Chapter 3 — Percolation
When two Coherent Phase Packets combined, a phase-coherency event occurred. The weaker oscillation diminished briefly, leaving an open site that quickly balanced through surrounding recurrence. The refilled site held amplitude but no phase direction — a dormant cell. Over successive cycles, the contrast across the lattice decreased, and amplitude spread more evenly. The lattice stabilized by balancing itself. Along their boundaries, opposing phases resolved into quiet corridors. These dormant channels traced thin paths through the lattice, creating the structural scaffolding that allowed the system to persist.
The geometry gradually favored a natural distribution. On average, two Uniteon domains appeared for every one Emeon and one Deniteon, while the Zeteon remained constant. The preference was statistical rather than fixed. Local regions fluctuated slightly as the lattice adjusted through each recurrence. No external rule enforced the pattern. It emerged from the arithmetic of repeated balance, converging toward a 2:1:1 relationship as coherence matured.
Simulation program · Chapter 3
The phase-state proportions settle near 1:2:1
Grid 96 · 10 seeds
1.993 median Uniteon-to-Emeon ratio
Median Emeon, Uniteon, and Deniteon shares were 25.07%, 50.12%, and 24.99%. This supports the internal consistency of the specified phase-chain model. It is not an independent prediction because the chain's stationary distribution has these proportions.
As coherence spread across the lattice, recurrence began to fold back on itself. Dormant corridors that once separated regions now carried rhythm between them. Oscillations across the continuum became linked through a shared phase ledger, and the lattice pulsed as a unified field of exchange.
At any moment, two amplitude families stood at different heights above the same mean. This difference was not imbalance but the expression of curvature flow — the alternating displacement that preserved coherence. Without these offsets, the lattice could not persist. They were the marks of continuity.
Summary
- Reinforcement and cancellation create corridors of dormancy.
- The lattice stabilizes through its own geometry.
- Uniteon alignment yields an average 2:1:1 distribution.
- Dormant cells conserve amplitude and reduce variance.
- Dormant Corridors form connected webs of dormant cells.
The inevitable
The Zeteon is the fixed phase reference of the lattice. With the Zeteon held fixed, the three remaining phase states — Emeon, Uniteon, and Deniteon — form a chain between two fixed ends, like a string held at both ends. Its allowed modes are standing waves, with amplitudes sin(kπ/4). The ground mode, the lowest of them and the one the coupled phase states relax toward, has amplitudes in the ratio 0.707 : 1 : 0.707.
A family's participation is the square of its amplitude, as for any wave. The ground mode therefore gives Emeon : Uniteon : Deniteon = 1 : 2 : 1. With the Zeteon at 25% of the lattice, that is 18.75%, 37.5%, and 18.75%. The Uniteon, at the center of the chain, carries twice the participation of each flanking family. The 2:1:1 distribution of Uniteon to Emeon to Deniteon is therefore not an imposed condition. It is the ground mode of the lattice's own phase geometry, the same kind of standing-wave mode found in resonators, cavities, and orbitals across physics.