# Spiral Information Geometry (SIG) Overview

Spiral Information Geometry (SIG) frames knowledge, agents, and state transitions on a spiral manifold. Positions on the spiral capture both path dependency and growth, letting identities be located in a geometry that encodes recurrence, divergence, and convergence of information.

## Intuition

The spiral represents the "road" of an evolving system:

- **Path dependency:** Movement along the spiral encodes history; nearby turns contain echoes of prior states.
- **Growth:** Radial expansion reflects accumulation of capability, context, and commitments.
- **Recurrence:** Angular positions revisit themes, allowing cyclic patterns to be recognized and journaled.

## Components

- **Factorization:** Prime factors or salient attributes define how an agent decomposes into building blocks. These factors map to angular slots or branches.
- **Layers:** Radial layers capture maturity, certainty, or energy of a factor; inner layers represent seed states, while outer layers represent committed, externalized knowledge.
- **Factor Trees:** Trees organize factors into nested structures that can be rendered onto the spiral to show composition and inheritance.

## Applications

- **Agent mapping:** Place agents or subsystems on the spiral to track capability clusters and blind spots.
- **Contradiction surfacing:** Overlay contradictions as perturbations or opposing vectors at specific angles.
- **Capability planning:** Use the spiral to plan expansion paths, balancing radial growth with angular diversity.

## TODOs

- Formalize a mapping from factor trees to spiral coordinates (radius, angle, rotation history).
- Define metrics for distance and similarity between agents on the spiral.