{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:AQHMI25F7Z6XMK5ANIXRG5S6YR","short_pith_number":"pith:AQHMI25F","schema_version":"1.0","canonical_sha256":"040ec46ba5fe7d762ba06a2f13765ec47a8372ed0b85455085c9f5f437d85ffc","source":{"kind":"arxiv","id":"2507.11098","version":2},"attestation_state":"computed","paper":{"title":"Faster algorithms for k-Orthogonal Vectors in low dimension","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anita D\\\"urr, Evangelos Kipouridis, Karol W\\k{e}grzycki, Michael Lampis","submitted_at":"2025-07-15T08:45:24Z","abstract_excerpt":"In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\\{1,\\ldots,d\\}$, each of size $n$, and the task is to decide whether there exists a pair $a \\in A$ and $b \\in B$ such that $a \\cap b = \\emptyset$. Straightforward algorithms for this problem run in $\\mathcal{O}(n^2 \\cdot d)$ or $\\mathcal{O}(2^d \\cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\\cdot n^{2-\\varepsilon}$ time algorithm that solves this problem for any constant $\\varepsilon > 0$.\n  Williams (FOCS 2024) presented a $\\tilde{\\mathcal{O}}(1.35^d \\cdot n)$-time algorithm for the problem, based"},"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":"2507.11098","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"cs.DS","submitted_at":"2025-07-15T08:45:24Z","cross_cats_sorted":[],"title_canon_sha256":"fb0c90543e7020ba118043862df0733d2afb857963862819b4ce9b764e062157","abstract_canon_sha256":"21db542a7b9f8f3abf1ecd6be4548aa8f9dabec332833aa69e25c8cdd87ae562"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T01:08:30.437346Z","signature_b64":"3uuFZVnMNXIB2ZptGWrId64GGs+ffTKUzprDcdHNkO35QZj0TOEQPWD4bwvId9PoVAR4NRNJQvjGKEFrwdNCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"040ec46ba5fe7d762ba06a2f13765ec47a8372ed0b85455085c9f5f437d85ffc","last_reissued_at":"2026-06-04T01:08:30.436726Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T01:08:30.436726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Faster algorithms for k-Orthogonal Vectors in low dimension","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Anita D\\\"urr, Evangelos Kipouridis, Karol W\\k{e}grzycki, Michael Lampis","submitted_at":"2025-07-15T08:45:24Z","abstract_excerpt":"In the Orthogonal Vectors problem (OV), we are given two families $A, B$ of subsets of $\\{1,\\ldots,d\\}$, each of size $n$, and the task is to decide whether there exists a pair $a \\in A$ and $b \\in B$ such that $a \\cap b = \\emptyset$. Straightforward algorithms for this problem run in $\\mathcal{O}(n^2 \\cdot d)$ or $\\mathcal{O}(2^d \\cdot n)$ time, and assuming SETH, there is no $2^{o(d)}\\cdot n^{2-\\varepsilon}$ time algorithm that solves this problem for any constant $\\varepsilon > 0$.\n  Williams (FOCS 2024) presented a $\\tilde{\\mathcal{O}}(1.35^d \\cdot n)$-time algorithm for the problem, based"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.11098","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.11098/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.11098","created_at":"2026-06-04T01:08:30.436800+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.11098v2","created_at":"2026-06-04T01:08:30.436800+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.11098","created_at":"2026-06-04T01:08:30.436800+00:00"},{"alias_kind":"pith_short_12","alias_value":"AQHMI25F7Z6X","created_at":"2026-06-04T01:08:30.436800+00:00"},{"alias_kind":"pith_short_16","alias_value":"AQHMI25F7Z6XMK5A","created_at":"2026-06-04T01:08:30.436800+00:00"},{"alias_kind":"pith_short_8","alias_value":"AQHMI25F","created_at":"2026-06-04T01:08:30.436800+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/AQHMI25F7Z6XMK5ANIXRG5S6YR","json":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR.json","graph_json":"https://pith.science/api/pith-number/AQHMI25F7Z6XMK5ANIXRG5S6YR/graph.json","events_json":"https://pith.science/api/pith-number/AQHMI25F7Z6XMK5ANIXRG5S6YR/events.json","paper":"https://pith.science/paper/AQHMI25F"},"agent_actions":{"view_html":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR","download_json":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR.json","view_paper":"https://pith.science/paper/AQHMI25F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.11098&json=true","fetch_graph":"https://pith.science/api/pith-number/AQHMI25F7Z6XMK5ANIXRG5S6YR/graph.json","fetch_events":"https://pith.science/api/pith-number/AQHMI25F7Z6XMK5ANIXRG5S6YR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR/action/storage_attestation","attest_author":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR/action/author_attestation","sign_citation":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR/action/citation_signature","submit_replication":"https://pith.science/pith/AQHMI25F7Z6XMK5ANIXRG5S6YR/action/replication_record"}},"created_at":"2026-06-04T01:08:30.436800+00:00","updated_at":"2026-06-04T01:08:30.436800+00:00"}