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title: "KP-Field Propagation — Schematic Specification" description: "Visual schematic and layer topology specifications for non-local resolvent Green operator propagation and coherence transport." layout: doc status: "canonical-figure-spec" claim_boundary: "Visual schematic specification only. Demarcates operator Green function propagation from empirical physical measurements."

KP-Field Propagation

Status Boundary

This work is part of the authorial PHYSICA / Science of Fabric Reality corpus. It is presented as a research framework, formalization target, computational model, or theoretical synthesis unless explicitly marked otherwise. It is not presented as accepted physics, external consensus, or experimentally confirmed science.

Scientific Purpose

Defines the visual and structural requirements for representing the KP-Field Propagation concept within the formal framework.

Concepts Visualized

• Resolvent Green Operator · Non-local operator propagation $G_E(x,y)=⟨x|(H-E{)}^{-1}|y⟩$ across metric-measure lattices.
• Coherence Envelopes · Exponential and polynomial spatial decay bounds $\kappa (r)\sim r^{-\alpha }{e}^{-\mu r}$ governing field influence.
• Spectral Transport · Phase coherence circulation across multi-node graph neighborhoods.

Symbols Visualized

• $G_E(x,y)$, $(H-E{)}^{-1}$, ${\kappa }_{\text{coh}}$, ${\mathcal{L}}_{\text{KP}}$, ${\mathrm{\Phi }}_{\text{res}}$, $\sigma (H)$

Equations Referenced

• KP-Field Operator Dynamics — Resolvent Green operators and spectral coherence transport.
• Fractal Quantum Field Theory — First resolvent operator identity (thm_first_resolvent_identity_algebraic).

Required SVG Layers

• base-topology: Lattice substrate and underlying discrete metric manifold.
• interaction-vectors: Green function propagation wavefronts, phase vectors, and coherence decay gradients.
• labels-and-nodes: Source node $x$, evaluation node $y$, operator resolvent parameters, and energy level markers.

Caption

Figure: Schematic representation of KP-Field non-local propagation, showing resolvent Green function envelopes and spectral decay.

Construction Notes

Do not use generic raster images. The final SVG must strictly adhere to the mathematical and topological constraints defined in the corresponding route.

Route Bindings

• Primary Theory: KP-Field Operator Dynamics
• Variational Field Core: Fabric Field Equation
• Computational Model: KP Field Closure Dynamics Simulation

Interpretation Boundary

This figure serves as a formalization target and visual aid for the authorial model. It must not be interpreted as empirical proof or accepted physics.