Kitaev surface drift detection

Encode a stream of trust-axis scores as a Kitaev surface-code lattice, inject synthetic drift, and watch the stabilizer syndrome flag it — drift detection as quantum-error-correction on the governance signal.
Headline number: 1 injected drift event → 1 non-trivial stabilizer syndrome.

Drift — the slow degradation of a model's trust-axis scores — is the governance equivalent of a qubit error. SZL borrows Kitaev's surface code: lay the 13 axes on a lattice, define stabilizers over neighborhoods, and a non-trivial syndrome means the surface has drifted.

Honest scope. This is a classical analogy used as a detector, not a physical quantum code. The KS-18 / QEC structure has Lean scaffolding in lutar-lean, but the detector here is a deterministic syndrome check on real-valued axis scores. Λ remains Conjecture 1.

Prerequisites

bash

python3 -m pip install numpy requests

Quickstart (runnable, no credentials)

python

import numpy as np, requests

# 1. Pull the live 13-axis baseline (the "ground state" surface).
axes = requests.get("https://szlholdings-killinchu.hf.space/api/killinchu/v1/lambda", timeout=60).json()
base = np.array([a["score"] for a in axes["axes"]])     # 13 axis scores, ~0.90–0.95

# 2. Define stabilizers: each is the parity of a windowed deviation from baseline.
def syndrome(scores, ref, tol=0.03):
    dev = np.abs(scores - ref) > tol                     # which axes drifted past tolerance
    # plaquette/star stabilizers over sliding windows of 3 axes
    return [int(dev[i] ^ dev[i+1] ^ dev[i+2]) for i in range(len(scores) - 2)]

print("clean syndrome:", syndrome(base, base))           # all zeros => no drift

# 3. Inject synthetic drift on 'calibration' and re-measure.
drift = base.copy(); drift[1] -= 0.08                    # calibration sags
print("drift syndrome:", syndrome(drift, base))          # non-zero => detected

A clean surface yields an all-zero syndrome; injected drift lights up the stabilizers whose window contains the drifted axis.

Full walkthrough

Step 1 — Define the lattice

Place the 13 yuyay_v3 axes on a 1-D ring (or a 2-D lattice for richer neighborhoods). Each axis is a "data qubit"; its value is its current trust score.

Step 2 — Choose stabilizers

A stabilizer is a parity check over a neighborhood: "did an odd number of axes in this window drift past tolerance?" Star (vertex) and plaquette (face) operators in the surface code map to overlapping windows here. Overlap is what localizes the drift.

Step 3 — Measure the syndrome over time

Stream successive /v1/lambda snapshots and compute the syndrome each tick. A persistent non-trivial syndrome — not a single noisy blip — is the drift signal. Decode (minimum-weight matching, conceptually) to localize the most likely drifted axis.

Step 4 — Route the alert to the policy gate

A confirmed drift syndrome is an action; feed it to the live a11oy gate (/api/a11oy/v1/mcp/call, tool a11oy_gate) so the response is itself gated and receipted (recipe 04 shows the verdict shape). The a11oy Sentinel ships inside a11oy; it has no standalone Space.

Step 5 — Tie drift to the PAC-Bayes margin

Drift erodes the confidence margin from recipe 09: recompute R̂ after a syndrome fires and confirm the bound still clears the Λ floor.

Cite this recipe

bibtex

@misc{szl_cookbook_kitaev_drift_2026,
  title        = {Kitaev surface drift detection (SZL Cookbook recipe 11)},
  author       = {{SZL Holdings}},
  year         = {2026},
  howpublished = {\url{https://github.com/szl-holdings/szl-cookbook/blob/main/recipes/11-kitaev-surface-drift-detection.md}},
  note         = {Classical surface-code analogy used as a drift detector. Λ = Conjecture 1.}
}

Reference: Kitaev 2003, Annals of Physics 303:2–30 (fault-tolerant computation by anyons).

Doctrine v11 LOCKED — 749/14/163 — kernel c7c0ba17 · Λ = Conjecture 1 · SLSA L1 (honest)

Kitaev surface drift detection ​

Prerequisites ​

Quickstart (runnable, no credentials) ​

Full walkthrough ​

Step 1 — Define the lattice ​

Step 2 — Choose stabilizers ​

Step 3 — Measure the syndrome over time ​

Step 4 — Route the alert to the policy gate ​

Step 5 — Tie drift to the PAC-Bayes margin ​

See also ​

Cite this recipe ​