Limit measures for affine cellular automata II
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Bibliographic record
Abstract
If M is a monoid, and A is an abelian group, then AM is a compact abelian group; a linear cellular automaton (LCA) is a continuous endomorphism F: AM − → AM that commutes with all shift maps. If F is diffusive, and µ is a harmonically mixing (HM) probability measure on AM, then the sequence {FNµ} ∞ N=1 weak*-converges to the Haar measure on AM, in density. Fully supported Markov measures on AZ are HM, and nontrivial LCA on A (ZD) are diffusive when A = Z/p is a prime cyclic group. In the present work, we provide sufficient conditions for diffusion of LCA on A (ZD) when A = Z/n is any cyclic group or when A = ( ) J Z /pr (p prime). We show that any fully supported Markov random field A (ZD) is HM (where A is any abelian group). We also provide examples of HM Markov measures not having full support, and measures on A Z which have the Kolmogorov property but which are not HM.
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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 | 0.001 | 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