Q<i><sub>p</sub></i>Spaces and Dirichlet Type Spaces
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract In this paper, we show that the Möbius invariant function space Q p can be generated by variant Dirichlet type spaces 𝒟 μ,p induced by finite positive Borel measures μ on the open unit disk. A criterion for the equality between the space 𝒟 μ,p and the usual Dirichlet type space 𝒟 p is given. We obtain a sufficient condition to construct different 𝒟 μ,p spaces and provide examples. We establish decomposition theorems for 𝒟 μ,p spaces and prove that the non-Hilbert space Q p is equal to the intersection of Hilbert spaces 𝒟 μ,p . As an application of the relation between Q p and 𝒟 μ,p spaces, we also obtain that there exist different 𝒟 μ,p spaces; this is a trick to prove the existence without constructing examples.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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) | 0.003 | 0.005 |
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