{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:Q5GG2E5LOVTK35OZJFS37TWSTI","short_pith_number":"pith:Q5GG2E5L","schema_version":"1.0","canonical_sha256":"874c6d13ab7566adf5d94965bfced29a255be52b302735684d0441fb3de81939","source":{"kind":"arxiv","id":"1709.05294","version":1},"attestation_state":"computed","paper":{"title":"The Orthogonal Vectors Conjecture for Branching Programs and Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Daniel Kane, Ryan Williams","submitted_at":"2017-09-15T16:26:34Z","abstract_excerpt":"In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all $d=\\omega(\\log n)$. Assuming the OVC, optimal time lower bounds have been proved for many prominent problems in $P$.\n  We prove that OVC is true in several computational models of interest:\n  * For all sufficiently large $n$ and $d$, OV for $n$ vectors in $\\{0,1\\}^d$ has branching program complexity $\\tilde{\\Theta}(n\\cdot \\min(n,2^d))$. In particular, the lower boun"},"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":"1709.05294","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-09-15T16:26:34Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"73b4404647a52e76123ac9fa22c106fb100adc5b695ff6958a77fa394f35af3b","abstract_canon_sha256":"5678e1e460c6f011c78ccf5cf81a20c367328c47954fda04c5f4e9c1fd33d4da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:06.086950Z","signature_b64":"BtDH7aNPoVszJgn1DOJ85U9+j9EWgGZddNqyoh/vYmDZ4ef9E/oBHNnWpN4URJPFfDqjIyhsVDFtq15gFtCHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"874c6d13ab7566adf5d94965bfced29a255be52b302735684d0441fb3de81939","last_reissued_at":"2026-05-18T00:35:06.086284Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:06.086284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Orthogonal Vectors Conjecture for Branching Programs and Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CC","authors_text":"Daniel Kane, Ryan Williams","submitted_at":"2017-09-15T16:26:34Z","abstract_excerpt":"In the Orthogonal Vectors (OV) problem, we wish to determine if there is an orthogonal pair of vectors among $n$ Boolean vectors in $d$ dimensions. The OV Conjecture (OVC) posits that OV requires $n^{2-o(1)}$ time to solve, for all $d=\\omega(\\log n)$. Assuming the OVC, optimal time lower bounds have been proved for many prominent problems in $P$.\n  We prove that OVC is true in several computational models of interest:\n  * For all sufficiently large $n$ and $d$, OV for $n$ vectors in $\\{0,1\\}^d$ has branching program complexity $\\tilde{\\Theta}(n\\cdot \\min(n,2^d))$. In particular, the lower boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05294","kind":"arxiv","version":1},"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":"1709.05294","created_at":"2026-05-18T00:35:06.086401+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.05294v1","created_at":"2026-05-18T00:35:06.086401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05294","created_at":"2026-05-18T00:35:06.086401+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q5GG2E5LOVTK","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q5GG2E5LOVTK35OZ","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q5GG2E5L","created_at":"2026-05-18T12:31:37.085036+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/Q5GG2E5LOVTK35OZJFS37TWSTI","json":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI.json","graph_json":"https://pith.science/api/pith-number/Q5GG2E5LOVTK35OZJFS37TWSTI/graph.json","events_json":"https://pith.science/api/pith-number/Q5GG2E5LOVTK35OZJFS37TWSTI/events.json","paper":"https://pith.science/paper/Q5GG2E5L"},"agent_actions":{"view_html":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI","download_json":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI.json","view_paper":"https://pith.science/paper/Q5GG2E5L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.05294&json=true","fetch_graph":"https://pith.science/api/pith-number/Q5GG2E5LOVTK35OZJFS37TWSTI/graph.json","fetch_events":"https://pith.science/api/pith-number/Q5GG2E5LOVTK35OZJFS37TWSTI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI/action/storage_attestation","attest_author":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI/action/author_attestation","sign_citation":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI/action/citation_signature","submit_replication":"https://pith.science/pith/Q5GG2E5LOVTK35OZJFS37TWSTI/action/replication_record"}},"created_at":"2026-05-18T00:35:06.086401+00:00","updated_at":"2026-05-18T00:35:06.086401+00:00"}