Fractal Chain of Thought (FCoT) models reasoning as a recursive optimization engine over hierarchical context apertures, dual-objective fitness functions, step-end phase-gates, and reflective hill-climbing — not an unconstrained token stream. This report formalizes that core and derives its operational variants.
The paper establishes the five primitives every FCoT instance shares, then shows how FCoT 2.0 (Sequential Aperture Matrix), FCoT 3.0 (Bounded Dynamic Graph Engine), and FCoT Lean (Token-Optimized Contract Engine) are formal projections of one unified engine. It maps each variant onto the Cost–Performance–Quality triangle and lays out an adaptive governance framework for allocating them across enterprise workloads. The interactive edition below renders the equations and topology diagrams inline; the full text is embedded for reading, with a link to open it full-screen.
↗ Open the full paper (equations & diagrams)
Inside the paper
- Five foundational primitives — hierarchical context apertures (Macro/Meso/Micro/Nano), dual-objective optimization, three-iteration cognitive breathing, step-end phase-gates, and reflective hill-climbing.
- The Cost–Performance–Quality trade-off triangle and where each variant sits on it.
- Derivation of FCoT 2.0, 3.0, and Lean as mathematical projections of the core engine, with a comprehensive comparison matrix.
- Visual topology workflows for each variant, and a domain-allocation / adaptive-governance framework for enterprise deployment.
- Appendix: full FCoT system protocols and prompt templates for Lean, 2.0, and 3.0.
