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Bibliographic record
Abstract
The recently suggested bipartite analysis extends the Kauffman planar decomposition to arbitrary N, i.e. extends it from the Jones polynomial to the HOMFLY polynomial. This provides a generic and straightforward non-perturbative calculus in an arbitrary Chern–Simons theory. Technically, this approach is restricted to knots and links which possess bipartite realizations, i.e. can be entirely glued from antiparallel lock (two-vertex) tangles rather than single-vertex R-matrices. However, we demonstrate that the resulting positive decomposition (PD), i.e. the representation of the fundamental HOMFLY polynomials as positive integer polynomials of the three parameters ϕ, ϕ¯ and D, exists for arbitrary knots, not only bipartite ones. This poses new questions about the true significance of bipartite expansion, which appears to make sense far beyond its original scope, and its generalizations to higher representations. We have provided two explanations for the existence of the PD for non-bipartite knots. An interesting option is to resolve a particular bipartite vertex in a not-fully-bipartite diagram and reduce the HOMFLY polynomial to a linear combination of those for smaller diagrams. If the resulting diagrams correspond to bipartite links, this option provides a PD even to an initially non-bipartite knot. Another possibility for a non-bipartite knot is to have a bipartite clone with the same HOMFLY polynomial providing this PD. We also suggest a promising criterium for the existence of a bipartite realization behind a given PD, which is based on the study of the precursor Jones polynomials.
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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 | 0.001 |
| 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