Triadic Fields

This unified document merges early conceptual descriptions with the newer structured taxonomy.

Quicklinks#

• docs README
• docs api integration examples
• docs api README
• docs api schema overview
• docs api using the schemas
• docs experiments faraday paradox experiment
• docs experiments README
• docs experiments replication checklist
• docs experiments resonance alignment tests
• docs experiments rotating conductor tests
• docs methods dimensional layers
• docs methods field equations
• docs methods operator definitions
• docs methods README
• docs methods substrate dynamics
• docs onboarding model map
• docs onboarding reading guide
• docs onboarding triadic quickstart
• docs onboarding verification tests
• docs overview comparison to gr models
• docs overview glossary
• docs overview introduction
• docs overview README
• docs overview resonance primitives
• docs overview theoretical background
• docs simulations boundary conditions
• docs simulations numerical methods
• docs simulations README
• docs simulations solver_architecture
• docs simulations validation metrics
• docs simulations core README
• previous folder

1. Field Types#

Scalar Field#

Represents intensity, potential, or resonance magnitude.

• evolves through diffusion, decay, and coupling
• may serve as a source term for resonance activation

Vector Field#

Represents directional flow, alignment, or spin orientation.

• evolves through alignment, diffusion, and coupling
• may influence resonance envelope activation

Resonance Envelope#

Represents localized activation or coherence within the substrate.

• activated through threshold, gradient, or operator-driven rules
• interacts with both scalar and vector fields

2. Interactions Among Triadic Fields#

Triadic fields are not independent; they form a coupled system:

• scalar → vector: gradients influence alignment
• vector → scalar: directional coherence affects scalar diffusion
• resonance → both: resonance pockets amplify or dampen local dynamics
• both → resonance: field intensity and alignment modulate activation

This coupling is central to emergent substrate behavior.

3. Operator Influence#

Triadic fields evolve through the core operator families:

• diffusion
• alignment
• coupling
• resonance activation
• decay / stabilization

Each operator may act on one or more field types, and their composition defines the substrate’s dynamic behavior.

4. Purpose and Role#

Triadic fields provide the substrate with:

• a minimal but expressive field basis
• multi-scale emergent behavior
• compatibility with classical, quantum, and semantic layers
• a foundation for operator-driven evolution

They are the “atoms” of the substrate’s dynamic universe.