This entry is the exact binary qubit CSS stabilizer code with generator row space span{XXXX, ZZZZ}. Local Clifford changes, qubit permutations, logical symplectic relabelings, circuit encoders, and different drawn squares may present an equivalent code, but the constructor fixes one representative so claims can be recomputed.
The four-term logical basis in the constructor is a presentation choice. The stabilizer row space, logical dimension, and distance are identity-level facts.
Rains describes the even-length optimal additive family with global X and Z checks. Self, Benedetti, and Amaro call the resulting [[k+2,k,2]] family Iceberg in an error-detected circuit setting (Rains, Self et al.). At its smallest nontrivial size it has exactly the two stabilizers exported here, so special_case_of iceberg is a typed relation.
The direction matters: this entry is not widened to arbitrary k. A family-scale penalty Hamiltonian or experiment must state whether its result was actually obtained at the four-qubit member.
A protocol may designate one encoded qubit as protected data and the other as gauge or a fixed spectator. Then the same four-qubit stabilizer space is used as a [[4,1,2]] subsystem code for that protocol. Linke's trapped-ion demonstration and Takita's superconducting preparation use this boundary explicitly. The physical block is the same; the protected logical contract is narrower.
This is not permission to rewrite the entry parameter as k=1. The constructor still has a four-dimensional codespace. A protocol-level gauge choice belongs in realizations and pedagogy.
The CPC formalism gives an encoder/check circuit presentation of a [[4,2,2]] detector. Roffe and collaborators implement such a presentation on IBM hardware (primary source). CPC is a broader circuit framework, not a second stabilizer identity and not a typed relation in the current Atlas grammar.
Rotated Surface patch. A four-data distance-two rotated patch commonly encodes one logical qubit and contains boundary checks of smaller support. It is not generated solely by the two global parities. A shared square drawing does not establish a relation to the live surface entry.
Color-code face. One four-body face operator inside a 4.8.8 or triangular color code is a local check, not the whole global-parity block. Removing checks from a color-code layout can participate in a larger concatenated construction, as in Criger–Terhal, but that construction is not a direct relation from this block to color_666 or toric.
Five-qubit and Steane codes. These are neighboring small stabilizer codes with different lengths, dimensions, distances, and check row spaces. Being listed together or used in comparative experiments is a bibliographic cousin relation, not one of the typed algebraic Atlas relations.
Error-prevention protocol. Vaidman, Goldenberg, and Wiesner use the four-particle encoding with frequent projection in a quantum-Zeno error prevention scheme (primary source). The projection schedule and slow independent-noise assumption are protocol claims. They do not turn the static block into an active unknown-position corrector.
The square arranges the four qubits so the chosen logical basis forms its edges. The two stabilizer spokes touch every node. This is a verified incidence scene: it says exactly which operator touches which qubit. It does not claim a lattice Hamiltonian, nearest-neighbor extraction, a Surface-code face, or a color-code cell. The tour states this before using the geometry.