Asymptotic average shadowable points for homeomorphisms
Why this work is in the frame
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Bibliographic record
Abstract
<p>In this paper, given a homeomorphism <span class="math inline">\(f\)</span> of a compact metric space <span class="math inline">\(X\)</span>, we show that the set of all asymptotic average shadowable points of <span class="math inline">\(f\)</span> is an open and invariant set and <span class="math inline">\(f\)</span> has the asymptotic average shadowing property if and only if the set of all asymptotic average shadowable points of <span class="math inline">\(f\)</span> is <span class="math inline">\(X\)</span> if and only if any Borel probability measure <span class="math inline">\(\mu\)</span> of <span class="math inline">\(X\)</span> has the asymptotic average shadowing property.</p>
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.001 | 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