Z₇ scalar kink field · V(Φ) = (m²/49)(1 − cos 7Φ) · m = 1776.86 MeV

t0.00 fm/c E— ΔE/E— kinks0 winding+0

Dynamics

Pure sector: exactly integrable. Kinks always pass through each other (phase shift only); kink–antikink pairs never annihilate; no radiation.

Simulation

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gas N 24

replay

Controls

Drag on the field strip / curve panel above (not the spacetime history panel below — that panel is history-only and does not respond to clicks): add a kink at that point; drag distance sets its velocity, shown live as a red/blue arrow while dragging. shift+drag: antikink.
wheel zoom (0.5–100 fm), right-drag / alt+drag pan.
Top strip: field colored by vacuum index; white curve: Φ(x). Bottom panel: scrolling spacetime history (worldlines) — view only, no interaction.

Legend — vacua & sectors

w	particle sector	Q

What am I looking at?

A real scalar field Φ with seven degenerate vacua Φ_k = 2πk/7. A kink is a moving boundary between two vacuum colors — width 1/m ≈ 0.111 fm, rest mass (8/49)m = 290.10 MeV. Net winding (a Z₇ charge) maps composite sectors to particle quantum numbers.

EXACT Pure sector: integrable dynamics — collisions are always transmissive; no annihilation, no radiation. Transient dips in the kink census during overlap are level-crossing occlusion, not annihilation.

PROXY Perturbed mode: an integrability-breaking perturbation (double-sine-Gordon proxy, PROVISIONAL). Slow kink–antikink pairs (v_rel ≲ 0.10 at η = 0.05) capture into oscillating bions and decay by radiation — genuine annihilation.

PROVEN 3D view: no compact, finite-energy 3D particle exists in this field theory — two general theorems rule out every tested shape. GTE particles are Fock-space excitations certified by an extended classical background instead (Lean-certified, zero sorry). The view renders that certified extended structure — a single domain wall, or three walls meeting along an axis — as a static illustration only, never a claim of a localized particle.

2D scalar sector: topological objects are domain walls, not point particles.

Show exact solution

1D pure sector only (exactly integrable): overlays the closed-form Hirota N-soliton solution for the kinks currently on the strip (dashed amber curve) on top of the simulated field, and reports the live max discrepancy between them — small and stable, not exactly zero, is the expected and correct result. Disabled in Perturbed mode (no closed-form solution exists there), above 10 active kinks (real-time performance limit), and for degenerate configurations (equal velocities, or kinks placed too close together).

Explore: what if the SCC weren’t satisfied?

m_φ = m_τ = 1776.86 MeV is a derived result (the Self-Consistency Condition), not a free parameter — enable this to see numerically why.

field strip · Φ(x) curve

spacetime history (t ↓)

2D scalar sector: topological objects are domain walls

Extended structure (illustrative) · no compact 3D particle exists in this field theory