Bruhat-Tits Readout Protocol: Measuring the ZBW Z2 Invariant in Majorana Systems

In plain language

The paper set out to discover how to measure a special Z₂ property (the ZBW invariant) in systems that host Majorana particles. Using that method, the authors found that the Majorana condition removes 57 % of the connections in the tree, making the graph much simpler. The same approach works with as few as 20 states to see the Gromov‑δ signature, and it can be tried on existing Majorana nanowire setups within 3–6 months. This matters because it gives experimentalists a practical, near‑term way to read out topological information that could be used for robust quantum computing.

Restated for a non-expert reader; the original wording follows. 2 statement(s) without support in the text were removed. Still uses some technical language.

In the paper's words

Proposes three measurement protocols for the p-adic Z_2 invariant: Direct current-correlator measurement, Hensel-lifting amplification via the Bruhat-Tits building, and Gromov delta-hyperbolicity comparison of ZBW trajectories in Dirac/Majorana systems.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. In P1, we constructed the Bruhat-Tits tree of ZBW-coupled eigenstates and found that the Majorana constraint $\psi = \psi^c$ prunes 57% of edges, creating a more structured transition graph [CODE-EXECUTED] .

   from 2.1 Physical Basis

2. With $10^4$ spin-flip events (approximately $10^3$ seconds at a 10 Hz event rate), a deviation of 0.1 in the discrete vs. continuous Kullback-Leibler divergence is detectable at $3\sigma$.

   from 2.5 Sensitivity Estimate

3. Both graphs have $\delta \to 0$ (tree-like MST) but the Majorana graph has 57% fewer edges [CODE-EXECUTED] .

   from 4.1 Physical Basis

4. Protocol Sensitivity Timescale Hardware Readiness A: Spin noise $3\sigma$ with $10^4$ events 3-6 months Existing Majorana nanowire setups B: EELS/RIXS $10$ meV resolution at $\mathbf{q} \sim 1/\lambda_C$ 1-2 years Synchrotron beamtime C: Gromov $\delta$ Detectable with $N \geq 20$ states 6-12 months Existing transport setups

   from 6. Sensitivity Estimates and Timeline

How it is done

1. Author: QNFO Research Agent | Date: 2026-07-05 | License: QNFO Unified License Agreement (QNFO-ULA): https://legal.qnfo.org/

   from Bruhat-Tits Readout Protocol: Measuring the ZBW $Z_{2}$ Invariant in Majorana Systems

2. Each protocol includes specific falsifiability conditions, estimated sensitivity, and realistic timeline.

   from Abstract

3. We propose three independent measurements, each testing a different physical consequence of the ZBW-Majorana hypothesis: Protocol A (Spin noise spectroscopy): If ZBW is ultrametric, spin-flip waiting times in Majorana systems should show discrete, hierarchical clustering — not the continuous distribution expected for Archimedean noise.

   from 1. Introduction

4. Parameter Specification System InSb/NbTiN Majorana nanowire or Fe-based topological superconductor Temperature $T \approx 50$ mK (sub-gap operation) Magnetic field $B \approx 0.5-2$ T (topological phase) Measurement Spin-dependent tunneling current $I(t)$ via quantum point contact Time resolution $\sim \mu$s (spin-flip telegraph noise) Event count $\geq 10^4$ spin-flip events

   from 2.2 Experimental Design

What would falsify it

1. # Measurement Protocol Dirac Prediction Majorana Prediction Decisive?

   from 5. Falsifiability Decision Matrix

2. The companion papers "Zitterbewegung as a p-Adic Observable" (P1, https://papers.qnfo.org/papers) and "Majorana Zitterbewegung Current Correlator" (P2, https://papers.qnfo.org/papers) establish that the Zitterbewegung contribution to the current-current correlator is a $\mathbb{Z}_2$ topological invariant: $\mathcal{O}_{\text{ZBW}} \approx 1$ for Dirac fermions (growing with momentum) and $\mathcal{O}_{\text{ZBW}} = 0$ for Majorana fermions at all momenta.

   from Abstract

3. Each protocol includes specific falsifiability conditions, estimated sensitivity, and realistic timeline.

   from Abstract

Where the claim stops

1. With $10^4$ spin-flip events (approximately $10^3$ seconds at a 10 Hz event rate), a deviation of 0.1 in the discrete vs. continuous Kullback-Leibler divergence is detectable at $3\sigma$.

   from 2.5 Sensitivity Estimate

Where to read

1. Abstract157 words · 1 min
2. 1. Introduction182 words · 1 min
3. 2. Protocol A: Spin Noise Spectroscopy230 words · 1 min
4. 3. Protocol B: Momentum-Resolved EELS/RIXS240 words · 1 min
5. 4. Protocol C: Gromov $\delta$ Measurement190 words · 1 min
6. 5. Falsifiability Decision Matrix130 words · 1 min
7. 6. Sensitivity Estimates and Timeline45 words · 1 min
8. 7. Discussion: From Measurement to Hardware122 words · 1 min