Higher Order Tangents to Analytic Varieties along Curves
Why this work is in the frame
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Bibliographic record
Abstract
Abstract Let V be an analytic variety in some open set in which contains the origin and which is purely k -dimensional. For a curve γ in , defined by a convergent Puiseux series and satisfying γ(0) = 0, and d ≥ 1, define V t := t −d (V − (t)). Then the currents defined by Vt converge to a limit current T γ,d [ V ] as t tends to zero. T γ,d [ V ] is either zero or its support is an algebraic variety of pure dimension k in . Properties of such limit currents and examples are presented. These results will be applied in a forthcoming paper to derive necessary conditions for varieties satisfying the local Phragmén-Lindelöf condition that was used by Hörmander to characterize the constant coefficient partial differential operators which act surjectively on the space of all real analytic functions on .
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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 | 0.002 |
| 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) | 0.003 | 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