Bibliographic record
Abstract
Let V={1,…,n} be a finite set. An r-configuration is a mapping p:V→Rr, where p1,…,pn are not contained in a proper hyper-plane. A framework G(p) in Rr is an r-configuration together with a graph G=(V,E) such that every two points corresponding to adjacent vertices of G are constrained to stay the same distance apart. A framework G(p) is said to be generic if all the coordinates of p1,…,pn are algebraically independent over the integers. A framework G(p) in Rr is said to be unique if there does not exist a framework G(q) in Rs, for some s, 1≤s≤n−1, such that ||qi−qj||=||pi−pj|| for all (i,j)∈E. In this paper we present a sufficient condition for a generic framework G(p) to be unique, and we conjecture that this condition is also necessary. Connections with the closely related problems of global rigidity and dimensional rigidity are also discussed.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.003 | 0.006 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.005 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 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".