Partition functions on slightly squashed spheres and flux parameters
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Bibliographic record
Abstract
A bstract We argue that the conjectural relation between the subleading term in the small-squashing expansion of the free energy of general three-dimensional CFTs on squashed spheres and the stress-tensor three-point charge t 4 proposed in arXiv:1808.02052 : $$ {F}_{{\mathbbm{S}}_{\varepsilon}^3}^{(3)}(0)=\frac{1}{630}{\pi}^4{C}_T{t}_4 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>ε</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> <mml:mfenced> <mml:mn>3</mml:mn> </mml:mfenced> </mml:msubsup> <mml:mfenced> <mml:mn>0</mml:mn> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mn>630</mml:mn> </mml:mfrac> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>4</mml:mn> </mml:msup> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:math> , holds for an infinite family of holographic higher-curvature theories. Using holographic calculations for quartic and quintic Generalized Quasi-topological gravities and general-order Quasi-topological gravities, we identify an analogous analytic relation between such term and the charges t 2 and t 4 valid for five-dimensional theories: $$ {F}_{{\mathbbm{S}}_{\varepsilon}^5}^{(3)}(0)=\frac{2}{15}{\pi}^6{C}_T\left[1+\frac{3}{40}{t}_2+\frac{23}{630}{t}_4\right] $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>F</mml:mi> <mml:msubsup> <mml:mi>S</mml:mi> <mml:mi>ε</mml:mi> <mml:mn>5</mml:mn> </mml:msubsup> <mml:mfenced> <mml:mn>3</mml:mn> </mml:mfenced> </mml:msubsup> <mml:mfenced> <mml:mn>0</mml:mn> </mml:mfenced> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>2</mml:mn> <mml:mn>15</mml:mn> </mml:mfrac> <mml:msup> <mml:mi>π</mml:mi> <mml:mn>6</mml:mn> </mml:msup> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>T</mml:mi> </mml:msub> <mml:mfenced> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>40</mml:mn> </mml:mfrac> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:mfrac> <mml:mn>23</mml:mn> <mml:mn>630</mml:mn> </mml:mfrac> <mml:msub> <mml:mi>t</mml:mi> <mml:mn>4</mml:mn> </mml:msub> </mml:mrow> </mml:mfenced> </mml:math> . We test both conjectures using new analytic and numerical results for conformally-coupled scalars and free fermions, finding perfect agreement.
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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)
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