Bibliographic record
Abstract
We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair within a set of n points) into R 2 Cartesian space preserving their l ∞ (or l1) metric distances. Its expected time is O(n 2 log 2 n) (i.e. within a poly-log of the size of the input) beating the previous O(n 3) algorithm. In contrast, we prove that detecting l 3 ∞ embeddings is NP-complete. The problem is also NP-complete within l 2 1 or l 2 ∞ with the added constraint that the locations of two of the points are given or alternatively that the two dimension are curved into a 3-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded in l3 ∞ , however, can be if any single point is removed. ∗ This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper. 1 1
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.007 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".