0.5 — Primordial CPP States

Primordial CPP States

Individual lattice cells may contain amplitude and phase offsets relative to the King Frequency. Cells whose amplitude exceeds the system mean and possess a phase offset are defined as Coherent Phase Packets, or CPPs.

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 cannot contain discontinuities. The lattice cell left behind during redistribution therefore retains a portion of the curvature previously present, but without the phase of the original CPP. This state is defined as 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 sequences of dormant cells referred to as Dormant Corridors. These corridors provide pathways through which curvature imbalances relax while preserving lattice continuity.

Oscillation alignment within the lattice defines four discrete eigen-phase states. These states correspond to the Primordials, also referred to as Prime CPPs, each defined by a fixed phase offset \(\phi\) relative to the King Frequency.

CPP amplitudes oscillate about a characteristic mean amplitude during each King cycle. These oscillatory states persist as stable modes of the lattice.

Repeated redistribution events progressively equalize amplitudes. The resulting statistical distribution converges toward the population ratio:

This ratio arises from the arithmetic of curvature redistribution within the lattice rather than from an externally imposed rule. The lattice configuration therefore minimizes net curvature while preserving continuity of the fabric.

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. Thus, native charge and intrinsic CPP curvature inventory are not independent primitives. Charge preserves signed phase orientation, while \(\mu_{\mathrm{cpp}}\) records the corresponding sign-invariant inventory.

Odd-Divisor Phase Survey

A possible objection to the four-CPP archetype set is that additional stable phases might occur at fractional phase separations of the form \( \Delta\phi = \pi/n \), especially for odd values of \( n \). The following survey evaluates the true odd-divisor cases \( n \in \{3,5,7,9,11\} \). Composite angles such as \(5\pi/6\) are excluded because they are not primitive \( \pi/n \) archetype candidates.

Stability Principles

• Orthogonal recurrence: Stable CPP eigen-archetypes occur only at quarter-turn phase positions, \( \Delta\phi = k\pi/2 \).
• Basis decomposition: Any non-quarter phase decomposes into the orthogonal zero-phase and quarter-phase basis and does not define an independent recurrence channel.
• Observational veto: A persistent non-canonical phase would introduce an additional coherence channel and produce measurable departures in spectral distortion, fine-structure stability, relativistic species count, or baryonic mass hierarchy. Such departures are not observed.

This identity shows that each tested odd-divisor phase resolves into the existing orthogonal basis rather than forming an independent eigen-state.

Observational Veto Anchors

• CMB spectral-distortion constraint: persistent non-canonical curvature channels would perturb the zero-phase baseline beyond the allowed \(\mu/y\)-era distortion limits.
• Fine-structure stability: an additional stable phase channel would alter long-baseline electromagnetic response and would appear as drift in \(\alpha\).
• Relativistic species count: an independent phase archetype would add a transport or closure channel and would be visible as an excess contribution to \(N_{\mathrm{eff}}\).
• Baryonic mass hierarchy: an additional stable CPP archetype would generate an additional stable compound Region family, which is not observed in the particle closure set.

Result

For all tested odd-divisor candidates, \( \Delta\phi = \pi/n \) resolves into the zero-phase and quarter-phase basis with projection weights \( \cos\delta \) and \( \sin\delta \). Because these phases do not sustain independent recurrence closure and because no corresponding observational channel is present, they are non-canonical.

The stable CPP archetypes therefore remain the four quarter-turn states: Zeteon, Emeon, Uniteon, and Deniteon.