Cross‑Module Integration — General Relativity
TriadicFrameworks /docs/theories/general_relativity/cross_module.md#
General Relativity (GR) is a geometric coherence theory of gravity. It provides the curvature substrate, geodesic structure, and causal adjacency used across the TriadicFrameworks canon.
Gravity = coherent curvature.
Geodesics = coherence trajectories.
Spacetime = a geometric operator field.
This file defines how GR integrates with other modules.
1. Integration with LDS (Low‑Dimensional Structures)#
LDS defines dimensional profiles and geometric surfaces.
GR provides:
- metric structure
- curvature operators
- geodesic coherence
- causal adjacency
LDS provides:
- dimensional embeddings
- curvature surfaces
- low‑dimensional constraints
Integration:
Curvature inherits dimensional profiles, enabling R2 → R3 behavior.
2. Integration with NoS (Nature of Similarity)#
NoS defines similarity as structural overlap.
GR provides:
- curvature fields
- geodesic structure
- causal adjacency
NoS provides:
- similarity geometry
- overlap metrics
- structural invariants
Integration:
Geometric similarity = curvature overlap under stable operators.
3. Integration with Information Theory#
Information Theory defines distinctions, coherence, and adjacency.
GR provides:
- causal distinctions
- geometric adjacency
- curvature‑driven coherence
Information Theory provides:
- distinction grammar
- coherence evaluation
- adjacency metrics
Integration:
Causal structure becomes distinction adjacency in Information Theory.
4. Integration with FFT (Framework Field Theory)#
FFT defines dimensional operators and multi‑layer transforms.
GR provides:
- curvature operators
- geodesic bundles
- causal structure
FFT provides:
- dimensional curvature operators
- multi‑layer geometric transforms
- field‑level propagation
Integration:
R3 curvature becomes dimensional curvature in FFT.
5. Integration with Thermodynamics (Triadic Version)#
Thermodynamics defines regime‑level stability and horizon behavior.
GR provides:
- horizon geometry
- curvature gradients
- causal boundaries
Thermodynamics provides:
- stability surfaces
- energy‑regime constraints
- horizon thermodynamics
Integration:
Horizon geometry becomes a thermodynamic stability surface.
6. Integration with QFT (Quantum Field Theory)#
QFT defines fields, operators, and amplitude structure.
GR provides:
- curved backgrounds
- geodesic structure
- causal adjacency
- curvature‑driven propagation
QFT provides:
- field operators
- amplitude dynamics
- vacuum structure
Integration:
QFT on curved spacetime = field operators on coherence geometry.
7. Integration with Cosmology#
Cosmology defines large‑scale geometric evolution.
GR provides:
- curvature evolution
- geodesic expansion
- causal horizons
Cosmology provides:
- large‑scale regimes
- expansion profiles
- structure formation
Integration:
Cosmology is GR at scale, with regime‑aware curvature evolution.
8. Integration with Computation#
Computation defines state transitions and process structure.
GR provides:
- causal adjacency
- geodesic propagation
- curvature‑driven constraints
Computation provides:
- execution models
- state machines
- algorithmic structure
Integration:
Computation becomes causal‑coherence processes on geometric
structure.
9. Integration with Cognition#
Cognition defines pattern formation and representation.
GR provides:
- causal adjacency
- curvature‑driven structure
- coherence constraints
Cognition provides:
- pattern operators
- representational dynamics
- recognition structure
Integration:
Cognitive patterns become coherent geometric structures.
Summary#
General Relativity integrates with the canon by providing:
- the curvature substrate
- the geodesic coherence framework
- the causal adjacency structure
- the regime‑aware geometric behavior
It supports:
- LDS
- NoS
- Information Theory
- FFT
- Thermodynamics
- QFT
- Cosmology
- Computation
- Cognition
Gravity = coherent curvature.
Geodesics = coherence trajectories.
Spacetime = a geometric operator field.