{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Q5GG2E5LOVTK35OZJFS37TWSTI","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":"5678e1e460c6f011c78ccf5cf81a20c367328c47954fda04c5f4e9c1fd33d4da","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-09-15T16:26:34Z","title_canon_sha256":"73b4404647a52e76123ac9fa22c106fb100adc5b695ff6958a77fa394f35af3b"},"schema_version":"1.0","source":{"id":"1709.05294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.05294","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"arxiv_version","alias_value":"1709.05294v1","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.05294","created_at":"2026-05-18T00:35:06Z"},{"alias_kind":"pith_short_12","alias_value":"Q5GG2E5LOVTK","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q5GG2E5LOVTK35OZ","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q5GG2E5L","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:c81c7aaf66eb71889aaa67c7b5db9fb1b069145c77dbc0086eece7acb81f255b","target":"graph","created_at":"2026-05-18T00:35:06Z","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":"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","authors_text":"Daniel Kane, Ryan Williams","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-09-15T16:26:34Z","title":"The Orthogonal Vectors Conjecture for Branching Programs and Formulas"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.05294","kind":"arxiv","version":1},"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":"sha256:37f4416f4c6cf51a3d98078548ae3605a4c8ece591e3fbd8419c3eb06b02fa84","target":"record","created_at":"2026-05-18T00:35:06Z","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":"5678e1e460c6f011c78ccf5cf81a20c367328c47954fda04c5f4e9c1fd33d4da","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2017-09-15T16:26:34Z","title_canon_sha256":"73b4404647a52e76123ac9fa22c106fb100adc5b695ff6958a77fa394f35af3b"},"schema_version":"1.0","source":{"id":"1709.05294","kind":"arxiv","version":1}},"canonical_sha256":"874c6d13ab7566adf5d94965bfced29a255be52b302735684d0441fb3de81939","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"874c6d13ab7566adf5d94965bfced29a255be52b302735684d0441fb3de81939","first_computed_at":"2026-05-18T00:35:06.086284Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:06.086284Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BtDH7aNPoVszJgn1DOJ85U9+j9EWgGZddNqyoh/vYmDZ4ef9E/oBHNnWpN4URJPFfDqjIyhsVDFtq15gFtCHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:06.086950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.05294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:37f4416f4c6cf51a3d98078548ae3605a4c8ece591e3fbd8419c3eb06b02fa84","sha256:c81c7aaf66eb71889aaa67c7b5db9fb1b069145c77dbc0086eece7acb81f255b"],"state_sha256":"2c87e05dc95975b6113c7f0006f8377a67e8f9173693bc1db0971d85e84eac70"}