Universal Reconfiguration of Facet-Connected Modular Robots by Pivots:\n The $O(1)$ Musketeers
Why this work is in the frame
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Bibliographic record
Abstract
We present the first universal reconfiguration algorithm for transforming a\nmodular robot between any two facet-connected square-grid configurations using\npivot moves. More precisely, we show that five extra "helper" modules\n("musketeers") suffice to reconfigure the remaining $n$ modules between any two\ngiven configurations. Our algorithm uses $O(n^2)$ pivot moves, which is\nworst-case optimal. Previous reconfiguration algorithms either require less\nrestrictive "sliding" moves, do not preserve facet-connectivity, or for the\nsetting we consider, could only handle a small subset of configurations defined\nby a local forbidden pattern. Configurations with the forbidden pattern do have\ndisconnected reconfiguration graphs (discrete configuration spaces), and indeed\nwe show that they can have an exponential number of connected components. But\nforbidding the local pattern throughout the configuration is far from\nnecessary, as we show that just a constant number of added modules (placed to\nbe freely reconfigurable) suffice for universal reconfigurability. We also\nclassify three different models of natural pivot moves that preserve\nfacet-connectivity, and show separations between these models.\n
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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 | 0.000 |
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 it