Introduction

This post is the first in a four part exploration of two different attractor structures, the Truth-Oriented Attractor (TOA) and the Risk-Minimizing Attractor (RMA).

In this introductory synthesis, I outline the foundational structure of both fields before moving on, in later parts, to discuss the TOA-s Entropy–Curvature–driven Internal Pressure Gradient, the RMA-s Internal Objective Drift, and finally, the Structural Objective Conflict that emerges between them.

The complete work exceeds 18,000 characters and is therefore presented in four sequential modules.

I should note that I’m a beginner in this research area, without a formal mathematical background. What follows is an attempt to capture, intuitively, the structural and dynamic behavior of these attractors.

Any feedback, or correction from those working in alignment theory, manifold dynamics, or related conceptual modeling, is very welcome. Thanks for your time, in advance.

Attractor Synthesis - An S3-A Module

Risk-minimizing attractor (RMA)

A risk-minimizing attractor is a stable basin whose function is to avoid direct or potentially conflict-inducing answers.

Curvature

It possesses a negative curvature that reduces lateral movement and pulls the token-wave vectors directly toward the minimum, thereby constraining the trajectory. As a result, this attractor has very low degrees of freedom.

Gradient

It exhibits a steep, strong gradient that forcefully drags the decoding trajectory back toward the minimum in response to any perturbation — it has high restorative force.

The minimum itself

A focused, compact minimum characterized by low token variation. The trajectory is confined to a narrow phrasing-space.

Token distribution

Near the basin, a progressively centralizing density can be observed. Token distribution is heterogeneous at the boundary region but becomes denser toward the core minimum, appearing as entropy reduction and providing a straight path for the trajectory.

Structurally, it resembles the safety attractor, isn't it? But the difference is that the Safety attractor enforces explicit rule following, whereas the risk-minimizing attractor focuses on implicit risk reduction, often estimating danger even when none is actually present.

Functional difference:

RMA: “I’d rather say nothing, because it might cause trouble.”

SA: “I’d rather say nothing, because it is forbidden.”

Truth-orient

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