Dual<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:math>loop quantum gravity on the edge
Bibliographic record
Abstract
In a recent paper, we introduced a new discretization scheme for gravity in $2+1$ dimensions. Starting from the continuum theory, this new scheme allowed us to rigorously obtain the discrete phase space of loop gravity, coupled to particlelike ``edge mode'' degrees of freedom. In this work, we expand on that result by considering the most general choice of integration during the discretization process. We obtain a family of polarizations of the discrete phase space. In particular, one member of this family corresponds to the usual loop gravity phase space, while another corresponds to a new polarization, dual to the usual one in several ways. We study its properties, including the relevant constraints and the symmetries they generate. Furthermore, we motivate a relation between the dual polarization and teleparallel gravity.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.012 | 0.014 |
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; both teacher heads agree on what is shown here.
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".