Bibliographic record
Abstract
The set agreement power of a shared object O describes O's ability to solve set agreement problems: it is the sequence (n_1, n_2, ..., n_k, ...) such that, for every k >= 1, using O and registers one can solve the k-set agreement problem among at most n_k processes. It has been shown that the ability of an object O to implement other objects is not fully characterized by its consensus number the first component of its set agreement power) [1, 3, 14]. This raises the following natural question: is the ability of an object O to implement other objects fully characterized by its set agreement power? We prove that the answer is no: every level n >= 2 of Herlihy's consensus hierarchy has two objects that have the same set agreement power but are not equivalent, i.e., at least one cannot implement the other. We also show that every level n >= 2 of the consensus hierarchy contains a deterministic object O_n with some set agreement power (n_1, n_2, ..., n_k, ...) such that being able to solve the k-set agreement problems among n_k processes, for all k >= 1, is not enough to implement O_n.
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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 | 0.001 | 0.000 |
| Open science | 0.001 | 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 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".