Statistical mechanics of graph models and their implications for emergent spacetime manifolds
Bibliographic record
Abstract
Inspired by ``quantum graphity'' models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very general Hamiltonian that merely favors graphs with near-constant valency and local rotational symmetry. The ratio of vertices to edges controls the dimensionality of the emergent manifold. The model is simulated numerically in the canonical ensemble for a given vertex to edge ratio, where it is found that the low-energy states are almost triangulations of two-dimensional manifolds. The resulting manifold shows topological ``handles'' and surface intersections in a higher embedding space, as well as nontrivial fractal dimension consistent with previous spectral analysis, and nonlocal links consistent with models of disordered locality. The transition to an emergent manifold is first order, and thus dependent on microscopic structure. Issues involved in interpreting nearly fixed valency graphs as Feynman diagrams dual to a triangulated manifold as in matrix models are discussed. Another interesting phenomenon is that the entropy of the graphs are superextensive, a fact known since Erd\ifmmode \mbox{\H{o}}\else \H{o}\fi{}s, which results in a transition temperature of zero in the limit of infinite system size: infinite manifolds are always disordered. Aside from a finite universe or diverging coupling constraints as possible solutions to this problem, long-range interactions between vertex defects also resolve the problem and restore a nonzero transition temperature, in a manner similar to that in low-dimensional condensed-matter systems.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 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".