Quarter-Earth tunnel motion under gravity and frictional forces
Why this work is in the frame
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Bibliographic record
Abstract
Abstract This study investigates the motion of a body through quarter-Earth gravity tunnels using three tunnel configurations under both frictionless and frictional conditions. Unlike traditional center-to-center or chord-based models, the quarter-Earth setup introduces a tunnel configuration that explores partial subsurface traversal between two distant surface points, offering a framework for analyzing how geometry and friction jointly govern motion behavior. Key performance metrics, travel time, maximum velocity, traveled distance, and tunnel-wall reaction forces, are analyzed as functions of tunnel geometry. In the absence of friction, one configuration yields the shortest travel time, while another achieves a higher velocity at the cost of excessive reaction forces. When friction is introduced, energy loss limits motion, making the traveled distance the primary indicator of performance. Threshold conditions for motion initiation and arc traversal are also explored, revealing their dependence on tunnel radius and friction level. The study demonstrates that tunnel design plays a critical role in determining motion efficiency and feasibility. It also provides meaningful pedagogical value by introducing Newtonian mechanics through the context of non-uniform gravitational fields, incorporating numerical modeling, energy conservation, and nonlinear dynamics governed by complex equations of motion.
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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