{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:J27ABZQVKVM5DHWAF5X7LNA3CI","short_pith_number":"pith:J27ABZQV","schema_version":"1.0","canonical_sha256":"4ebe00e6155559d19ec02f6ff5b41b1230585b486114b3b6b248cd8fdb04c4ea","source":{"kind":"arxiv","id":"1406.3672","version":3},"attestation_state":"computed","paper":{"title":"Deterministic polynomial factoring under the assumption of the Extended Riemann Hypothesis (ERH)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aurko Roy","submitted_at":"2014-06-14T00:47:14Z","abstract_excerpt":"We consider the problem of deterministically factoring a univariate polynomial over a finite field under the assumption of the Extended Riemann Hypothesis (ERH). This work builds upon the line of approach first explored by Gao in $2001$. The general approach has been to implicitly construct a graph with the roots as vertices and the edges formed by some polynomial time computable relation. The algorithm then fails to factor a polynomial if this associated graph turns out to be \\emph{regular}. In the first part of our work we strengthen the edge relation so that the resulting set of graphs we o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1406.3672","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-14T00:47:14Z","cross_cats_sorted":[],"title_canon_sha256":"335dd53c34a2ed992ca2fc12f5f74c3066c8b1c7e081e3748956759bd12c9956","abstract_canon_sha256":"ed30ab88fb0d49ed799296682a7a7b2b5e183ffc6d13124a04fe0275b18cda37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:21.818104Z","signature_b64":"6XU4Wo87BBBnlt8FccEbl3rxLWu9iZOVffa9nSQgEb0AYGzsJYyP3Arvyua8tiLB3A4u/T9W7Vx3CiL+1FtjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ebe00e6155559d19ec02f6ff5b41b1230585b486114b3b6b248cd8fdb04c4ea","last_reissued_at":"2026-05-18T01:24:21.817481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:21.817481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Deterministic polynomial factoring under the assumption of the Extended Riemann Hypothesis (ERH)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Aurko Roy","submitted_at":"2014-06-14T00:47:14Z","abstract_excerpt":"We consider the problem of deterministically factoring a univariate polynomial over a finite field under the assumption of the Extended Riemann Hypothesis (ERH). This work builds upon the line of approach first explored by Gao in $2001$. The general approach has been to implicitly construct a graph with the roots as vertices and the edges formed by some polynomial time computable relation. The algorithm then fails to factor a polynomial if this associated graph turns out to be \\emph{regular}. In the first part of our work we strengthen the edge relation so that the resulting set of graphs we o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3672","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1406.3672","created_at":"2026-05-18T01:24:21.817583+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.3672v3","created_at":"2026-05-18T01:24:21.817583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3672","created_at":"2026-05-18T01:24:21.817583+00:00"},{"alias_kind":"pith_short_12","alias_value":"J27ABZQVKVM5","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"J27ABZQVKVM5DHWA","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"J27ABZQV","created_at":"2026-05-18T12:28:33.132498+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI","json":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI.json","graph_json":"https://pith.science/api/pith-number/J27ABZQVKVM5DHWAF5X7LNA3CI/graph.json","events_json":"https://pith.science/api/pith-number/J27ABZQVKVM5DHWAF5X7LNA3CI/events.json","paper":"https://pith.science/paper/J27ABZQV"},"agent_actions":{"view_html":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI","download_json":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI.json","view_paper":"https://pith.science/paper/J27ABZQV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.3672&json=true","fetch_graph":"https://pith.science/api/pith-number/J27ABZQVKVM5DHWAF5X7LNA3CI/graph.json","fetch_events":"https://pith.science/api/pith-number/J27ABZQVKVM5DHWAF5X7LNA3CI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI/action/storage_attestation","attest_author":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI/action/author_attestation","sign_citation":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI/action/citation_signature","submit_replication":"https://pith.science/pith/J27ABZQVKVM5DHWAF5X7LNA3CI/action/replication_record"}},"created_at":"2026-05-18T01:24:21.817583+00:00","updated_at":"2026-05-18T01:24:21.817583+00:00"}