Positivity of relativistic spin network evaluations
Why this work is in the frame
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Bibliographic record
Abstract
Let G be a compact Lie group. Using suitable normalization conventions, we show that the evaluation of G x G-symmetric spin networks is non-negative whenever the edges are labeled by representations of the form V V* where V is a representation of G, and the inter twiners are generalizations of the Barrett-Crane intertwiner. This includes in particular the relativistic spin networks with symmetry group Spm(4) or 50(4) on a large class of graphs, not restricted to the graph underlying the lOj-symbol. We also present a counterexample, using the finite group 53, to the stronger conjecture that all spin network evaluations are non-negative as long as they can be written using only group integrations and index contractions. This counterexample applies in particular to the product of five Gj-symbols which appears in the spin foam model of the Ss-symmetric .BF-theory on the two-complex dual to a triangulation of the sphere 5 3 using five tetrahedra. We show that this product is negative real for a particular assignment of representations to the edges.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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