Closed-path spinor transport yields non-commuting 2×2 unitaries — a step beyond sim_56's detached Pauli product.

Purpose

**512² CuPy** adiabatic spinor transport around multi-vortex loops; build $2\times2$ unitaries from path-dependent phase mixing.

What it proves

U(1) holonomy gates from sim_56 preserved; non-Abelian loop $||[U_1,U_2]||>0.1$ .

Relation to current theory

First ψ-transport SU(2) holonomy beyond fixed Pauli matrices in sim_56.

Key equation

U=\mathcal P\exp\Bigl(i\oint A\,d\ell\Bigr)\ \mathrm{(adiabatic\ limit)}

Interactive visualization

Every bar below is a real measured output of this simulation run (2 numeric metrics scraped from its validation block). Sort, filter, or switch to a log scale to compare magnitudes across many orders.

validation PASS

U(1) holonomy moduli1 , 1.0000

det U11 +0.000000j

SVT predictionClosed-path spinor transport yields non-commuting 2×2 unitaries — a step beyond sim_56's detached Pauli product.

Plots

Scalar metrics

U(1) holonomy moduli1 , 1.0000

det U11 +0.000000j

stdout tail

=================================================================
 SVT Simulation #77: SU(2) holonomy from ψ transport
=================================================================
  U(1) holonomy moduli       : 1.0000, 1.0000
  ||[U1,U2]||               : 2.2928  (tol > 0.1)
  det U1                     : 1.000000+0.000000j

=================== VALIDATION ===================
  U(1) holonomy (sim_56)   : PASS
  non-Abelian commutator     : PASS
  Overall                  : PASS

  SVT Prediction: Closed-path spinor transport yields non-commuting 2×2 unitaries — a step beyond sim_56's detached Pauli product.
==================================================

  Matches data:   YES — Validated