Representation dictionary

No single representation makes every Honeycomb claim transparent. The useful maps form a chain, and every arrow has a different proof status.

Schedule and ISG

Objects: measured Pauli words grouped into ordered rounds; a commuting binary symplectic row space updated after each outcome.

Best for: exact round content, commutation within a round, startup rank, periodic rank, dynamic_k, and machine export.

Atlas status: executable. constructor.py, Schedule, and ISGTracker recompute these facts.

Blind spot: physical outcome signs, preparation/readout circuits, detectors, and geometry coordinates are not present.

Plaquette backbone and moving matching

Objects: rank-eight span of weight-six plaquette products plus the currently measured perfect matching.

Best for: understanding the steady ISG rank and why incompatible measurements do not erase the code.

Atlas status: recomputed by reproduce.py; the first plaquette words and all row-space memberships are asserted.

Blind spot: the logical anyon labels require the toric-frame conversion.

Instantaneous toric code

Map: contract the just-measured matching and apply local Clifford changes of basis.

Best for: two torus logical qubits, winding strings, topological order, and the meaning of electric/magnetic labels.

Atlas status: curated from Hastings-Haah. The current engine checks the rank consequence but does not replay the local Clifford circuit.

Blind spot: one frame omits measurement faults and logical transport through time.

Majorana / parton gauge theory

Represent a spin by four Majoranas b^x,b^y,b^z,c with a local parity constraint. A directional edge term factors schematically as

sigma_u^a sigma_v^a = (i b_u^a b_v^a)(i c_u c_v).

The first factor is a Z2 gauge link and the second pairs matter Majoranas. Plaquette products become gauge fluxes. Cycling measurements changes the pairing pattern.

Best for: the local anticommuting edge algebra, gauge-invariant plaquettes, and weak/coherent-measurement extensions.

Atlas status: curated from Kitaev and later monitored-fermion work. There is no generic fermionic compiler in the repository, so this view is not machine-derived.

Blind spot: a static Kitaev Hamiltonian and a projective measurement schedule have different dynamics.

Spacetime detector model

Map: compile the physical parity circuit into measurement outcomes, detector parities, logical observables, and fault-to-detector incidence.

Best for: matching, correlations, timelike boundaries, leakage, logical error rates, and fault distance.

Atlas status: literature-curated. The ideal schedule is exported, but no Honeycomb circuit/DEM is produced by this constructor.

Blind spot: detector graphs depend on the circuit and noise model; there is no circuit-independent threshold graph.

Anyon automorphism

Map: compose the local equivalences between consecutive instantaneous topological frames.

Best for: the e <-> m exchange, logical-frame transport, twist defects, and cross-cap gates.

Atlas status: curated from Hastings-Haah and the automorphism-code framework.

Blind spot: naming an automorphism does not supply detector circuits or hardware costs.

Measurement QCA

Objects: a locality-preserving transformation of quantum information induced by periodic measurement and classical outcomes.

Best for: anomalous boundary information flow and why bulk stabilizer rank misses boundary dynamics.

Atlas status: curated from Aasen, Haah, Li, and Mong.

Blind spot: the classification is coarser than a device noise model.

ZX spacetime

Objects: a graphical tensor network in which parity measurements, preparations, fusions, and feed-forward are ZX nodes and connections.

Best for: relating circuit, measurement-based, fusion-based, and Floquet protocols by local diagram rewrites.

Atlas status: curated from Bombin et al.; no Honeycomb ZX artifact ships with the entry.

Blind spot: a local diagram equivalence preserves logical structure under its assumptions, not the numerical noise performance of every physical realization.

Conversion ledger

This ledger prevents a derived rank from lending machine certainty to a curated conversion farther down the chain.