Bibliographic record
Abstract
We study a random system of cn linear equations over n variables in GF(2), where each equation contains exactly r variables; this is equivalent to r-XORSAT. Previous work has established a clustering threshold, c^*_r for this model: if c=c_r^*-εfor any constant ε>0 then with high probability all solutions form a well-connected cluster; whereas if c=c^*_r+ε, then with high probability the solutions partition into well-connected, well-separated clusters (with probability tending to 1 as n goes to infinity). This is part of a general clustering phenomenon which is hypothesized to arise in most of the commonly studied models of random constraint satisfaction problems, via sophisticated but mostly non-rigorous techniques from statistical physics. We extend that study to the range c=c^*_r+o(1), and prove that the connectivity parameters of the r-XORSAT clusters undergo a smooth transition around the clustering threshold.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 teacher head, 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".