Quarter-pinched Einstein metrics interpolating between real and complex\n hyperbolic metrics
Bibliographic record
Abstract
We show that the one-loop quantum deformation of the universal hypermultiplet\nprovides a family of complete $1/4$-pinched negatively curved quaternionic\nK\\"ahler (i.e. half conformally flat Einstein) metrics $g^c$, $c\\ge 0$, on\n$\\mathbb R^4$. The metric $g^0$ is the complex hyperbolic metric whereas the\nfamily $(g^c)_{c>0}$ is equivalent to a family of metrics $(h^b)_{b>0}$\ndepending on $b=1/c$ and smoothly extending to $b=0$ for which $h^0$ is the\nreal hyperbolic metric. In this sense the one-loop deformation interpolates\nbetween the real and the complex hyperbolic metrics. We also determine the\n(singular) conformal structure at infinity for the above families.\n
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 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; a candidate call from one teacher head, not a consensus.
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".