{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIWV2HSSJNVXCHOL26YZ6HUOJA","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":"1a42c029ec8dd3abbaae25754d38b7b01edb173b0447fb2aaff28beefb6604b6","cross_cats_sorted":["cs.CC","cs.DS","cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T21:09:01Z","title_canon_sha256":"0db6be640a5f52ec1292e5a062e60c88235e3238d046ce5f0b40baa3ed78bd79"},"schema_version":"1.0","source":{"id":"1606.00898","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.00898","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.00898v1","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00898","created_at":"2026-05-18T01:13:00Z"},{"alias_kind":"pith_short_12","alias_value":"TIWV2HSSJNVX","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIWV2HSSJNVXCHOL","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIWV2HSS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:99e52e528d81552edd18aad4922c69346f4ce201ecc657210cfa32cadc3970ce","target":"graph","created_at":"2026-05-18T01:13:00Z","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 present novel algorithms to factor polynomials over a finite field $\\F_q$ of odd characteristic using rank $2$ Drinfeld modules with complex multiplication. The main idea is to compute a lift of the Hasse invariant (modulo the polynomial $f(x) \\in \\F_q[x]$ to be factored) with respect to a Drinfeld module $\\phi$ with complex multiplication. Factors of $f(x)$ supported on prime ideals with supersingular reduction at $\\phi$ have vanishing Hasse invariant and can be separated from the rest. A Drinfeld module analogue of Deligne's congruence plays a key role in computing the Hasse invariant lif","authors_text":"Anand Kumar Narayanan","cross_cats":["cs.CC","cs.DS","cs.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T21:09:01Z","title":"Factoring Polynomials over Finite Fields using Drinfeld Modules with Complex Multiplication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00898","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":"sha256:844c063b4be20440e5211b7e2bb6d9a1d9051e3fbdb5e8ae5c6dd450314eab27","target":"record","created_at":"2026-05-18T01:13:00Z","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":"1a42c029ec8dd3abbaae25754d38b7b01edb173b0447fb2aaff28beefb6604b6","cross_cats_sorted":["cs.CC","cs.DS","cs.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-06-02T21:09:01Z","title_canon_sha256":"0db6be640a5f52ec1292e5a062e60c88235e3238d046ce5f0b40baa3ed78bd79"},"schema_version":"1.0","source":{"id":"1606.00898","kind":"arxiv","version":1}},"canonical_sha256":"9a2d5d1e524b6b711dcbd7b19f1e8e4834a8deb89d8ad8323ae985c4d5d90460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a2d5d1e524b6b711dcbd7b19f1e8e4834a8deb89d8ad8323ae985c4d5d90460","first_computed_at":"2026-05-18T01:13:00.098781Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:00.098781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mBte4bBjVrIbCD2IGA6U+FEiPkzeScblTaTLqTJmNl+dUnRVgMOZ2juDPFfdcpJA7SyXXzwyM5aLlH6RZZ7yDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:00.099150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.00898","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:844c063b4be20440e5211b7e2bb6d9a1d9051e3fbdb5e8ae5c6dd450314eab27","sha256:99e52e528d81552edd18aad4922c69346f4ce201ecc657210cfa32cadc3970ce"],"state_sha256":"f435a67536b890e80923c6437bf68bd7ecc213edd8204e490be8d2ed7f0d159a"}