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
AbstractA fractional automorphism of a graph is a doubly stochastic ma-trix which commutes with the adjacency matrix of the graph. If weapply an ordinary automorphism to a set of vertices with a particularproperty, such as being independent or dominating, the resulting setretains that property. We examine the circumstances under whichfractional automorphisms preserve the fractional properties of func-tions on the vertex set. 1 Introduction In [6] a fractional isomorphism between two graphs with adjacency matricesA,B is defined to be a doubly stochastic matrix S with the property thatAS = SB. This definition is found by generalising the view of ordinarygraph isomorphisms as permutation matrices. It is natural to consider thecase when A = B; any doubly-stochastic matrix S such that SA = AS canbe considered a fractional automorphism. It is understood that a matrix hasthe property of being a fractional automorphism (or isomorphism) subjectto a certain ordering of the vertices, imposed by the ordering used in theadjacency matrix.Fractional automorphisms have been studied, though not under thatname, by Tinhofer in [4, 5] and Godsil in [2]. It is obvious that the set ofall fractional automorphisms of a graph with adjacency matrix A, which weshall denote by S(A), contains the convex hull of the set of automorphismstaken as permutation matrices; a graph is called compact if these two setsare in fact equal. While several classes of graphs are known to be compact,as yet no good characterisation of compact graphs has been found.
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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 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