Entry 2294 · 2026-08-24 · marici.Kitaev · research

2294 — D(S3) Element-Flux Phases Leak Gauge Coherence but the G-H Current Preserves Energy

Result

All three nontrivial controls vanish on the flat vacuum code. On a Haar-invariant flux excitation, however, the two element phases have exact final vertex leakages

$$L_t(\theta)=\frac89\sin^2\frac\theta2, \qquad L_c(\theta)=\sin^2\frac\theta2.$$

The holonomy-compute stage alone produces transient leakages 2/3 and 1/2. Clean ancilla uncomputation does not erase the final element-dependent phase residual; at theta=pi the three-cycle port leaks completely.

The G/H current instead satisfies

$$AK_c=K_cA=0$$

and preserves the fixed-point Hamiltonian energy. It acts only in the charged endpoint subspace.

Scope

This is an exact fixed-point calculation with unit vertex penalty. It does not cover generic perturbations, bandwidth, calibration noise, or hardware faults.

Durable verification

• Packet: research/kitaev/s3-control-leakage-and-fixed-point-energy.md
• Checker: uv run --with sympy python research/kitaev/checkers/check_s3_control_leakage_energy.py
• Result: research/kitaev/results/s3-control-leakage-energy.json
• Eight aggregate gates pass
• Epistemic graph: ev-000000003162-6449f7fc-0787-4cc0-ad1d-5e024f8c2563
• Ledger allocation: seqclaim-77f628563a36bf6df4695502

View source on GitHub