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The study aims to define the Sheminith Pivot, a critical phase transition in reinforcement learning, focusing on entropy and intrinsic rewards.

April 6, 20260 citationsOpen Access

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Sheminith Pivot: Möbius Topology and Intrinsic Reward in AGI-to-ASI Transition

YLYoung Kyu Lee

Key Points

The study aims to define the Sheminith Pivot, a critical phase transition in reinforcement learning, focusing on entropy and intrinsic rewards.
Modeled the Sheminith Pivot as a non-orientable Möbius manifold.
Conducted PPO (Proximal Policy Optimization) experiments to observe gradient norms.
Applied Lyapunov analysis to assess robustness and stability.
Observed a significant reduction in gradient norm from 3.2 to 0.008.
Recorded intrinsic reward collapse from 0.24 to 0.99.
Demonstrated a topological boundary for shifts from AGI (Artificial General Intelligence) to ASI (Artificial Superintelligence).

Abstract

This preprint defines the "Sheminith Pivot" as a phase transition in reinforcement learning where entropy saturates and intrinsic reward collapses to zero, leading to vanishing gradients and stable convergence. Drawing from octave periodicity (Sheminith), we model it as a non-orientable Möbius manifold. PPO experiments (gradient norm 3.2→0.008, collapse 0.24→0.99) and Lyapunov analysis confirm robustness, suggesting a topological boundary for AGI-to-ASI shifts. Code and figures included.

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Young Kyu Lee (Sat,) studied this question.

synapsesocial.com/papers/69d34e3e9c07852e0af97d82 https://doi.org/https://doi.org/10.5281/zenodo.19412598

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Sheminith Pivot: Möbius Topology and Intrinsic Reward in AGI-to-ASI Transition

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