{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TRNNPKH2SOLH6MUDATTN2WQHXZ","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":"27b39507857c68645ddda6f4cf253172e38a05c287f7f2bce7858342796750c8","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2010-09-16T16:21:15Z","title_canon_sha256":"13417a3950004ee8a17ca1c995434cc380fcee7f5105eca99529184117571204"},"schema_version":"1.0","source":{"id":"1009.3214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3214","created_at":"2026-05-18T04:32:11Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3214v2","created_at":"2026-05-18T04:32:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3214","created_at":"2026-05-18T04:32:11Z"},{"alias_kind":"pith_short_12","alias_value":"TRNNPKH2SOLH","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRNNPKH2SOLH6MUD","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRNNPKH2","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:4b59f88d00a0e3149a00913b8cd55cdc80f5b589d26721f600a7440150b78b3a","target":"graph","created_at":"2026-05-18T04:32:11Z","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 the problem of finding a sparse multiple of a polynomial. Given f in F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h in F[x] of f such that h has at most t non-zero terms, and if so, to find such an h. When F=Q and t is constant, we give a polynomial-time algorithm in d and the size of coefficients in h. When F is a finite field, we show that the problem is at least as hard as determining the multiplicative order of elements in an extension field of F (a problem thought to have complexity similar to that of factoring ","authors_text":"Daniel S. Roche, Hrushikesh Tilak, Mark Giesbrecht","cross_cats":["cs.CC","cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2010-09-16T16:21:15Z","title":"Computing sparse multiples of polynomials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3214","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":"sha256:71444017eac78cf00699a27181c548733349554d06e28a7ddfc506c4f3d945a1","target":"record","created_at":"2026-05-18T04:32:11Z","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":"27b39507857c68645ddda6f4cf253172e38a05c287f7f2bce7858342796750c8","cross_cats_sorted":["cs.CC","cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2010-09-16T16:21:15Z","title_canon_sha256":"13417a3950004ee8a17ca1c995434cc380fcee7f5105eca99529184117571204"},"schema_version":"1.0","source":{"id":"1009.3214","kind":"arxiv","version":2}},"canonical_sha256":"9c5ad7a8fa93967f328304e6dd5a07be6e0aa1173b5081ac6950d8b669e178d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c5ad7a8fa93967f328304e6dd5a07be6e0aa1173b5081ac6950d8b669e178d2","first_computed_at":"2026-05-18T04:32:11.627005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:11.627005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X7Mup75PnUdYXljVcZNtOt5R5J5AtYhvMOnqO2R2HLLDie3+Q+M9tKpmNRQPdo+50XNldZN7g4BTzQiQaU3QBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:11.627545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71444017eac78cf00699a27181c548733349554d06e28a7ddfc506c4f3d945a1","sha256:4b59f88d00a0e3149a00913b8cd55cdc80f5b589d26721f600a7440150b78b3a"],"state_sha256":"c746bf0ea14f1486d84fa158c9ae061665eaeaadf847f9be9c154532b7541e37"}