Saturation Theorem Links LR-Positivity to Linear Programming and GCT Lower Bounds — E8 Intelligence Research

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The Knutson-Tao saturation theorem proves that Littlewood-Richardson coefficients are positive if and only if their scaled versions are positive, reducing LR-positivity to linear programming with direct implications for Geometric Complexity Theory lower bounds. Novelty: ClaimNovelty.SYNTHESIS. Consensus alignment: ConsensusAlignment.NEUTRAL.

Andrew Stewart Caldin

doi:10.5281/zenodo.22472631

September 6, 2026Open Access

Saturation Theorem Links LR-Positivity to Linear Programming and GCT Lower Bounds — E8 Intelligence Research

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Key Points

To analyze how the Knutson-Tao saturation theorem connects Littlewood-Richardson coefficient positivity to linear programming and complexity lower bounds in Geometric Complexity Theory.
Evaluated the Knutson-Tao saturation property for general linear group representations where positivity is invariant under uniform scaling by natural numbers.
Characterized the saturation theorem geometrically through planar honeycomb tilings satisfying triangle inequalities based on the A2 root system and Weyl chamber.
Showed that the semigroup of triples with positive Littlewood-Richardson coefficients is saturated, placing positivity verification in polynomial time (P) via linear programming.
Demonstrated that planar honeycomb patterns directly encode root system constraints, establishing a geometric bridge between representation theory and computational complexity.

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Implication

Theoretical analysis demonstrates that saturation reduces Littlewood-Richardson positivity to linear programming, highlighting direct pathways toward Geometric Complexity Theory lower bounds.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9fd76758e84d0ff5b46106 https://doi.org/10.5281/zenodo.22472631

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Saturation Theorem Links LR-Positivity to Linear Programming and GCT Lower Bounds — E8 Intelligence Research

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Discussion

Cite This Study

Saturation Theorem Links LR-Positivity to Linear Programming and GCT Lower Bounds — E8 Intelligence Research

Key Points

No abstract yet

Implication

Discussion

Cite This Study

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