Generalized Matryoshka: Computational Design of Nesting Objects
Why this work is in the frame
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Bibliographic record
Abstract
Abstract This paper generalizes the self‐similar nesting of Matryoshka dolls (“Russian nesting dolls”) to arbitrary solid objects. We introduce the problem of finding the largest scale replica of an object that nests inside itself. Not only should the nesting object fit inside the larger copy without interpenetration, but also it should be possible to cut the larger copy in two and remove the smaller object without collisions. We present a GPU‐accelerated evaluation of nesting feasibility. This test can be conducted at interactive rates, providing feedback during manual design. Further, we may optimize for some or all of the nesting degrees of freedom (e.g., rigid motion of smaller object, cut orientation) to maximize the smaller object's scale while maintaining a feasible nesting. Our formulation and tools robustly handle imperfect geometric representations and generalize to the nesting of dissimilar objects in one another. We explore a variety of applications to aesthetic and functional shape design.
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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