{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:QDRXIFDR5NKP4SDY7DT5WWPMCQ","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":"2622c61f94efd42a92a207c8dd28550e16bdc46a7ef816119d1f57e2fe855b60","cross_cats_sorted":["math.CO","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-28T13:47:16Z","title_canon_sha256":"af3fb129bc206592c6a261ad4ee023c2d6b1e7ba1ac9f500c514985cd85dcf7b"},"schema_version":"1.0","source":{"id":"2308.14580","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.14580","created_at":"2026-07-05T11:44:38Z"},{"alias_kind":"arxiv_version","alias_value":"2308.14580v1","created_at":"2026-07-05T11:44:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.14580","created_at":"2026-07-05T11:44:38Z"},{"alias_kind":"pith_short_12","alias_value":"QDRXIFDR5NKP","created_at":"2026-07-05T11:44:38Z"},{"alias_kind":"pith_short_16","alias_value":"QDRXIFDR5NKP4SDY","created_at":"2026-07-05T11:44:38Z"},{"alias_kind":"pith_short_8","alias_value":"QDRXIFDR","created_at":"2026-07-05T11:44:38Z"}],"graph_snapshots":[{"event_id":"sha256:02e1ec58f3d7dd3a3abb8f1fc02ae79d00f45a8a07319d7725a207d92bb98e7f","target":"graph","created_at":"2026-07-05T11:44:38Z","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/2308.14580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the probability distribution of the number of zeros of multivariable polynomials with bounded degree over a finite field. We find the probability generating function for each set of bounded degree polynomials. In particular, in the single variable case, we show that as the degree of the polynomials and the order of the field simultaneously approach infinity, the distribution converges to a Poisson distribution.","authors_text":"Han-Bom Moon, Peter Wu, Ritik Jain","cross_cats":["math.CO","math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-28T13:47:16Z","title":"Distribution of the number of zeros of polynomials over a finite field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.14580","kind":"arxiv","version":1},"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:f380bad54a90595481cb38307fb3efc8aefb267d502136d68b86ebb77dba76d4","target":"record","created_at":"2026-07-05T11:44:38Z","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":"2622c61f94efd42a92a207c8dd28550e16bdc46a7ef816119d1f57e2fe855b60","cross_cats_sorted":["math.CO","math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-28T13:47:16Z","title_canon_sha256":"af3fb129bc206592c6a261ad4ee023c2d6b1e7ba1ac9f500c514985cd85dcf7b"},"schema_version":"1.0","source":{"id":"2308.14580","kind":"arxiv","version":1}},"canonical_sha256":"80e3741471eb54fe4878f8e7db59ec14082dac2109b561c02c27768e815a9608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e3741471eb54fe4878f8e7db59ec14082dac2109b561c02c27768e815a9608","first_computed_at":"2026-07-05T11:44:38.316585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:38.316585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJBZX4xfCEwmq2hWpmJwMy0UzjkwXT+JpSIoIfZCCAlBg1I4x+NxbxuaNQcqFMXrRWfUMfdXIvjLZPvBv5FVDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:38.317133Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.14580","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f380bad54a90595481cb38307fb3efc8aefb267d502136d68b86ebb77dba76d4","sha256:02e1ec58f3d7dd3a3abb8f1fc02ae79d00f45a8a07319d7725a207d92bb98e7f"],"state_sha256":"d735daf8f00447d744425bfb9ab8665f06aea2e8de9d0e56c3740d3fc4f94439"}