{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:FNJL544IZAGCJQVEU4V3YYBA3I","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":"ab0bc8eb14b098c9763d09da785f31b5a713132dc876ed3797fea0ed8061960e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-13T18:44:43Z","title_canon_sha256":"40dfdebc020f6c23fd52c780cd386898037b7332570e3b8f4f1505bb93a0d58b"},"schema_version":"1.0","source":{"id":"0901.1848","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1848","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1848v2","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1848","created_at":"2026-05-18T02:24:56Z"},{"alias_kind":"pith_short_12","alias_value":"FNJL544IZAGC","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"FNJL544IZAGCJQVE","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"FNJL544I","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8c156f05d4ca8de8b57c2452c70366fe8875cae563b5abe1dcba81ba2f06f844","target":"graph","created_at":"2026-05-18T02:24:56Z","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 consider solutions to the equation f = h^r for polynomials f and h and integer r > 1. Given a polynomial f in the lacunary (also called sparse or super-sparse) representation, we first show how to determine if f can be written as h^r and, if so, to find such an r. This is a Monte Carlo randomized algorithm whose cost is polynomial in the number of non-zero terms of f and in log(deg f), i.e., polynomial in the size of the lacunary representation, and it works over GF(q)[x] (for large characteristic) as well as Q[x]. We also give two deterministic algorithms to compute the perfect root h give","authors_text":"Daniel S. Roche, Mark Giesbrecht","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-13T18:44:43Z","title":"Detecting lacunary perfect powers and computing their roots"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1848","kind":"arxiv","version":2},"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":"sha256:46bb19408ed4ef958afd40e8fa3ef22527858da1e9bfa7ad2d948d8607ac2214","target":"record","created_at":"2026-05-18T02:24:56Z","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":"ab0bc8eb14b098c9763d09da785f31b5a713132dc876ed3797fea0ed8061960e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-13T18:44:43Z","title_canon_sha256":"40dfdebc020f6c23fd52c780cd386898037b7332570e3b8f4f1505bb93a0d58b"},"schema_version":"1.0","source":{"id":"0901.1848","kind":"arxiv","version":2}},"canonical_sha256":"2b52bef388c80c24c2a4a72bbc6020da055b5ea5831dc4d67697f470ea8e9bbc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b52bef388c80c24c2a4a72bbc6020da055b5ea5831dc4d67697f470ea8e9bbc","first_computed_at":"2026-05-18T02:24:56.581009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:56.581009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QirQwQ9HmEnC2I7rt2Ju0waDw98wy/61/nhqpTBbC3zRZvK9czzOWuIKE3APeFdgy9lYE5i6fRDHhC/kIQsiBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:56.582246Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1848","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46bb19408ed4ef958afd40e8fa3ef22527858da1e9bfa7ad2d948d8607ac2214","sha256:8c156f05d4ca8de8b57c2452c70366fe8875cae563b5abe1dcba81ba2f06f844"],"state_sha256":"d3d0920034b3d1b6c377da03210edae452cfbd0167c27d16eae96a4bb80e6fd2"}