A constructive approach for reducing the state complexity of self-dual lattices
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Bibliographic record
Abstract
This work presents a systematic method to successively minimize the state complexity of the self-dual lattices. This is based on representing the lattice on an orthogonal co-ordinate system corresponding to the Gram-Schmidt (GS) vectors of a Korkin-Zolotarev (KZ) reduced basis. We give expressions for the GS vectors of a KZ basis of the E/sub 8//sup (3/), K/sub 12/, BW/sub n/ and /spl Lambda//sub 24/ lattices. Using the proposed method, we have re-derived the trellis diagrams given previously in a systematic and unified approach. It is also shown that for certain complex representation of the /spl Lambda//sub 24/ and the BW/sub n/ lattices, we have: (i) the corresponding GS vectors are along the standard co-ordinate system, and (ii) the branch complexity at each section of the resulting trellis meets a given lower bound. This results in a very efficient trellis representation for these lattices.
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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 | 0.001 | 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 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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