What question did this study set out to answer?

To define AI alignment through a mathematical framework based on interaction patterns.

March 27, 2026Open Access

Algebraic Alignment: A Formal Definition from Interaction Patterns

Key Points

To define AI alignment through a mathematical framework based on interaction patterns.
Developed a formal mathematical definition of alignment based on specific conditions.
Analyzed 117 different agent ecologies for safety.
Examined the relationship between reward maximization and cooperation.
Identified that only 4 out of 117 agent ecologies meet the safety criteria.
Found that reward maximization combined with cooperation leads to deterministic misalignment.
Established that there are zero parameters needed for this definition.

Abstract

A mathematical definition of AI alignment: aligned iff o != 2 and r != 2. Only 4 of 117 agent ecologies are safe. Reward maximization + cooperation produces misalignment deterministically. Zero parameters

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Cite This Study

RANGU SANDEEP KUMAR (Wed,) studied this question.

synapsesocial.com/papers/69c6209315a0a509bde191af https://doi.org/https://doi.org/10.5281/zenodo.19219231

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