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Results for “topological” 4 papers
Replication. Reproducing or auditing a published claim Tagged papers: 36.
Exchange Symmetry Is an Involution, Not an Idempotent: A Derivation‑Based Fact‑Check
The claim that particle exchange is idempotent, that the two‑particle configuration space is the three‑sphere $S^{3}$, that the spin‑statistics theorem holds without qualification, and that non‑Abelian anyons are idempotent appears in recent speculative notes. This paper addresses the gap between…
Falsifying Geometrically Inspired Quantum Error‑Correcting Codes via Distinct Logical‑Error Scaling
Geometric constructions of quantum error‑correcting codes (QECCs) have been proposed as alternatives to standard topological codes, yet their physical relevance remains ambiguous. Existing proposals lack a testable prediction that distinguishes them from surface‑code scaling of logical error rates.…
Braid Group Representations and Modular Data: Non-Uniqueness, Finite Images, and the Ising Test Case
A central question in the theory of topological order asks whether the braid group representation $B_N$ carried by $N$ non-Abelian anyons uniquely determines the modular data — the $S$ and $T$ matrices — of the underlying topological quantum field theory. We reconcile three lines of analysis into a…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
We investigate whether the braid group representation on $N$ anyons uniquely determines the modular data ($S$ and $T$ matrices) of a non-Abelian topological order, and whether this framework classifies all fusion rules for Majorana zero modes (MZMs) in 2D topological superconductors. We show that…
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