blackroad-os-research/sig/sig-overview.md

Spiral Information Geometry (SIG) Overview

Version: 0.1 — 2025-02-08

Spiral Information Geometry (SIG) models stateful knowledge as trajectories on a logarithmic spiral. Coordinates embed temporal rotation (angle), growth (radius), and recurrence (turn count) so that an agent's history and intent can be located in a geometry instead of a flat list of events.

Spiral Coordinate System

• Polar triple (r, θ, τ): r encodes maturity/energy, θ is the semantic angle, and τ counts revolutions to retain recurrence memory. The triple supports consistent interpolation between snapshots.
• Logarithmic growth rule: r = a·e^(b·θ) captures the intuition that knowledge expands multiplicatively as it circles the attractor.
• Coordinate frames: Local frames rotate with the spiral to preserve parallel transport of factors (skills, beliefs) during agent movement.

Interference Patterns

• Constructive overlap: When two factors share angle but differ in τ, their interference builds a higher-confidence ridge recorded as a "braided" path.
• Destructive overlap: Orthogonal or phase-shifted factors produce null regions; the truth engine flags these as contradiction basins.
• Signal envelopes: Sliding windows over θ aggregate local density to surface clusters that merit promotion into the factor tree.

Attractor-Based Cognition

• Attractors as intents: Each attractor anchors a desired equilibrium (goal, constraint, or operating principle).
• Spiral drift: Agents orbit attractors; drift speed measures cognitive load or uncertainty. Slow drift suggests stable commitments.
• Perturbation logging: Deviations from attractor orbits are journaled as high-energy points that later feed PS-SHA∞ anchoring.

Prime-Factor DNA

• Prime slots: The spiral is discretized into prime-indexed angular slots; each slot holds a minimal competency or claim.
• Factor composition: Composite behaviors decompose into products of prime slots, preserving interpretability.
• Mutations: Shifts in slot occupancy mark "mutations" of the agent's DNA and are tracked as lineage events.

Factor-Tree Structure

• Rooted by origin layer: The tree root references the origin layer of the Road and maps into the spiral origin.
• Branching: Each branch inherits the angle of its parent; child radius increments represent deeper materialization of capability.
• Projection: The factor tree projects onto the spiral, giving every node a (r, θ, τ) coordinate for rendering and similarity.

Road Integration

• SIG provides the spatial substrate for the Interference Engine to mark contradictions, for Lucidia to route cognition, and for RoadChain to anchor events to a geometric location.
• Prime-factor DNA keeps agent identity coherent while PS-SHA∞ journals the transitions between turns of the spiral.