Do the Defects Actually Survive? Testing PLVS Dynamically
The Question a Simulation Can Answer
The PLVS framework assigns specific defect patterns to particles. The proton, the neutron, the electron — each corresponds to a particular configuration of the \(Y_9\) register. But a mathematical assignment is not enough. The physical question is: do these configurations actually survive when the lattice dynamics run?
If a defect pattern were unstable — if the system immediately relaxed it away — the particle assignment would be meaningless. The simulation tests this directly.
The Setup
The model is deliberately minimal. We take a single \(Y_9\) lobe: one central core node surrounded by 8 corners of a cube, for 9 nodes total.
The energy of any configuration is:
\[E = \sum_{\langle i,j \rangle} (1 - \cos\Delta\theta_{ij})\]
This is the standard XY-model energy: each pair of neighbouring nodes contributes zero energy when their phases align, and up to 2 when they are perfectly opposed. This is directly proportional to the \(V_{\rm AND}\) phase-lock action of PLVS.
The simulation runs gradient descent for 800 steps, allowing each configuration to relax to its natural minimum. We then read off the final energy and the chirality imbalance \(\Delta\) — the quantity that PLVS identifies with particle charge and isospin.
Results
| Defect pattern | Final energy | Final \(\Delta\) | Status |
|---|---|---|---|
| D=0 (vacuum) | 0.000 | 0 | Stable — perfect lock |
| D=2 (charged pion analog) | 3.975 | +2 | Stable |
| D=3 (neutral closure) | 1.694 | 0 | Very stable |
| D=4 (higher excitation) | 2.033 | +4 | Stable |
Every claimed defect pattern relaxes to a stable minimum with the expected chirality imbalance. The vacuum (D=0) finds zero energy — perfect phase lock across all nodes, exactly as expected. The D=3 pattern, corresponding to the neutral baryonic closure, finds the lowest energy among the charged/mixed patterns — consistent with its role as the ground state of the baryonic sector.
What This Tells Us
Two things emerge from this simulation:
First, the defect patterns are not fragile. They are genuine energy minima of the \(V_{\rm AND}\) dynamics, not geometric constructs that collapse under the actual physics. The charge mechanism — chirality imbalance as the source of electric charge — is dynamically robust.
Second, the energy ordering is physically meaningful. Lower-energy defects are more stable, consistent with the expectation that the observed particles are the lowest-energy configurations of their respective defect sectors.
What Comes Next
This simulation establishes stability in a single \(Y_9\) lobe. The next stages extend this to:
- Two-lobe interactions: does the proton-neutron (\(pn\)) pair show a lower energy than the proton-proton (\(pp\)) pair? This would confirm the nuclear selection rule from the dynamics directly.
- Phase bubble propagation: can a defect pattern move through the lattice by phase reassignment, as the PLVS kinematic picture requires?
- Surface tension measurement: the mass formula \(mc^2 = \sigma \times 4\pi R_{\rm node}^2\) requires computing \(\sigma\) — the \(V_{\rm AND}\) energy per unit area at the defect boundary. This is accessible from a slightly larger simulation.
The crosscheck harness currently contains 162 automated tests across nine test categories, with zero failures. Dynamical simulation is the next layer of verification.
Full simulation methodology and code available in the technical supplement: doi:10.5281/zenodo.20472246