Bibliographic record
Abstract
Abstract Let v ≥ k ≥ 1 and λ ≥ 0 be integers. A block design BD( v , k , λ) is a collection of k -subsets of a v -set X in which every unordered pair of elements from X is contained in exactly λ elements of . More generally, for a fixed simple graph G , a graph design GD( v , G , λ) is a collection of graphs isomorphic to G with vertices in X such that every unordered pair of elements from X is an edge of exactly λ elements of . A famous result of Wilson says that for a fixed G and λ, there exists a GD( v , G , λ) for all sufficiently large v satisfying certain necessary conditions. A block (graph) design as above is resolvable if can be partitioned into partitions of (graphs whose vertex sets partition) X . Lu has shown asymptotic existence in v of resolvable BD( v , k , λ), yet for over twenty years the analogous problem for resolvable GD( v , G , λ) has remained open. In this paper, we settle asymptotic existence of resolvable graph designs.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.035 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".