Classification of sofic projective subdynamics of multidimensional shifts of finite type
Bibliographic record
Abstract
Motivated by Hochman’s notion of subdynamics of a Z d \mathbb {Z}^d subshift (2009), we define and examine the projective subdynamics of Z d \mathbb {Z}^d shifts of finite type (SFTs) where we restrict not only the action but also the phase space. We show that any Z \mathbb {Z} sofic shift of positive entropy is the projective subdynamics of a Z 2 \mathbb {Z}^2 ( Z d \mathbb {Z}^d ) SFT, and that there is a simple condition characterizing the class of zero-entropy Z \mathbb {Z} sofic shifts which are not the projective subdynamics of any Z 2 \mathbb {Z}^2 SFT. We define notions of stable and unstable subdynamics in analogy with the notions of stable and unstable limit sets in cellular automata theory, and discuss how our results fit into this framework. One-dimensional strictly sofic shifts of positive entropy admit both a stable and an unstable realization, whereas Z \mathbb {Z} SFTs only allow for stable realizations and a particular class of zero-entropy proper Z \mathbb {Z} sofics only allows for an unstable realization. Finally, we prove that the union of finitely many Z k \mathbb {Z}^k subshifts, all of which are realizable in Z d \mathbb {Z}^d SFTs, is again realizable when it contains at least two periodic points, that the projective subdynamics of Z 2 \mathbb {Z}^2 SFTs with the uniform filling property (UFP) are always stable, thus sofic, and we exhibit a class of non-sofic
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 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 source (direct Gemma or distilled Codex), 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".