Maxwellian velocity distributions in slow time
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We extend Maxwellian velocity distributions to long observational timescales in much the same way that short timescale statistical mechanics distributions are averaged to yield normal laboratory timescale thermodynamic distributions. This long timescale view has several novel effects: Fluctuating overall velocities (i.e. “wind”) thermalizes into an additional component of temperature, while returning a Maxwellian velocity distribution. However, fluctuating temperature results in a new distribution with a Gaussian core but heavy polynomial tails. The power of the polynomial tail is either -3 or -2 depending on whether the precision of the temperature is allowed to extend to ± infinity or is required to remain strictly positive. The distribution is also interesting in the way it remains almost exactly Gaussian up to a certain velocity after which it quickly breaks off to become polynomial. The distributions are carefully analyzed mathematically, and physical consequences are drawn.
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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 | 0.000 | 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 | 0.000 | 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