The Bilateral Ladder

Every particle as a shard of zero — positioned on the prime number line

Every particle has a Yukawa position \(n = -\ln(m\sqrt{2}/v)\) on the bilateral ladder. Free particles (leptons) sit on primes. Confined particles (quarks) sit in prime gaps — shards that couldn't reach the next rung. Click any particle to see where it sits, how far it is from the nearest prime, and whether it is free or trapped.

Particle Zoo — The Prime Ladder

Colour	Particle type	Ladder position
Blue	Leptons (e, μ, τ)	Sit ON a prime. Free particles. The geometry closes cleanly at a prime rung. Mass = K × e^−p × v/√2.
Red	Quarks (u, d, s, c, b, t)	Sit IN a prime gap. Confined. The geometry cannot close between rungs. The confinement depth δ = \|n − p\| measures how far from the nearest prime.
Purple	Mesons (π, K, …)	Standing waves between two confined quarks. Their mass is mostly the gap energy — not the quark masses directly.
Gold	Prime rungs / Λ_QCD	The prime number positions on the bilateral ladder. Λ_QCD = √(M_Z × m_e) sits in the gap [5,7] — the confinement scale.
Teal	Neutrinos	Sit at τ₀ (prime 0) — the crossing point itself. Massless in the exact bilateral limit. The ingress face of the crossing.

Ladder view The bilateral prime ladder — a vertical axis with prime rungs at positions 0, 2, 3, 5, 7, 11, 13, 17, … Every particle is a dot at its Yukawa position n = −ln(m√2/v). Click a particle to highlight it, see its position, confinement depth, and Koide prefactor. Leptons (blue) sit on primes. Quarks (red) sit between primes. The gap between a quark dot and the nearest prime rung is the confinement depth — how far the shard is from the rung it cannot reach.

Wormhole view The selected particle shown in the wormhole — the bilateral crossing geometry. The throat width is set by the Koide value K_n. Free particles (leptons) have wide open throats centred on a prime. Confined particles (quarks) have their throat displaced from the prime — the displacement is the confinement depth δ. The pion is a standing wave between two displaced throats. Toggle between particles to see how each sits in the wormhole geometry.