A simple proof of orientability in the colored Boulatov model
Bibliographic record
Abstract
University of Waterloo,Waterloo, Ontario N2L 3G1, CanadaandPerimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5, CanadaandMax Planck Institute for Gravitational Physics (Albert Einstein Institute),Am Muhlenb erg 1, D-14476 Golm, Germany(Dated: December 21, 2010)In this short note we use results from the theory of crystallizations to prove that color in group eld theories garantees orientability of the piecewise linear pseudo-manifolds associated to eachgraph generated perturbatively. For the colored Boulatov model the only graphs which representorientable manifolds are those that have a particular relation between the perturbative order andthe number of 2- and 3- bubbles. This relation is the combinatorial requirement of having 3-bubbleswhich are homeomorphic to 2-spheres.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.013 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".