Closest-point problems simplified on the RAM
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Basic proximity problems for low-dimensional point sets, such as closest pair (CP) and approximate nearest neighbor (ANN), have been studied extensively in the computational geometry literature, with well over a hundred papers published (we merely cite the survey by Smid [10] and omit most references). Generally, optimal algorithms designed for worst-case input require hierarchical spatial structures with sophisticated balancing conditions (we mention, for example, the BBD trees of Arya et al., balanced quadtrees, and Callahan and Kosaraju's fair-split trees); dynamization of these structures is even more involved (relying on Sleator and Tarjan's dynamic trees or Frederickson's topology trees). In this note, we point out that much simpler algorithms with the same performance are possible using standard, though nonalgebraic, RAM operations. This is interesting, considering that nonalgebraic operations have been used before in the literature (e.g., in the original version of the BBD tree [2], as well as in various randomized CP methods). The CP algorithm can be stated completely in one paragraph. Assume coordinates are positive integers bounded by U = 2 w. Given a point p in a constant dimension d where the i-th coordinate p i is the number p iw p i0 in binary, dene its shue (p) to be the number p 1w pdw p 10 p d0 in binary, and dene shifts i (p) = (p 1 + bi2
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it