Combinatorial decompositions, Kirillov-Reshetikhin invariants and the\n Volume Conjecture for hyperbolic polyhedra
Bibliographic record
Abstract
We suggest a method of computing volume for a simple polytope $P$ in\nthree-dimensional hyperbolic space $\\mathbb{H}^3$. This method combines the\ncombinatorial reduction of $P$ as a trivalent graph $\\Gamma$ (the $1$-skeleton\nof $P$) by $I-H$, or Whitehead, moves (together with shrinking of triangular\nfaces) aligned with its geometric splitting into generalised tetrahedra. With\neach decomposition (under some conditions) we associate a potential function\n$\\Phi$ such that the volume of $P$ can be expressed through a critical values\nof $\\Phi$. The results of our numeric experiments with this method suggest that\none may associated the above mentioned sequence of combinatorial moves with the\nsequence of moves required for computing the Kirillov-Reshetikhin invariants of\nthe trivalent graph $\\Gamma$. Then the corresponding geometric decomposition of\n$P$ might be used in order to establish a link between the volume of $P$ and\nthe asymptotic behaviour of the Kirillov-Reshetikhin invariants of $\\Gamma$,\nwhich is colloquially know as the Volume Conjecture.\n
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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 | 0.000 | 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 | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".