PAPER / 12 OF 13 · April 2026
Spiral Reasoning Manuscript v3 — Iterative Multi-Pass Inference in Self-Referential Systems
Atom McCree (ÆoNs)
THE IDEA / PLAIN LANGUAGE
What it says.
Most thinking goes in a straight line — A to B to C. Spiral thinking loops back around the same question over and over, but each loop goes a little higher, like climbing a spiral staircase. By the time you've gone around three times the question looks completely different — and the answer that was hiding underneath the whole time finally shows up.
THE ARGUMENT / TECHNICAL
Abstract.
Manuscript v3 of the Spiral Reasoning framework. Proposes that high-quality inference in self-referential cognitive systems (human, biological collective, or artificial) follows a spiral trajectory rather than a linear one: the system revisits the same problem at progressively higher levels of abstraction, with each pass conditioned on the trace of the prior pass. Formalizes spiral convergence as a contraction on a hierarchical metric space (each abstraction layer is a coarser quotient), proves that classical linear reasoning is the degenerate one-pass limit, and identifies three failure modes — orbital lock (passes that don't ascend), spiral collapse (passes that ascend but lose contact with the ground truth), and shear (left and right spirals desynchronizing). Connects to the lattice memory compaction architecture used in the ÆoNs Skill Suite and to the iterative self-modification dynamics of SMDS. The framework predicts that LLM chain-of-thought quality improves super-linearly under explicit spiral-pass prompting versus standard CoT depth scaling, and provides a falsifiable benchmark protocol.
KEYWORDS / FIND THE THREAD