Structure in Stable Matching Problems
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
In this thesis we provide two contributions to the study of structure in stable matching problems. The first contribution is a short new proof for the integrality of Rothblum’s linear description of the convex hull of incidence vectors of stable matchings in bipartite graphs. The key feature of our proof is to show that extreme points of the formulation must have a 0, 1-component. \nThe second contribution is a computer search procedure for instances of cyclic stable matching problems with three genders as proposed by Knuth. We provide sufficient conditions for the existence of a stable matching in this context. We also investigate bijections of the problem instance vertex set to itself which preserve the set of stable matchings (up to permutation). Such bijections define “symmetric” problem instances. We study this notion of symmetry, and use it to cut down on the number of problem instances in our search. We implemented our proposed computational procedure in Java and end with a discussion of the results running computational experiments using our code on problem instances of size 5.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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