Bibliographic record
Abstract
This work solves a 28-year conjecture by showing that two major invariants of smooth 4-manifolds, the shadow model (motivated by statistical mechanics [V. G. Turaev, Topology of shadows (1991)]) and the simplicial Crane–Yetter model (motivated by topological quantum field theory [L. Crane and D. Yetter, A categorical construction of 4D topological quantum field theories, in Quantum Topology (World Scientific, 1993), pp. 120–130, https://doi.org/10.1142/9789812796387_0005 ]), are in fact equal. These invariants, both of which degenerate to the 3D Witten–Reshetikhin–Turaev model in a special case, had been open for years to clarify their relationship. Despite the seeming difference in their origins and formal constructions, we prove their equivalence. Along the way, we sketch a dictionary between the two models, provide a brief survey of the shadow construction à la Turaev, and suggest once again that the semisimple models have reached their limits.
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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 | 0.004 | 0.002 |
| 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".