Polynomial identities for ternary intermolecular recombination
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Bibliographic record
Abstract
The operation of binary intermolecular recombination, originating in the theory of DNAcomputing, permits a natural generalization to $n$-ary operations which performsimultaneous recombination of $n$ molecules. In the case $n = 3$, we use computeralgebra to determine the polynomial identities of degree $\le 9$ satisfied by this trilinearnonassociative operation. Our approach requires computing a basis for the nullspace ofa large integer matrix, and for this we compare two methods: the row canonical form, andthe Hermite normal form with lattice basis reduction. In the conclusion, we formulatesome conjectures for the general case of $n$-ary intermolecular recombination.
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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 | 0.001 | 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