b4cf0eaf5772fcb9d993176049c5d188175ea226ca45e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-06-30T18:26:08Z","title_canon_sha256":"3ee80b0ac330123ad62ea021bc343eee83ab57d5379a914f09511c788353d47e"},"schema_version":"1.0","source":{"id":"2207.00047","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.00047","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"arxiv_version","alias_value":"2207.00047v3","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.00047","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_12","alias_value":"7UMMA3JBMMIL","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_16","alias_value":"7UMMA3JBMMILLAII","created_at":"2026-07-05T06:34:45Z"},{"alias_kind":"pith_short_8","alias_value":"7UMMA3JB","created_at":"2026-07-05T06:34:45Z"}],"graph_snapshots":[{"event_id":"sha256:369851abd6c5b23d5b67e96c03baac81adee9c84afcaaa69bcb517a2b3dddde8","target":"graph","created_at":"2026-07-05T06:34:45Z","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/2207.00047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the study of the summatory $k$-free indicator and totient functions in the classical setting, we investigate their function field analogues. First, we derive an expression for the error terms of the summatory functions in terms of the zeros of the associated zeta function. Under the Linear Independence hypothesis, we explicitly construct the limiting distributions of these error terms and compute the frequency with which they occur in an interval $[-\\beta, \\beta]$ for a real $\\beta > 0$. We also show that these error terms are unbiased, that is, they are positive and negative equa","authors_text":"Hamilton Wan, Hannah Lang, Nancy Xu, Sanjana Das","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-06-30T18:26:08Z","title":"The Distribution of $k$-Free Effective Divisors and the Summatory Totient Function in Function Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.00047","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":"sha256:48060b2df6464fb5c7386031ffcc3048690e1a82e7c49a27b7c007f88d1deb14","target":"record","created_at":"2026-07-05T06:34:45Z","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":"911744d06927fe20e97b4cf0eaf5772fcb9d993176049c5d188175ea226ca45e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2022-06-30T18:26:08Z","title_canon_sha256":"3ee80b0ac330123ad62ea021bc343eee83ab57d5379a914f09511c788353d47e"},"schema_version":"1.0","source":{"id":"2207.00047","kind":"arxiv","version":3}},"canonical_sha256":"fd18c06d216310b58108692f3de9930effb86f1c2488319bfdaef6064c27a57e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd18c06d216310b58108692f3de9930effb86f1c2488319bfdaef6064c27a57e","first_computed_at":"2026-07-05T06:34:45.244949Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:34:45.244949Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lVd658l8a+7C6UsrxJPzJSMkxTZV9kk+nlu+dastHYmasLlO/pKGhJn34UkB3h9+vxHytT3ZUXxz4VTjjZvLCA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:34:45.245518Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.00047","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:48060b2df6464fb5c7386031ffcc3048690e1a82e7c49a27b7c007f88d1deb14","sha256:369851abd6c5b23d5b67e96c03baac81adee9c84afcaaa69bcb517a2b3dddde8"],"state_sha256":"9b3774340013fb14127afe57a090cd6620b35966efafd427cb6d308df7c9df77"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s+9lksAAnmqiT7hPGB3h+eWpR/T0o23TEsGf0D+xFREwM3m2bR3C0p2vy4MCfykdpPk10I5rt4wyBV0ZkitDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T03:29:18.651636Z","bundle_sha256":"3c58cfca403eb316164cfdfaadd34bb142c35b59ce1131530c6cfa37bd601ff9"}}