Bibliographic record
Abstract
The \textit{metric dimension} of a graph Γ = ( V , E ) , denoted by dim ( Γ ) , is the least cardinality of a set of vertices in Γ such that each vertex in Γ is determined uniquely by its vector of distances to the vertices of the chosen set. The topological distance between an edge ε = y z ∈ E and a vertex k ∈ V is defined as d ( ε , k ) = min { d ( z , k ) , d ( y , k ) } . A subset of vertices R Γ in V is called an edge resolving set for Γ if for each pair of different edges e 1 and e 2 in E , there is a vertex j ∈ R Γ such that d ( e 1 , j ) ≠ d ( e 2 , j ) . An edge resolving set with minimum cardinality is called the edge metric basis for Γ and this cardinality is the edge metric dimension of Γ , denoted by dim E ( Γ ) . In this article, we show that the cardinality of the minimum edge resolving set is three or four for two classes of convex polytopes ( S n and T n ) that exist in the literature.
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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 | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".