Congruences and trajectories in planar semimodular lattices
Why this work is in the frame
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Bibliographic record
Abstract
A 1955 result of J. Jakubík states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size). The problem is how to determine whether con(p) ≥ con(q) involving only prime intervals. Two recent papers approached this problem in different ways. G. Czédli’s used trajectories for slim rectangular lattices-a special subclass of slim, planar, semimodular lattices. I used the concept of prime-projectivity for arbitrary finite lattices. In this note I show how my approach can be used to reprove Czédli’s result and generalize it to arbitrary slim, planar, semimodular lattices.
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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 | 0.000 | 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