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This work introduces the concept of Bounded Randomness and its implications for thermodynamic computation.

March 23, 2026Open Access

The Topological Resonance Hypothesis v5.4: Bounded Randomness, Thermodynamic Computation, and the Architecture of Reality

Key Points

This work introduces the concept of Bounded Randomness and its implications for thermodynamic computation.
Introduces the term 'Bounded Randomness' as a conceptual framework.
Critiques gradient decoherence models in Section 4.2.
Formalizes the Entanglement Density parameter D_E linked to von Neumann entropy.
Establishes the Planck time as a lower bound for phase transition timescales.
Identifies Bounded Randomness as a constrained computational resource.
Presents formal links between Entanglement Density and entanglement entropy.
Critiques existing models of gradient decoherence in light of this framework.

Abstract

This work introduces the term 'Bounded Randomness' as an original conceptual framework by the author, defining randomness as a computational resource constrained by physical budget. V5. 4 adds a formal critique of gradient decoherence models (Section 4. 2), introduces the Entanglement Density parameter DE formally linked to von Neumann entanglement entropy, and establishes the Planck time as the absolute lower bound on the phase transition timescale.

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David Stamboltsyan

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The Topological Resonance Hypothesis v5.4: Bounded Randomness, Thermodynamic Computation, and the Architecture of Reality

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