Bibliographic record
Abstract
This thesis constitutes a first attempt to derive aspects of standard model particle physics from purely abstract mathematical objects. We begin abstractly with an algebra, and argue that physical concepts such as particles, causality, and irreversible time may emerge from the algebra acting on itself. \n \n \nWe then focus on a special case by considering the algebra R⊗C⊗H⊗O, the tensor product of the only four normed division algebras over the real numbers. Using nothing more than R⊗C⊗H⊗O acting on itself, we set out to find standard model particle representations: a task which occupies the remainder of this text. \n \n \nFrom the C⊗H portion of the algebra, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model. \n \n \nFrom the C⊗O portion of the algebra, we find minimal left ideals, and show that they mirror the behaviour of a generation of quarks and leptons under su(3)_c and u(1)_em. These unbroken symmetries, su(3)_c and u(1)_em, appear uniquely in this model as symmetries of the algebra's ladder operators. Electric charge, here, is seen to be simply a number operator for the system. \n \n \nWe then combine the C⊗H and C⊗O portions of R⊗C⊗H⊗O, and focus on a leptonic subspace, so as to demonstrate a rudimentary electroweak model. Here, the underlying ladder operators are found to have a symmetry generated uniquely by su(2)_L and u(1)_Y. Furthermore, we find that this model yields a straightforward explanation as to why SU(2)_L acts only on left-handed states. \n \n \nWe then make progress towards a three-generation model. The action of C⊗O on itself can be seen to generate a 64-complex-dimensional algebra, wherein we are able to identify generators of SU(3)_c. We apply these generators to the rest of the space, and find that it breaks down into the SU(3)_c representations of exactly three generations of quarks and leptons. Furthermore, we show that these three-generation results can be extended, so as to include U(1)_em charges.
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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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".