Transition asymptotics for reaction-diffusion in random media
Why this work is in the frame
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Bibliographic record
Abstract
We describe a universal transition mechanism between annealed and quenched regimes in the context of reaction-diffusion in random media. We study the total population size for random walks which branch and annihilate on Z d, with time-independent random rates. The random walks are independent, continuous time, rate 2dκ, simple, symmetric, with κ ≥ 0. A random walk at x ∈ Z d, binary branches at rate v+(x), and annihilates at rate v−(x). The random environment w has coordinates w(x) = (v−(x), v+(x)) which are i.i.d. We identify a natural way to describe the annealed-Gaussian transition mechanism under mild conditions on the rates. Indeed, we introduce the exponents Fθ(t): = H1((1+θ)t)−(1+θ)H1(t), and assume that
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.000 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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