Recursive comparison tests for dicot and dead-ending games under misère play
Bibliographic record
Abstract
In partizan games, where players Left and Right may have different options, there is a partial order defined as preference by Left: G ⩾ H if Left wins G + X whenever she wins H + X for any game position X. In normal play, there is an easy test for comparison: G ⩾ H if and only if Left wins G−H playing second. In misère play, where the last player to move loses, the same test does not apply-for one thing, there are no additive inverses-and very few games are comparable. If we restrict the arbitrary game X to a subset of games u, then we may have G ⩾ H “modulo U”; but without the easy test from normal play, we must give a general argument about the outcomes of G + X and H + X for all X ∈ U. In this paper, we use the novel theory of absolute combinatorial games to develop recursive comparison tests for the well-studied universes of dicots and dead-ending games. This is the first constructive test for comparison of dead-ending games under misère play using a new family of end-games called perfect murders.
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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 | 0.004 | 0.025 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.002 | 0.009 |
| Scholarly communication | 0.004 | 0.011 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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".