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 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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".