Dynamics of the Cellular Automaton Rule 142
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Bibliographic record
Abstract
We investigate dynamics of the cellular automaton Rule 142. This rule possesses additive invariant of the second order, namely it conserves the number of blocks "10." Rule 142 can be alternatively described as an operation on a binary string in which we simultaneously flip all symbols which have dissenting right neighbors. We show that the probability of having a dissenting neighbor can be computed exactly using the fact that the surjective Rule 60 transforms Rule 142 into Rule 226. We also demonstrate that the conservation of the number of 10 blocks implies that these blocks move with speed -1 or stay in the same place, depending on the state of the preceding site. At the density of blocks 10 equal to 0.25, Rule 142 exhibits a phenomenon similar to the jamming transitions occurring in discrete models of traffic flow.
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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 | 0.001 | 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