substrate

Triadic Substrate

The substrate/ directory contains the core implementation of the Resonance Substrate Model.
Where the manuscript defines the theory, this directory defines the runtime substrate that executes it.

The substrate is organized into three layers:

• core/ — field definitions, state containers, update loops
• operators/ — diffusion, alignment, coupling, activation, stabilization
• utils/ — shared helpers, math routines, loaders, schema validators

This directory is domain‑agnostic.
All Earth, telescope, or other overlays plug into this substrate without modifying it. # Substrate Core

The core/ directory contains the fundamental runtime components:

• field containers (phi, V, R)
• timestep integrators
• operator pipelines
• simulation loop orchestration
• state serialization and snapshotting

This is the execution engine of the Resonance Substrate Model.
All overlays (Earth, telescopes, etc.) map their domain data into these core structures. # Operator System

The operators/ directory implements the five operator families defined in the manuscript:

• Diffusion
• Alignment
• Coupling
• Activation
• Stabilization

Each operator acts on one or more of the triadic fields:

• scalar field phi
• vector field V
• resonance envelope R

Operators are pure functions:
they take field states + coefficients and return updated fields.
This keeps the substrate modular, testable, and easy to extend. # Substrate Utilities

The utils/ directory provides shared helper functions used across the substrate:

• numerical routines (gradients, Laplacians, normalization)
• coherence functional helpers
• logistic and nonlinear activation helpers
• schema validation utilities
• configuration loaders
• grid and mesh utilities

These utilities are intentionally lightweight and dependency‑minimal.
They support the operator system without imposing domain assumptions.