Dual relations and the branch‐dualising rule of the duality principle
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The most important dual relationships of the duality principle include the relationship between node and mesh, and the relationship between branch and branch. They both appear in the patterns of duality, and the latter is also further represented as dual relations of the passive elements, of the active elements, of the controlled‐source elements, of the switching elements and also of the two‐port coupling elements. This study presents the branch‐dualising rule of the duality principle by joining the topological graphs of dual circuits together with physical properties of their elements, proves its adaptability for all the regular circuits and gives a solution for non‐regular circuit elements with each just put into a dual element list of the rule one after another after finding its specific dualising mode. The branch‐dualising rule is easy and practical for use to obtain the dual circuit diagram directly from its primal, greatly expanding the range of applications of the duality principle.
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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 | 0.000 |
| 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