Boundaries and variant axes

Honeycomb geometry, Pauli schedule, boundary termination, qudit dimension, and physical circuit are independent design axes. This map prevents results from one axis choice from being silently attached to another.

Open boundaries

Planar Floquet Codes shows why a large instantaneous distance is not enough: short spacetime fault paths can use a boundary and the measurement order. Boundaries must be designed together with detectors.

Boundaries for the Honeycomb Code gives terminations compatible with the original Pauli pattern and planar logical encodings. This Atlas constructor implements only closed tori. It does not infer a planar patch by deleting wraparound edges because doing so would omit boundary checks, schedule changes, detector endpoints, and readout rules.

Pauli-pattern variants

CSS honeycomb. Davydova, Tantivasadakarn, and Balasubramanian introduce schedules with CSS measurements and no parent subsystem code. The shared lattice does not make its ISG, detector graph, or gate set identical to the Hastings-Haah code.
X3Z3. Setiawan and McLauchlan tailor a dynamical code to biased noise and retain a stabilizer-product symmetry. Its bias performance belongs to its changed Pauli pattern and circuits.
Aperiodic dynamic trees. Switching among schedules changes the temporal code itself; period-three rank checks do not certify an aperiodic protocol.

Geometry variants

Hyperbolic Floquet codes. Negative-curvature constructions trade Euclidean locality for finite rate and logarithmic distance. A reported [[400,52,8]] instance and its thresholds are properties of that hyperbolic family, not a large honeycomb torus.
Twist networks. Condensation lines and twist endpoints change the defect content while retaining trivalent connectivity and two-body measurements.
Three-dimensional descendants. Tricoordinated 3D schedules can realize fermionic toric or fracton orders with different logical sectors. They are not additional (L1,L2) instances of this entry.

Hardware and fabrication variants

McLauchlan, Gehér, and Moylett remove defective qubits and stabilizers without adding connectivity, then simulate planar performance under a fabrication-defect model. Their roughly 12% fabrication-defect tolerance is tied to that prescription and model. Deleting a vertex from the torus constructor without implementing the compensating schedule would not reproduce it.

Claes's dynamic circuit changes which physical qubits act as data and measurement resources. Majorana and spin-photonic proposals change the native fault alphabet. These are circuit variants even when the ideal parity graph looks familiar.

Qudit and defect generalizations

Twist constructions extend the schedule to Z_N qudits and use fermion-condensation lines for protected processing. Qudit commutation phases, detector values, and decoder alphabets differ from binary symplectic arithmetic. The present Pauli and CheckMatrix objects are qubit-only and do not machine-certify those variants.

Transfer matrix

claim	torus original	planar original	CSS/X3Z3	hyperbolic/qudit
local weight-two ideal checks	yes	often	often	construction-dependent
shipped `dynamic_k = 2`	yes	no transfer	no transfer	no transfer
torus face-color constraint	yes	boundary removes it	schedule-dependent	geometry-dependent
periodic MWPM graph	source model	rebuild boundaries	rebuild Pauli/circuit model	rebuild geometry
original anyon exchange	source result	boundary action needs analysis	variant-dependent	phase-dependent

The safe rule is simple: locality may transfer as motivation; logical counts, distance, thresholds, and operations require a fresh certificate.