Bibliographic record
Abstract
We consider a CFT defined on a static metric that is the product of time with a smooth closed space of positive scalar curvature. We expect the theory to exhibit an energy gap and our aim is to investigate how that gap depends on the geometry of the space. For a free conformal scalar it is straightforward to show the gap normalised by the minimum value of the Ricci scalar of the space is minimized when the space is a sphere. Our main result is then to show using geometric arguments that precisely the same result holds for fluctuations of a scalar operator in any holographic CFT. We prove this under the assumption that the dual vacuum geometry is a smooth Einstein metric ending only on the conformal boundary, and then consider fluctuations of a minimally coupled massive scalar field about this. We also argue the holographic CFT will have states dual to small bulk black holes whose existence is related to the energy gap. We show the thermodynamic properties of these black holes obey a bound of a similar nature to that of the scalar fluctuations—the ratio of CFT energy to a power of entropy for the states dual to black holes in the ‘small’ limit is bounded from below when appropriately normalized by the minimum Ricci scalar of the boundary space. Again the bound is saturated for a sphere.
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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 | 0.000 | 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 | 0.001 |
| 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)
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".