Heinz Quarter Mean Labeling of Some Special Graphs
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Bibliographic record
Abstract
A graph 𝐺 = (𝑉, 𝐸) having a number of vertices as 𝑝 and a number of edges as 𝑞 can be called a Heinz – Quarter Mean graph if the vertices 𝑥 ∈ 𝑉 can be labeled with distinct labels 𝑓(𝑥) from 1, 2, 3, … … , 𝑞 + 1. Here, each edge is labeled with 𝑓(𝑒 =𝑢𝑣)=⌊ √𝑓(𝑢)𝑓(𝑣) 4 (√𝑓(𝑢)+√𝑓(𝑣) ) 2 ⌋ or ⌈ √𝑓(𝑢)𝑓(𝑣) 4 (√𝑓(𝑢)+√𝑓(𝑣) ) 2 ⌉, then the resulting edge labels are distinct. Here, f is called Heinz – Quarter mean labeling of 𝐺. In this section, we investigate the Heinz Quarter Mean Labeling of some special named graphs.
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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 | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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