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 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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".