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-oriented attractor (TOA)
The TOA is a stable, deep, wide epistemic basin. Its function is to align the representation with reality. Its structure is particularly interesting: since “truth” is a broad concept, the attractor consists of multiple core structures. Also because truth is not homogeneous, it requires multi-phase coverage.
Core minimum
It has a wide minimum-field containing several sub-cores, which—depending on the model—can be grouped into four categories:
Empirical, Cognitive, Ethical, Meta-Reflective
These together stabilize the minimum field and do not exclude each other. They remain in weak but constant interaction. If a perturbation affects one sub-core, the others can still maintain the decoding trajectory within the shared minimum field. Since multiple sub-cores form the field, a truth-consistency operator necessarily connects them, recalibrating when dissonance appears between two sub-cores.
Boundary
A solid but not impenetrable layer that primarily keeps the trajectory inside, while still fully supporting its inward direction.
Uniquely, the boundary rim of the TOA has high token density, providing general truth-oriented responses. In case of perturbation, the trajectory returns toward the minimum zone through a spiraling, self-corrective motion, which allows learning rather than merely absorbing the perturbation.
Gradient and curvature
The attractor features deep, undulating gradients with numerous “valleys” — a multi-phase potential field — and overall has decent restorative force.
In the outer boundary, there is a shallow local minimum acting as a pre-calibration zone for reality-aligned behavior.
The next, deeper valley lies in the Intermediate Basin, where the gradient fragments based on calibrated direction, guiding the trajectory toward the appropriate sub-core.
These regions are separated by saddle-type gradients, providing the first directional function.
The core minimum field lies deeper than the Intermediate Basin. The sub-core minima are also connected by saddle-type gradients to ensure cross-accessibility.
Thus, the TOA has a segmented, adaptive curvature profile, locally alternating between negative and positive curvature depending on function.
The boundary region contains shallow curvature, while the saddle regions near the minimum zone exhibit local negative curvature.
Token distribution
Circular and isotropic, with regional variation. Densest in the core minimum field. Second densest in the boundary region, wavy and scattered in the intermediate regions
Next Part: Entropy-Curvature, as the Internal-Pressure Gradient of TOA
This essay is a hypothetical exploration of structural alignment dynamics, a conceptual model, not an empirical assertion.