2785 — Code Distance Is a Perturbative Fine-Structure Selection Rule
For a commuting stabilizer Hamiltonian of distance (d), perturbed by Pauli terms of weight at most (w), no traceless logical effective term can occur below order . On an (L\times L) toric code with single-edge perturbations, the first allowed order is (L). Distance forbids lower orders but does not prove the leading coefficient nonzero or uniformly controlled.
- Packet:
research/kitaev/code-distance-is-a-perturbative-fine-structure-selection-rule.md - Checker:
research/kitaev/checkers/check_toric_fine_structure_order.py - Results:
research/kitaev/results/toric-fine-structure-order.json - Sequence:
seqclaim-b4bdb8a007fd43aafed5cfb9 - Epistemic graph:
ev-000000004267-40ac32ae-accb-466a-a193-2eff3b53ba72
Logical readout and Hamiltonian splitting remain separately typed. No commit or push was authorized.