Bibliographic record
Abstract
We present measurements of the fractal dimension of a turbulent asymptotically anti--de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as $E(k)\ensuremath{\sim}{k}^{\ensuremath{-}2}$ is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of $E(k)\ensuremath{\sim}{k}^{\ensuremath{-}5/3}$, but we obtain fractal dimensions $D$ for spatial sections of the horizon $H\ensuremath{\cap}\mathrm{\ensuremath{\Sigma}}$ in both cases: $D=2.584(1)$ and $D=2.645(4)$, respectively. These results are consistent with the upper bound of $D=3$, thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014)] that $D=3+1/3$. We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon $H\ensuremath{\cap}\mathrm{\ensuremath{\Sigma}}$ in a covariant manner, and we speculate on assigning a ``bootstrapped'' value of fractal dimension to the entire horizon $H$ when it is in a statistically quasisteady turbulent state.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 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 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".