{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LKUTVI3IRFFQV2Y2LGET2X3BLC","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":"97ec8026b161cf83cfc8cf69a5a6449c9c74b9255e316211ef3ae7fb43b5ad46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-15T22:51:50Z","title_canon_sha256":"59552ec26d177c760ae1c4dc3165605d6ba9df00ee65f54835579488b9dd05ad"},"schema_version":"1.0","source":{"id":"1810.06740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.06740","created_at":"2026-05-18T00:03:11Z"},{"alias_kind":"arxiv_version","alias_value":"1810.06740v1","created_at":"2026-05-18T00:03:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06740","created_at":"2026-05-18T00:03:11Z"},{"alias_kind":"pith_short_12","alias_value":"LKUTVI3IRFFQ","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"LKUTVI3IRFFQV2Y2","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"LKUTVI3I","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:1dd705dd5310a16c80b66842ffc12d7d4c0cb9f4a03f1b12eda3109c019349d5","target":"graph","created_at":"2026-05-18T00:03:11Z","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":"The Light Bulb Problem is one of the most basic problems in data analysis. One is given as input $n$ vectors in $\\{-1,1\\}^d$, which are all independently and uniformly random, except for a planted pair of vectors with inner product at least $\\rho \\cdot d$ for some constant $\\rho > 0$. The task is to find the planted pair. The most straightforward algorithm leads to a runtime of $\\Omega(n^2)$. Algorithms based on techniques like Locality-Sensitive Hashing achieve runtimes of $n^{2 - O(\\rho)}$; as $\\rho$ gets small, these approach quadratic.\n  Building on prior work, we give a new algorithm for ","authors_text":"Josh Alman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-15T22:51:50Z","title":"An Illuminating Algorithm for the Light Bulb Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06740","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":"sha256:91c973e9ca3007b114469f3d673ef86dfc2247dc6adc425c6319cd409f22fc49","target":"record","created_at":"2026-05-18T00:03:11Z","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":"97ec8026b161cf83cfc8cf69a5a6449c9c74b9255e316211ef3ae7fb43b5ad46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-10-15T22:51:50Z","title_canon_sha256":"59552ec26d177c760ae1c4dc3165605d6ba9df00ee65f54835579488b9dd05ad"},"schema_version":"1.0","source":{"id":"1810.06740","kind":"arxiv","version":1}},"canonical_sha256":"5aa93aa368894b0aeb1a59893d5f615894c02112f9d307a9e65e08a1a114219a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5aa93aa368894b0aeb1a59893d5f615894c02112f9d307a9e65e08a1a114219a","first_computed_at":"2026-05-18T00:03:11.729801Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:11.729801Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g/g1PN0JzczfaX0XXb6VFLXCwehU25ZTOubWRMOoT6Ib7IV5sXaVb5r6veNLxfiCIl96HroiMLQ8iFQFafKKCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:11.730553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.06740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91c973e9ca3007b114469f3d673ef86dfc2247dc6adc425c6319cd409f22fc49","sha256:1dd705dd5310a16c80b66842ffc12d7d4c0cb9f4a03f1b12eda3109c019349d5"],"state_sha256":"33bc7c556a728e884096ac435cc289c35501f938d93f7d94e72e834573cb6d33"}