Bibliographic record
Abstract
We develop the concept of anti-self dual Lagrangians that seems inherent to many problems in mathematical physics, Riemannian geometry, and differential equations. On one hand, they represent gradients of convex functions which usually drive dissipative systems, and on the other, their structure is rich enough to also cover – certain representations of – skew-symmetric operators which normally generate unitary flows. These Lagrangians provide variational formulations and resolutions for several non-potential boundary value problems many of which do not fit in the Euler–Lagrange theory. Solutions are minima of functionals of the form L ( u , Λ u ) where L is an anti-self dual Lagrangian and where Λ is a skew-adjoint operator. However, and just like the self (antiself) dual equations of quantum field theory (e.g. Yang–Mills) the equations associated to minimal solutions of our variational problems are not derived from the fact they are critical points of the associated functionals, but because they are also zeroes of the corresponding Lagrangians.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".