Sixfold Discrete Symmetry of Fermion Fields as Explanation for Dark Matter
Bibliographic record
Abstract
We address the question, what is dark matter? The method used is the Pauli algebra form of the Dirac equation, equivalent to the standard one but allowing to use the multiplicative structure of the algebra. In this form discrete symmetries of fermion fields are the same as the automorphisms of the Pauli group. We construct the prototype Dirac equation in the Clifford algebra and then use its six representations by complex two by two matrices to construct the six symmetric versions, indexed by permutations of three letters. The solutions of symmetric equations form the six sectors of fermion fields. It is shown that the sectors are genuinely distinct, by proving that any fermion field belonging to two different sectors must have mass zero. Also shown is the lack of electromagnetic interaction between one sector and another, since each sector has its own matrix coupling the fermion field to the electromagnetic field. The key tool used is the mass inversion symmetry, introduced in []. The sixfold symmetry predicts the ratio of dark to ordinary matter of 5:1 which is close to the observed ratio of 5.2:1. However this symmetry is constructed only for interactions between fermion fields and the electromagnetic field, not yet taking into account the weak and strong interactions. So this article is an indication that maybe the complete answer can be found if the sixfold symmetry extends to these interactions.
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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 | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".