{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:6H72KBXMYOB2CW3TXVTOFP5ADC","short_pith_number":"pith:6H72KBXM","schema_version":"1.0","canonical_sha256":"f1ffa506ecc383a15b73bd66e2bfa018b9f1643d2928fd6d8c3e52cf3cf078d7","source":{"kind":"arxiv","id":"1401.3714","version":2},"attestation_state":"computed","paper":{"title":"Testing Equivalence of Polynomials under Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amir Shpilka, Rafael Oliveira, Zeev Dvir","submitted_at":"2014-01-15T19:29:48Z","abstract_excerpt":"Two polynomials $f, g \\in \\mathbb{F}[x_1, \\ldots, x_n]$ are called shift-equivalent if there exists a vector $(a_1, \\ldots, a_n) \\in \\mathbb{F}^n$ such that the polynomial identity $f(x_1+a_1, \\ldots, x_n+a_n) \\equiv g(x_1,\\ldots,x_n)$ holds. Our main result is a new randomized algorithm that tests whether two given polynomials are shift equivalent. Our algorithm runs in time polynomial in the circuit size of the polynomials, to which it is given black box access. This complements a previous work of Grigoriev (Theoretical Computer Science, 1997) who gave a deterministic algorithm running in ti"},"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":"1401.3714","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2014-01-15T19:29:48Z","cross_cats_sorted":[],"title_canon_sha256":"1fad41e5bbcf246da8850c0cca9b93cd1a93c7d688dd68573a6ebebebb0a0d83","abstract_canon_sha256":"c0f12be1cb07ae8880f868a191fcb557f29f54fb76e68e3de542de5847503086"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:34.230654Z","signature_b64":"ZFC/w835YxpqcoH6uWKT0LqpcyeoZT7ZtcHNTsMHXXJwtrjaf+Hz5hOaJ3IVShVK/NcUm6n5ZWl6EP94u11mDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1ffa506ecc383a15b73bd66e2bfa018b9f1643d2928fd6d8c3e52cf3cf078d7","last_reissued_at":"2026-05-18T02:58:34.230024Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:34.230024Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Testing Equivalence of Polynomials under Shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amir Shpilka, Rafael Oliveira, Zeev Dvir","submitted_at":"2014-01-15T19:29:48Z","abstract_excerpt":"Two polynomials $f, g \\in \\mathbb{F}[x_1, \\ldots, x_n]$ are called shift-equivalent if there exists a vector $(a_1, \\ldots, a_n) \\in \\mathbb{F}^n$ such that the polynomial identity $f(x_1+a_1, \\ldots, x_n+a_n) \\equiv g(x_1,\\ldots,x_n)$ holds. Our main result is a new randomized algorithm that tests whether two given polynomials are shift equivalent. Our algorithm runs in time polynomial in the circuit size of the polynomials, to which it is given black box access. This complements a previous work of Grigoriev (Theoretical Computer Science, 1997) who gave a deterministic algorithm running in ti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3714","kind":"arxiv","version":2},"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":"1401.3714","created_at":"2026-05-18T02:58:34.230106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.3714v2","created_at":"2026-05-18T02:58:34.230106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.3714","created_at":"2026-05-18T02:58:34.230106+00:00"},{"alias_kind":"pith_short_12","alias_value":"6H72KBXMYOB2","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_16","alias_value":"6H72KBXMYOB2CW3T","created_at":"2026-05-18T12:28:16.859392+00:00"},{"alias_kind":"pith_short_8","alias_value":"6H72KBXM","created_at":"2026-05-18T12:28:16.859392+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/6H72KBXMYOB2CW3TXVTOFP5ADC","json":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC.json","graph_json":"https://pith.science/api/pith-number/6H72KBXMYOB2CW3TXVTOFP5ADC/graph.json","events_json":"https://pith.science/api/pith-number/6H72KBXMYOB2CW3TXVTOFP5ADC/events.json","paper":"https://pith.science/paper/6H72KBXM"},"agent_actions":{"view_html":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC","download_json":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC.json","view_paper":"https://pith.science/paper/6H72KBXM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.3714&json=true","fetch_graph":"https://pith.science/api/pith-number/6H72KBXMYOB2CW3TXVTOFP5ADC/graph.json","fetch_events":"https://pith.science/api/pith-number/6H72KBXMYOB2CW3TXVTOFP5ADC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC/action/storage_attestation","attest_author":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC/action/author_attestation","sign_citation":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC/action/citation_signature","submit_replication":"https://pith.science/pith/6H72KBXMYOB2CW3TXVTOFP5ADC/action/replication_record"}},"created_at":"2026-05-18T02:58:34.230106+00:00","updated_at":"2026-05-18T02:58:34.230106+00:00"}