Diffusion characters: Breaking the spectral barrier
Why this work is in the frame
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Bibliographic record
Abstract
Combinatorial graphs are used as mathematical models of a broad variety of phenomena including communications networks, gene regulation networks, food webs, or even to map out resource conflicts. The diffusion character matrix of a graph injects the vertices of a graph into Euclidean space so that Euclidean distances between vertices are closely tied to connectivity between those vertices in the graph. In this paper diffusion characters and their associated matrices are defined, elementary properties are derived, and it is demonstrated that diffusion character matrices contain information not contained in the eigenvalues of the graph. This latter property is demonstrated by computing the diffusion character matrices of two famous co-spectral graphs, two of the three (3,10)-cages, which are cubic graphs on 70 vertices.
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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 | 0.000 | 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 | 0.001 |
| 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 it