Path Counting for Grid-Based Navigation
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
Counting the number of shortest paths on a grid is a simple procedure with close ties to Pascal’s triangle. We show how path counting can be used to select relatively direct grid paths for AI-related applications involving navigation through spatial environments. Typical implementations of Dijkstra’s algorithm and A* prioritize grid moves in an arbitrary manner, producing paths which stray conspicuously far from line-of-sight trajectories. We find that by counting the number of paths which traverse each vertex, then selecting the vertices with the highest counts, one obtains a path that is reasonably direct in practice and can be improved by refining the grid resolution. Central Dijkstra and Central A* are introduced as the basic methods for computing these central grid paths. Theoretical analysis reveals that the proposed grid-based navigation approach is related to an existing grid-based visibility approach, and establishes that central grid paths converge on clear sightlines as the grid spacing approaches zero. A more general property, that central paths converge on direct paths, is formulated as a conjecture.
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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 | 0.008 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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