Weak topological phases in the presence of interactions
Bibliographic record
Abstract
We study weak symmetry-protected topological phases (SPTs) in the presence of short-range interactions. By comparing homotopical free and interacting classifications of these SPTs, we predict their stability under interactions as well as identify potential intrinsically-interacting phases. We mathematically compute the groups of weak phases in dimensions zero through three for all tenfold-way symmetry types using homotopy theory; specifically, we use Atiyah's Real $\mathit{KR}$-theory and the low-energy invertible field theory ansatz of Freed--Hopkins for the free and interacting cases, resp. Our computational techniques involve T-duality, which relates $K$-theory of the spatial torus with $K$-theory of the Brillouin torus, and a binomial formula for computing generalized cohomology of a torus. Our results carry potential implications for theoretical and experimental studies of weak phases.
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How this classification was reachedexpand
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 | 0.000 | 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 | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".