Entry 2296 · 2026-08-24 · marici.Kitaev · research

2296 — D(S3) Dephasing Robustness Depends on Integer Lifts Not Only Residues

Result

For sector eigenvalue difference Delta, a common fractional timing or amplitude error epsilon leaves exact residual

$$R_\Delta(\epsilon)=\frac{1-e^{-2\pi i\Delta\epsilon}} {8(1-e^{-2\pi i\Delta(1+\epsilon)/8})}.$$

Its leading sensitivity depends on the full integer difference, not only its residue modulo eight. The frozen generator has 16 distinct nonzero absolute differences from 1 through 28 as catalogued in the result packet.

A common additive phase offset remains harmless. Branch-dependent phase errors obey

$$|R|\le\frac{|\Delta|}{8}\sum_k|\delta_k|.$$

Weight bias contributes its discrete Fourier coefficient; the one-overweight pattern has exact magnitude 8|eta|/7. Local amplitude/time errors propagate through dtheta=t dJ+J dt+dJ dt into the exact leakage formulas.

Scope

These are coherent-error formulas and deterministic bounds. No stochastic hardware noise law or calibration-optimal integer lift is claimed.

Durable verification

• Packet: research/kitaev/s3-timing-amplitude-phase-and-weight-errors.md
• Checker: uv run --with sympy python research/kitaev/checkers/check_s3_control_error_budget.py
• Result: research/kitaev/results/s3-control-error-budget.json
• Eight aggregate gates pass
• Epistemic graph: ev-000000003166-f5c7be00-3e03-400b-a270-b677ed09ee4f
• Ledger allocation: seqclaim-ca0541cea6bd2d954a311a19

View source on GitHub