Separating layered treewidth and row treewidth
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
Layered treewidth and row treewidth are recently introduced graph parameters that have been key ingredients in the solution of several well-known open problems. It follows from the definitions that the layered treewidth of a graph is at most its row treewidth plus 1. Moreover, a minor-closed class has bounded layered treewidth if and only if it has bounded row treewidth. However, it has been open whether row treewidth is bounded by a function of layered treewidth. This paper answers this question in the negative. In particular, for every integer $k$ we describe a graph with layered treewidth 1 and row treewidth $k$. We also prove an analogous result for layered pathwidth and row pathwidth.
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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.004 | 0.006 |
| 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 it