GWT Cross-Well Gravity & Soliton Mass Calculator

Geometric Wave Theory — Multi-Well Cosmology from V(x) = (ka²/π²)[1 − cos(πx/a)]

Cosine Potential: Multi-Well Structure

Highlight well: 0

Cross-Well Gravitational Coupling

T(n) = exp(−n × π) — Evanescent transmission

Barrier height V_max 0.1292 E_Planck

Barrier width a = 1.616 × 10⁻³⁵ m

Penetration depth δ a/π = 5.14 × 10⁻³⁶ m

Well 0 → Well ±1 coupling 4.32%

Well 0 → Well ±2 coupling 0.187%

Equilibrium time ~150 t_Planck

Gravity (lattice compression) transmits through barrier evanescently. Matter (standing waves) does not cross — too large for the barrier.

Kink Soliton Properties

m_kink = (8/π²) × √(2k/η) × (a/π) = 16/π⁴ × m_P

Kink mass (Planck units) 0.1642 m_Planck

Kink mass (kg) 3.57 × 10⁻⁹ kg

Kink mass (GeV) 2.00 × 10¹⁸ GeV

Kink width ~a (one lattice spacing)

Topological charge ±1 (stable, cannot decay)

Interaction Gravity only (no EM, no strong)

Kink solitons are domain walls between adjacent wells. They are topologically protected — infinite lifetime. Invisible to EM, but gravitate normally → dark matter candidate.

Evanescent Gravity Decay Through Barrier

Gravitational compression amplitude as it crosses from well 0 through the domain wall into well 1. Exponential decay with depth δ = a/π.

Dark Matter Mass Budget

Soliton density (per Mpc³): 10⁴⁵

Multi-Well Mass Accounting

Number of occupied wells (including well 0): 3

Mass distribution: equal across wells? Asymmetry factor: 1.0

Well	Own Ω_m	Coupling to Well 0	Gravity felt in Well 0	Status

Totals Seen From Well 0

Own matter (Ω_b with G_eff) —

Cross-well gravity contribution —

Soliton (domain wall) contribution —

Total effective Ω_m seen —

Implied Ω_Λ = 1 − Ω_m —

Planck observed Ω_Λ 0.685 ± 0.007

Framework exact Ω_Λ 2/3 = 0.6667

Gap explained? —

Diffusion Rates Summary

What Diffuses	Speed	Coupling per Barrier	Equilibrium Time	Crosses Wells?
Static gravity field	c	4.32%	~150 t_P ≈ 10⁻⁴² s	✓ Yes (attenuated)
Gravitational waves	c	4.32%	Propagation delay only	✓ Yes (attenuated)
EM radiation (light)	c (in own well)	~0%	N/A	✗ Stays in well
Matter (standing waves)	0	~0%	N/A	✗ Stays in well
Kink solitons (domain walls)	< c	N/A (they ARE the barrier)	Stable forever	— They define the boundary

Diffusion rate: Γ = T × (c/a) ≈ 0.043 × 1.86×10⁴³ s⁻¹ ≈ 8.0 × 10⁴¹ s⁻¹

The diffusion rate Γ tells us how quickly gravitational information crosses one barrier. At ~10⁴¹ crossings per second, cross-well gravity reaches steady state in ~10⁻⁴² seconds. Over cosmic time (4.35 × 10¹⁷ s), the gravitational coupling is fully equilibrated.