Systematic Escape Using Billiard Moves
Bibliographic record
Abstract
We consider a robot that can move in a straight line, until it hits any wall of a given 2D rectangle room. If the robot hits a corner of the room then it will stop, otherwise the robot bounces off the wall using the laws of reflection and again move in another straight line. The room may contain an unbroken opening of unit length on a wall, which is unknown to the robot. If the robot reaches any point of the opening with a non-zero angle, then it escapes through the opening. The objective of the problem is to devise an algorithm for the robot which enables it to find if there is an opening on the perimeter of any given rectangle or detect that the room contains no opening. This work is a continuation of our previous publication [1], where we presented an algorithm that enables the robot to find the opening or correctly declare that there is none, when any two adjacent sides of the rectangle are integer and co-prime. In this work, we study the problem for rectangles of any lengths and we have proposed a strategy where the robot is guaranteed to find the opening or correctly declare that there is none. Additionally, We provide other interesting results related to our proposed algorithm.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".