Bibliographic record
Abstract
A sorting network (also known as a reduced decomposition of the reverse permutation) is a shortest path from 12 ⋯ n 12 \cdots n to n ⋯ 21 n \cdots 21 in the Cayley graph of the symmetric group S n S_n generated by adjacent transpositions. We prove that in a uniform random n n -element sorting network σ n \sigma ^n , all particle trajectories are close to sine curves with high probability. We also find the weak limit of the time- t t permutation matrix measures of σ n \sigma ^n . As a corollary of these results, we show that if S n S_n is embedded into R n \mathbb {R}^n via the map τ ↦ ( τ ( 1 ) , τ ( 2 ) , … τ ( n ) ) \tau \mapsto (\tau (1), \tau (2), \dots \tau (n)) , then with high probability, the path σ n \sigma ^n is close to a great circle on a particular ( n − <
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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 | 0.002 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 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".