bc063c0b74
- Z-Framework: universal feedback/equilibrium - 1-2-3-4 Pauli Model: ontological primitives - n=π Duality: discrete↔continuous interface - Creative Energy: contradiction amplification - Remainder Principle: deviation as signal - Spiral Information Geometry: planned formalization
1.4 KiB
1.4 KiB
1-2-3-4 Pauli Model
Overview
Maps ontological primitives to the su(2) Lie algebra (Pauli matrices).
The Four Primitives
| # | Name | Symbol | Pauli Matrix | Interpretation |
|---|---|---|---|---|
| 1 | Structure | Û | σ_z | What exists, identity, being |
| 2 | Change | Ĉ | σ_x | Transformation, becoming |
| 3 | Scale | L̂ | σ_y | Relation, proportion, context |
| 4 | Strength | Ŝ | iI | Emergent intensity, scalar invariant |
Algebraic Structure
The first three form an su(2) algebra:
[Û, Ĉ] = 2iL̂
[Ĉ, L̂] = 2iÛ
[L̂, Û] = 2iĈ
The fourth emerges from their triple product:
Û · Ĉ · L̂ = iI = Ŝ
Interpretation
- 1-2-3 are the generators (directions of change)
- 4 is the invariant (what's preserved under change)
- Together: complete description of any dynamic system
Connection to Physics
The fine structure constant α ≈ 1/137 may encode the relationship between these primitives and electromagnetic coupling.
Applications to BlackRoad
- Agent State: Each agent has (Û, Ĉ, L̂, Ŝ) attributes
- Coherence Metrics: Measure alignment via inner products
- Contradiction Resolution: Pauli algebra handles non-commuting observables
Open Questions
- Why su(2) and not a larger algebra?
- What is the physical meaning of Ŝ?
- How does this connect to spinor geometry?