Maximum independent sets of the 120-cell and other regular polytopes
Why this work is in the frame
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Bibliographic record
Abstract
A d -code in a graph is a set of vertices such that all pairwise distances are at least d . As part of a study of d -codes of three-and four-dimensional regular polytopes, the maximum independent set order of the 120 -cell is calculated. A linear program based on counting arguments leads to an upper bound of 221 . An independent set of order 110 in the antipodal collapse of the 120 -cell (also known as the hemi- 120 -cell) gives a lower bound of 220 for the 120 -cell itself. The gap is closed by the computation described here, with the result that the maximum independent set order of the 120 -cell is 220 . All maximum d -code orders of the icosahedron, dodecahedron, 24 -cell, 600 -cell and 120 -cell are reported.
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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