Generalised kinematics for double field theory
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Bibliographic record
Abstract
A bstract We formulate a kinematical extension of Double Field Theory on a 2 d -dimensional para-Hermitian manifold $$ \left(\mathcal{P},\eta, \omega \right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>P</mml:mi> <mml:mi>η</mml:mi> <mml:mi>ω</mml:mi> </mml:mfenced> </mml:math> where the O ( d, d ) metric η is supplemented by an almost symplectic two-form ω . Together η and ω define an almost bi-Lagrangian structure K which provides a splitting of the tangent bundle $$ T\mathcal{P}=L\oplus \tilde{L} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mi>P</mml:mi> <mml:mo>=</mml:mo> <mml:mi>L</mml:mi> <mml:mo>⊕</mml:mo> <mml:mover> <mml:mi>L</mml:mi> <mml:mo>˜</mml:mo> </mml:mover> </mml:math> into two Lagrangian sub-spaces. In this paper a canonical connection and a corresponding generalised Lie derivative for the Leibniz algebroid on $$ T\mathcal{P} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mi>P</mml:mi> </mml:math> are constructed. We find integrability conditions under which the symmetry algebra closes for general η and ω , even if they are not flat and constant. This formalism thus provides a generalisation of the kinematical structure of Double Field Theory. We also show that this formalism allows one to reconcile and unify Double Field Theory with Generalised Geometry which is thoroughly discussed.
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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 | 0.001 | 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