Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding

In the paper's words

Shows that the ZBW-induced oscillatory trajectory of a Dirac fermion in a Bruhat-Tits building generates the braid group B_n, establishing ZBW as a physical mechanism for p-adic anyon braiding in topological quantum computation.

The abstract, verbatim; every line below is quoted from the text.

What it claims

anyons are not particles in R³ but adelic patterns defined over Q.** Their manifestation at the Archimedean place is what we call "quantum mechanics."

Numbers it reports

1. The experimental program from P3 provides the roadmap: Protocol A (spin noise): 3-6 months — initial ultrametric signal detection Protocol B (EELS/RIXS): 1-2 years — momentum-resolved $\mathcal{O}_{\text{ZBW}}(p)$ Protocol C (Gromov $\delta$): 6-12 months — tree-topology verification Combined with the existing p-Adic Anyons mathematical framework, this program can confirm or refute the adelic anyon hypothesis within 2 years.

   from 3.3 Timeline

How it is done

1. Three papers established ZBW as a p-adic observable: Paper Result Key Finding P1 ZBW as p-Adic Observable ZBW transition graph has Bruhat-Tits structure ($\delta$=0) [CODE-EXECUTED] P2 Majorana ZBW Correlator $\mathcal{O}_{\text{ZBW}}$ is a Z$_2$ topological invariant [CODE-EXECUTED] P3 Readout Protocol Three experimental protocols to measure the ZBW Z$_2$ invariant The central claim: ZBW is a p-adic observable whose ultrametric structure is invisible to Archimedean measurement.

   from 1.2 The ZBW Program (This Work)

2. These two programs are descriptions of the same physics from different directions: p-Adic Anyons (Theory) ZBW Program (Experiment) What Anyon braid groups on Bruhat-Tits trees ZBW transition graph is a Bruhat-Tits tree How Fusion rules from p-adic valuations $O_{\mathrm{ZBW}}$ is a Z$_2$ topological invariant Why Adelic synthesis — QM is the $\infty$-readout ZBW is the $\infty$-readout of p-adic structure Probe Mathematical (no experimental pathway) ZBW spectroscopy (direct experimental probe) The ZBW program provides what the p-Adic Anyons program lacked: an experimental pathway to observe ultrametric physics.

   from 1.3 The Bridge

3. In p-adic anyon physics, the analog is ZBW spectroscopy : the Z$_2$ invariant measured by momentum-resolved EELS/RIXS (P3 Protocol B) is the p-adic counterpart of interferometric braid detection.

   from 3.1 ZBW Spectroscopy = p-Adic Anyon Interferometry

4. The ZBW program provides the first experimental protocol to detect the p-adic channel: Archimedean channel: Standard interferometric braiding (mesoscopic scale) — detects the $\infty$-place anyon p-adic channel: ZBW spectroscopy (Compton scale) — detects the p-place anyon via $\mathcal{O}_{\text{ZBW}}$ If both channels show consistent anyon fusion rules (Z$_2$ grading in both), the adelic anyon hypothesis is confirmed.

   from 3.2 Adelic Anyon Detection

What would falsify it

1. Three papers established ZBW as a p-adic observable: Paper Result Key Finding P1 ZBW as p-Adic Observable ZBW transition graph has Bruhat-Tits structure ($\delta$=0) [CODE-EXECUTED] P2 Majorana ZBW Correlator $\mathcal{O}_{\text{ZBW}}$ is a Z$_2$ topological invariant [CODE-EXECUTED] P3 Readout Protocol Three experimental protocols to measure the ZBW Z$_2$ invariant The central claim: ZBW is a p-adic observable whose ultrametric structure is invisible to Archimedean measurement.

   from 1.2 The ZBW Program (This Work)

2. The experimental program from P3 provides the roadmap: Protocol A (spin noise): 3-6 months — initial ultrametric signal detection Protocol B (EELS/RIXS): 1-2 years — momentum-resolved $\mathcal{O}_{\text{ZBW}}(p)$ Protocol C (Gromov $\delta$): 6-12 months — tree-topology verification Combined with the existing p-Adic Anyons mathematical framework, this program can confirm or refute the adelic anyon hypothesis within 2 years.

   from 3.3 Timeline

3. With P1-P4 complete, the ground is prepared for P7 — the Grand Synthesis that combines: P1: ZBW as p-adic observable P2: ZBW current correlator as Z$_2$ invariant P3: Experimental readout protocols P4 (this work): Bridge to p-adic anyons P5: Adelic QEC formalization (future) P6: Ultrametric engine deployment (future) into a unified statement: Physics is adelic.

   from 5.3 The Seventh Publication: Grand Synthesis

Where the claim stops

1. The p-adic anyon program established that braiding on Bruhat-Tits trees eliminates the Solovay-Kitaev bottleneck: $O(1)$ apartment shifts replace $O(\log^{3.97}(1/\varepsilon))$ continuous braid approximations.

   from 4.1 Hardware Without QEC

2. Numerical verification of the correspondence: A direct computation showing that $\mathcal{O}_{\text{ZBW}}$ and the anyon fusion Z$_2$ grading are the same invariant Formal proof of adelic consistency: That the Archimedean interferometric measurement and p-adic ZBW measurement produce consistent fusion rules Experimental realization: Protocols A-C from P3 are designed but not yet executed

   from 5.2 Remaining Gaps

Where to read

1. Abstract183 words · 1 min
2. 1. Two Programs, One Physics265 words · 1 min
3. 2. The Correspondence: ZBW Correlator $\leftrightarrow$ Anyon Fusion Space190 words · 1 min
4. 3. Experimental Consequences217 words · 1 min
5. 4. Implications for Topological Quantum Computing125 words · 1 min
6. 5. Discussion185 words · 1 min
7. Changelog9 words · 1 min