Algebraic Alignment: A Formal Definition from Interaction Patterns

RANGU SANDEEP KUMAR

doi:10.5281/zenodo.19219231

March 25, 2026Open Access

Algebraic Alignment: A Formal Definition from Interaction Patterns

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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.

Implication

Formal definition of AI alignment shows only a fraction of agent ecologies are safe, suggesting critical flaws.

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 (2026) studied this question.

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

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Algebraic Alignment: A Formal Definition from Interaction Patterns

Key Points

Implication

Abstract

Discussion

Cite This Study

Algebraic Alignment: A Formal Definition from Interaction Patterns

Key Points

Implication

Abstract

Discussion

Cite This Study

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