Bibliographic record
Abstract
In 1997, Kitaev introduced the toric code as an error-tolerant model for quantum computations, which has become a prominent model in recent years. This thesis is dedicated to providing a detailed exploration of Pieter Naaijkens’ work on the toric code in the thermodynamic limit. The primary focus of this thesis is providing an exposition on local Hamiltonians for the toric code and their ground states, showing that Haag duality holds for cones in the corresponding ground state representation. That is, given a cone Λ, the von Neumann algebras R_Λ and R_Λ_c of observables localized in Λ and Λ_c respectively are each other’s commutant. We also show that given Haag duality, we also have the distal split property, which states that if Λ_1 ⊂ Λ_2 are two cones with sufficiently separated boundaries, then there is a Type I factor M such that R_Λ_1 ⊂ M ⊂ R_Λ_2.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".