Bibliographic record
Abstract
A new vision in multidimensional statistics is proposed impacting severalareas of application. In these applications, a set of noisy measurementscharacterizing the repeatable response of a process is known as a realizationand can be seen as a single point in $\mathbb{R}^N$. The projections of thispoint on the N axes correspond to the N measurements. The contemporary visionof a diffuse cloud of realizations distributed in $\mathbb{R}^N$ is replaced bya cloud in the shape of a shell surrounding a topological manifold. Thismanifold corresponds to the process's stabilized-response domain observedwithout the measurement noise. The measurement noise, which accumulates overseveral dimensions, distances each realization from the manifold. Theprobability density function (PDF) of the realization-to-manifold distancecreates the shell. Considering the central limit theorem as the number ofdimensions increases, the PDF tends toward the normal distribution N($μ$,$σ$^2) where $μ$ fixes the center shell location and $σ$fixes the shell thickness. In vision, the likelihood of a realization is afunction of the realization-to-shell distance rather than therealization-to-manifold distance. The demonstration begins with the work ofClaude Shannon followed by the introduction of the shell manifold and ends withpractical applications to monitoring equipment.
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How this classification was reachedexpand
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 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.009 | 0.019 |
| Research integrity | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
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".