Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
For a set $\mathcal{S}$ of connected graphs, a subgraph $F$ of a graph $G$ is defined as an $\mathcal{S}$-factor of $G$ if $F$ satisfies that $V(F)=V(G)$ and every component of $F$ is isomorphic to an element of $\mathcal{S}$. If every component of $F$ is a star, then $F$ is said to be a star-factor. A star-factor with size at most $n$ may be written for a $\{K_{1,t}: 1\leq t\leq n\}$-factor. A graph $G$ is called a $\{K_{1,t}: 1\leq t\leq n\}$-factor deleted graph if $G-e$ has a $\{K_{1,t}: 1\leq t\leq n\}$-factor for every $e\in E(G)$. The sun toughness of a graph $G$ is denoted by $s(G)$ and defined as follows :$$ s(G)=\min \big\{\frac{|X|}{sun(G-X)}: X\subseteq V(G), \ sun(G-X)\geq2 \big\} $$ if $G$ is not a complete graph, and $s(G)=+\infty$ if $G$ is a complete graph, where $sun(G-X)$ denotes the number of sun components of $G-X$. In this paper, we prove that (1) if $G$ is a connected graph, and its sun toughness satisfies $s(G)\geq\frac{1}{n}$, then $G$ admits a $\{K_{1,t}: 1\leq t\leq n\}$-factor; (2) if $G$ is a $(k+1)$-connected graph, and its sun toughness $s(G)>\frac{k+1}{n+1}$, then $G-Y$ admits a $\{K_{1,t}: 1\leq t\leq n\}$-factor for any $Y\subseteq V(G)$ with $|Y|=k$; (3) if $G$ is a 2-edge-connected graph, and its sun toughness $s(G)\geq\frac{1}{n-1}$, then $G$ is a $\{K_{1,t}: 1\leq t\leq n\}$-factor deleted graph. Furthermore, it is shown that our results are sharp.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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