Random finite noncommutative geometries and topological recursion
Bibliographic record
Abstract
In this paper, we investigate a model for quantum gravity on finite noncommutative spaces using the theory of blobbed topological recursion. The model is based on a particular class of random finite real spectral triples {(\mathcal{A}, \mathcal{H}, D, \gamma, J)} , called random matrix geometries of type {(1,0)} , with a fixed fermion space {(\mathcal{A}, \mathcal{H}, \gamma, J)} and a distribution of the form {e^{- \mathcal{S} (D)}\, {\mathrm{d}} D} over the moduli space of Dirac operators. The action functional {\mathcal{S} (D)} is considered to be a sum of terms of the form {\prod_{i=1}^s \mathrm{Tr} ({D^{n_i}})} for arbitrary {s \geqslant 1} . The Schwinger–Dyson equations satisfied by the connected correlators {W_n} of the corresponding multi-trace formal 1-Hermitian matrix model are derived by a differential geometric approach. It is shown that the coefficients {W_{g,n}} of the large N expansion of {W_n} ’s enumerate discrete surfaces, called stuffed maps, whose building blocks are of particular topologies. The spectral curve {( {\Sigma, \omega_{0,1}, \omega_{0,2}} )} of the model is investigated in detail. In particular, we derive an explicit expression for the fundamental symmetric bidifferential {\omega_{0,2}} in terms of the formal parameters of the model.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".