Speed of Light – ΛΦ Coupling

Within Pattern Field Theory (PFT™), the speed of light, c, is not defined as an equilibrium between “forces” or as a ratio of cosmological parameters. It is treated as the global feed-rate ceiling of the Allen Orbital Lattice (AOL): the maximum rate at which coherent updates can propagate once structure is admitted and committed.

This page defines ΛΦ Coupling in the current PFT sense: Λ and Φ describe two families of lattice load that compete for the same finite update budget. They do not compute c; they determine how much of the available feed-rate is consumed locally.

Definition

ΛΦ Coupling is the interaction between:

• Λ (Lambda-load): expansion bias and large-scale baseline divergence pressure expressed as a lattice-wide tendency toward de-correlation unless constrained.
• Φ (Phi-load): curvature and compression bias expressed as a local constraint-gradient that increases restoration pressure and coherence-routing demand.

Together, Λ and Φ specify a region’s update demand profile: how hard the lattice must work to preserve coherent geometry.

What c Is in This Context

In PFT shorthand, the speed of light corresponds to a feed-rate limit:

c_feed = Σ(ψ₂…)/t

This is not a statement about a wave moving “through spacetime.” It is a statement about the maximum coherent throughput the lattice can sustain. When local update demand increases, the lattice does not raise c. It redistributes how coherence is expressed (timing, phase, wavelength, redshift behavior), while the ceiling remains fixed.

ΛΦ as Load, Not as a Formula for c

Earlier drafts sometimes attempted to write c as a direct function of Λ and Φ. That is not compatible with current PFT because it turns a lattice ceiling into a local ratio. In the current model:

• Λ and Φ do not determine the value of c.
• Λ and Φ determine how much of the c-budget is consumed in a region.
• Observable effects arise when the region approaches saturation of that budget.

A correct PFT-form statement is therefore budget-based:

UpdateDemand(Λ, Φ, geometry, boundary) ≤ c_feed

When the inequality is comfortably satisfied, propagation and restoration are stable. When the system approaches saturation, the lattice must change expression to remain admissible while keeping the ceiling invariant.

How ΛΦ Coupling Produces Observable Light Behavior

In PFT, “light behavior” is the visible surface of an update process constrained by lattice capacity. ΛΦ Coupling changes how often 3-D restoration can be sustained, how phase alignment holds, and how coherence is routed.

• High Φ-load regions: stronger constraint gradients demand more restoration work; coherence routing becomes tighter and wavelength behavior shifts accordingly.
• High Λ-load regions: de-correlation pressure increases; maintaining stable propagation consumes more of the available update capacity.
• Combined ΛΦ load: the lattice spends more of its budget on keeping geometry coherent, leaving less slack for unconstrained propagation formats.

This preserves the central PFT separation: gravity and curvature set permission and restoration conditions, while c sets the maximum throughput of any permitted coherence propagation.

Relation to Flattening and 3-D Restoration

ΛΦ Coupling connects directly to the flattening and restoration language used elsewhere in PFT. Flattening is the low-demand propagation format; restoration is the higher-demand format that becomes locally necessary under sufficient gradients.

In that mapping:

• Φ-load increases restoration pressure (more 3-D alignment demand).
• Λ-load increases baseline coherence maintenance cost (more budget spent keeping propagation admissible).
• c remains the global ceiling for how fast any of this can update.

Implications

This framing provides a clean structural interpretation of common phenomena while keeping PFT commitments intact:

• Redshift behavior: not a change in c, but a change in expression required to remain coherent under different ΛΦ load profiles.
• Strong-field environments: higher Φ-load increases restoration demand; observed light behavior shifts because more of the budget is consumed by constraint satisfaction.
• Large-scale acceleration narratives: Λ-load expresses as baseline divergence pressure; the lattice maintains coherence without violating the global feed ceiling.

Summary

• c is the feed-rate ceiling of the Allen Orbital Lattice, not a Λ/Φ equilibrium output.
• ΛΦ Coupling is a load interaction: it determines how much of the finite update budget is consumed locally.
• Observable “light behavior” changes through expression adaptation under load, while the ceiling remains invariant.

This keeps the model mechanically consistent across the site: permission and restoration are local, the ceiling is global, and ΛΦ Coupling is the bridge between local load and global throughput.