Quantum statistics in Network Geometry with Fractional Flavor
Bibliographic record
Abstract
Abstract Quantum statistics have been shown to emerge to describe the statistical properties of growing networks when nodes are associated to a fitness value. Recently it has been shown that quantum statistics emerge also in a growing simplicial complex model called Network Geometry with Flavor (NGF) which allows for the description of many-body interactions between the nodes. This model depends on an external parameter called flavor that is responsible for the underlying topology of the simplicial complex. When the flavor takes the value s = −1 the d -dimensional simplicial complex is a manifold in which every -dimensional face can only have an incidence number . In this case the faces of the simplicial complex are naturally described by the Bose–Einstein, Boltzmann and Fermi–Dirac distribution depending on their dimension. In this paper we extend the study of NGF to fractional values of the flavor s = −1/ m in which every -dimensional face can only have incidence number . We show that in this case the statistical properties of the faces of the simplicial complex are described by the Bose–Einstein or the Fermi–Dirac distribution only. Finally we comment on the spectral properties of the networks constituting the underlying structure of the considered simplicial complexes.
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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 | 0.001 | 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) | 0.002 | 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 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".