Why this work is in the frame
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Bibliographic record
Abstract
We present a method which efficiently generates Lie group invariants in the classical invariant theory of polynomials and its extensions to vector spaces of inhomogeneous polynomials under the actions of the general affine group and pseudo-Euclidean subgroups.Our derivation of the invariants uses the classical Cartan method of moving frames and requires no assumption on the degree of the polynomial or the number of variables.Consequently, we are able to express the invariants in a compact indicial notation.We employ our results to solve the equivalence and canonical forms problems for the vector space of inhomogeneous cubic polynomials in two real variables under the action of the Euclidean group.We show that the space partitions into twelve distinct classes of canonical forms, each admitting a system of invariants which globally separates its associated orbits.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.001 | 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