Maximal time existence of unnormalized conical Kähler–Ricci flow
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Bibliographic record
Abstract
Abstract We generalize the maximal time existence of Kähler–Ricci flow in [ G. Tian and Z. Zhang , On the Kähler–Ricci flow on projective manifolds of general type, Chin. Ann. Math. Ser. B 27 (2006), no. 2, 179–192] and [ J. Song and G. Tian , The Kähler–Ricci flow through singularities, Invent. Math. 207 (2017), no. 2, 519–595] to the conical case. Furthermore, if the log canonical bundle <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>K</m:mi> <m:mi>M</m:mi> </m:msub> <m:mo>+</m:mo> <m:mrow> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>-</m:mo> <m:mi>β</m:mi> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> <m:mo></m:mo> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mi>D</m:mi> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> </m:mrow> </m:math> {K_{M}+(1-\beta)[D]} is big or big and nef, we can examine the limit behaviors of such conical Kähler–Ricci flow. Moreover, these results still hold when D is a simple normal crossing divisor.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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