Pi Light & Breach — Curvature Threshold into Light Propagation
How Pi-particle curvature reaches a breach threshold to initiate light propagation along 2D fields, leading to wave emergence and volumetric transitions.
Last updated: 2025-10-04
Curvature Breach into Light
In Pattern Field Theory (PFT™), Pi-particle curvature stores recursive tension on a flattened (2D) coherence layer. When local curvature exceeds a stability threshold, a breach occurs: the field converts stored curvature into a propagating instruction—the onset of light. Light here is not a pellet in flight; it is the conversion wave that re-forms coherently at permissive nodes on the lattice.
Light Initiation Formula
The onset amplitude for propagation is modeled by a curvature–to–frequency conversion:
$$ L_{\text{init}} \;=\; \mu \,\big(P_{\pi} - B_{\text{threshold}}\big) $$
where \(L_{\text{init}}\) is the initial propagation amplitude, \(\mu\) is the curvature→frequency conversion constant, \(P_{\pi}\) is the local Pi-curvature potential, and \(B_{\text{threshold}}\) is the breach boundary for stable propagation. (Operationally, one may clamp negative values via \(\max(0,\cdot)\) when fitting to data.)
Breach Cascade (2D → wavefront)
- Phase disruption: planar coherence accumulates tension beyond tolerance.
- Out-of-plane birth (z): the field curls out of plane; the z-component appears.
- Wave induction: a stable conversion wave forms along adjacent Pi-loops.
- Coherent propagation: the wave re-forms at lattice nodes—this is the observed “light.”
Propagation Along 2D Curvature
Once initiated, the conversion wave travels along neighboring curvature loops on the 2D layer, forming coherent wavefronts. Propagation continues while the local coherence budget supports re-formation; strong perturbations or boundary changes can divert, attenuate, or collapse the wavefront.
Triggering Volumetric Transition (2D → 3D)
When the out-of-plane component grows beyond planar containment, the system undergoes a dimensional breach into 3D expression (volumetric curvature). This extends the wavefront into spherical/volumetric behavior while preserving the underlying instruction.
Consistency with Φλ and ΛΦ
- Φλ (Phi Lambda): the internal conversion invariant—rate of coherent phase resolution along π-axes. Instruments read its flat-projection as the operational constant \(c\).
- ΛΦ duplex: expansion (Λ) and fold (Φ) balance to maintain coherence. Breach events express this balance dynamically: conversion emits the wave at the lattice’s allowed rate.
Gravitational Refraction & PPC Note
Mass density tightens node spacing and re-routes the preferred coherence path (gravitational lensing). Parasitic Phase Conversion (PPC) can damage the instruction chain during transit, altering spectra or polarization, without changing the conversion constant itself.