blackroad-os-docs/docs/papers/spiral-information-geometry/sig-overview.md

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.