Bibliographic record
Abstract
<p>Graph burning studies how fast a contagion, modelled as a set of fires, spreads in a graph. The burning process takes place in discrete time-steps, or rounds. In each round, a fire breaks out at a given node (or vertex), thus burning it. Between rounds, fires from burning nodes spread to adjacent nodes. The burning number of a graph G, denoted b(G), is the minimum number of rounds necessary for every node of G to burn. We consider b(Gm,n), where Gm,n is the m × n Cartesian grid. For m = ω( √ n), the asymptotic value of b(Gm,n) was determined, but only the growth rate of b(Gm,n) was investigated in the case m = O( √ n). Accordingly, we provide new explicit bounds on b(Gc √ n,n) for valid c > 0. Graph burning is analogous to a pebble game, which typically involves the placement of pebbles on nodes of a graph. Burning of a node is comparable to a pebbling step (or pebbling move): the removal of two pebbles from a node, where one of the removed pebbles is placed on an adjacent node while the other is discarded. In a certain pebble game iii variant (discussed in Section 1.7), the existence of a winning strategy has an interesting characterization: expressibility of the relevant constraint satisfaction problem (or CSP) in the logic programming language Datalog. If a structure with a non-empty domain is restricted to relation symbols only, then we call that structure a template. We show that the CSP for any finite template admitting terms of the weak J ́onsson type has a property known as bounded pathwidth duality. This implies the expressibility of the complement CSP in linear Datalog, and places the CSP in NL.</p> <p><br></p>
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How this classification was reachedexpand
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 | 0.000 |
| Open science | 0.001 | 0.004 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".