SurfaceCode
plain-language theorem explainer
SurfaceCode encodes the parameters of a 2D lattice stabilizer code with lattice size L, L squared physical qubits, one logical qubit and distance L. Quantum information researchers working in Recognition Science would cite the definition when mapping surface codes onto the eight-tick phase redundancy. The declaration is a plain structure with three default field assignments.
Claim. A surface code on an $L$-by-$L$ lattice is specified by lattice size $L$, $n_0 = L^2$ physical qubits, one logical qubit, and distance $L$.
background
The module derives quantum error correction from the eight-tick redundancy of Recognition Science, where the eight phases supply natural repetition that maps to stabilizer measurements. Surface codes are presented as the leading scalable approach, with qubits on a 2D lattice, plaquette stabilizers, and matching-based correction; the 2D geometry is noted to relate to the holographic boundary. Upstream structures such as PhiForcingDerived.of supply the J-cost framework while SpectralEmergence.of fixes the gauge content and generation count that any RS-derived code must respect.
proof idea
The declaration is a structure definition that directly assigns the three default values n_physical := L * L, n_logical := 1 and distance := L.
why it matters
The definition supplies the concrete interface for surface codes inside the QEC module whose target is to derive error correction from eight-tick redundancy (T7). It records the holographic-boundary remark that links the 2D lattice to the Recognition Science forcing chain. No downstream theorems are listed, leaving open the explicit embedding into the eight-tick logical code.
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