{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KO3EP4E7FPYZLBBJL57IER6FIU","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":"4a2cc86197e2df02d5213d81f233567189c761130bd4c1c091c1963a86491c13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-15T22:21:14Z","title_canon_sha256":"4bc5d15855aaf109b1b8fb23cf371e0be670d47425e2e6f20ce3308e06c0b56c"},"schema_version":"1.0","source":{"id":"1903.06823","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.06823","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"arxiv_version","alias_value":"1903.06823v1","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.06823","created_at":"2026-05-17T23:51:08Z"},{"alias_kind":"pith_short_12","alias_value":"KO3EP4E7FPYZ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KO3EP4E7FPYZLBBJ","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KO3EP4E7","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:6aae7c25b35b3d8b2aed699f62d6dee1220fd4c223acce6bacb2989ceb51ab11","target":"graph","created_at":"2026-05-17T23:51:08Z","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":"Monier and Rabin proved that an odd composite can pass the Strong Probable Prime Test for at most $\\frac 14$ of the possible bases. In this paper, a probable prime test is developed using quadratic polynomials and the Frobenius automorphism. The test, along with a fixed number of trial divisions, ensures that a composite $n$ will pass for less than $\\frac 1{7710}$ of the polynomials $x^2-bx-c$ with $\\left(b^2+4c\\over n\\right)=-1$ and $\\left(-c\\over n\\right)=1$. The running time of the test is asymptotically $3$ times that of the Strong Probable Prime Test.","authors_text":"Jon Grantham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-15T22:21:14Z","title":"A Probable Prime Test With High Confidence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.06823","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":"sha256:87e98d544b128f09b64fc653c7024127835e6e93036b84a3a8d6d9227c1c5830","target":"record","created_at":"2026-05-17T23:51:08Z","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":"4a2cc86197e2df02d5213d81f233567189c761130bd4c1c091c1963a86491c13","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-15T22:21:14Z","title_canon_sha256":"4bc5d15855aaf109b1b8fb23cf371e0be670d47425e2e6f20ce3308e06c0b56c"},"schema_version":"1.0","source":{"id":"1903.06823","kind":"arxiv","version":1}},"canonical_sha256":"53b647f09f2bf19584295f7e8247c5450e3c58ee5357875c8a89000ca2642cde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"53b647f09f2bf19584295f7e8247c5450e3c58ee5357875c8a89000ca2642cde","first_computed_at":"2026-05-17T23:51:08.926420Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:08.926420Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S9mPP1ABNOFrTj7SMZTw3HOQ94e7F7ZKbDCj3MWpPKFoNbqCP3jFt+Zps6sj1akHGdR5Ghgq67EbqJ8fPpIwDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:08.927030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.06823","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87e98d544b128f09b64fc653c7024127835e6e93036b84a3a8d6d9227c1c5830","sha256:6aae7c25b35b3d8b2aed699f62d6dee1220fd4c223acce6bacb2989ceb51ab11"],"state_sha256":"e8127191afd2976801d4d2552f8a474304e4dcf000eb0a29b8572984f338526c"}