Tree composition condition and moments vanishing
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Bibliographic record
Abstract
We consider the problem of vanishing of moments , k = 0, 1, 2, .... A sufficient vanishing condition is given by a 'tree composition condition' introduced in (Brudnyi 2006 Am. J. Math. 128 419–51). We analyse this notion and show that for 'non-rigid' functions P, Q = ∫q it is indeed weaker than the 'segment composition condition' of (Alwash and Lloyd 1987 Proc. R. Soc. Edinb. A 105 129–52, Briskin et al 1999 Erg. Theory Dyn. Syst. 19 1201–20), while for real entire or rational P, Q these two conditions coincide. Next we describe some classes of 'definite' P, for which vanishing of the moments implies tree composition. Finally, we analyse the mutual relation of different moment vanishing conditions in terms of the topology and geometry of the curve Γ = ΓP,Q = (P, Q)([a, b]) in .
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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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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