0.5 — Primordial CPP States

From Continuous Phase to Four Eigenstates

Before coherence, fabric phase is continuous. The quadrature-degenerate nonlinear interaction described in Pre-Coherence Continuum removes the second-harmonic phase preference. For the saturating response, the first surviving phase-selection term is

Its stable minima are separated by \(\pi/2\). Once the common King recurrence is established, those relative-phase families become four fixed phase offsets. The framework therefore derives the four-family structure from scalar recurrence, equal coupling through conjugate quadratures, and saturating nonlinear response; it does not assign four discrete states before coherence.

Cells whose amplitude exceeds the system mean and possess one of these phase offsets are defined as Coherent Phase Packets, or CPPs. The four eigen-phase states correspond to the Primordials, also referred to as Prime CPPs.

Redistribution and Dormant Cells

A difference in amplitude produces a redistribution during the King cycle in which the lesser-amplitude CPP relocates to the cell of greater amplitude and the amplitudes combine. The lattice cell left behind retains a portion of the curvature previously present, but without the phase of the original CPP. This phase-neutral state is a Dormant Cell.

Dormant cells remain part of the continuous fabric and function as reservoirs that absorb and redistribute curvature. Successive redistribution events form connected Dormant Corridors, which provide pathways for curvature imbalances to relax while preserving lattice continuity.

CPP amplitudes oscillate about a characteristic mean amplitude during each King cycle. Repeated redistribution progressively equalizes amplitudes, and the mature statistical distribution converges toward

This population relationship is distinct from the interaction that selects four phase families. The quarter-cycle phases follow from the Fabric response above; the population shares arise later through the lattice's redistribution and phase-geometry account.

Charge and Curvature Inventory

The native charge channel is the signed curvature-deviation expression of a CPP. The intrinsic CPP curvature inventory \(\mu_{\mathrm{cpp}}\) is the unsigned King-cycle average of the square of that same deviation. Native charge and intrinsic CPP curvature inventory are therefore not independent primitives.

Derivation Boundary

The four-family derivation depends on three stated Fabric properties: scalar oscillatory recurrence, equal coupling through the two conjugate quadratures, and a saturating nonlinear interaction response. It would fail if a complete permitted interaction retained a nonzero second-harmonic phase-selection term, if the two quadratures did not couple equivalently, or if the surviving nonlinear term did not support quarter-cycle minima.