What question did this study set out to answer?

The theorem aims to demonstrate that fixed first-order constraints are inadequate for preserving semantic continuity in adaptive systems.

May 29, 2026Open Access

Theorem 2: Open-World Recursive Systems Require Meta-Semantic Constraint Preservation

Key Points

The theorem aims to demonstrate that fixed first-order constraints are inadequate for preserving semantic continuity in adaptive systems.
Formalization of the Self-Preserving Flow concept in relation to recursive adaptive intelligent systems
Proof of the theorem regarding semantic continuity and constraints
Analysis of the effects of unbounded novelty on system performance
Demonstrated that systems without higher-order constraints face epistemic lock-in or semantic collapse
Proved the necessity of a Meta-Semantic Consistency Layer for maintaining interpretive framework evolution

Abstract

This theorem formalizes a central claim of Self-Preserving Flow (SPF): recursively adaptive intelligent systems operating in open-world environments cannot preserve long-horizon semantic continuity through fixed first-order constraints alone. We prove that in the presence of semantically unbounded novelty, any system lacking higher-order admissibility constraints on semantic-frame revision inevitably undergoes either epistemic lock-in or semantic collapse. The theorem establishes the necessity of a Meta-Semantic Consistency Layer (Meta-SCL) as a second-order continuity constraint governing the admissible evolution of interpretive frameworks themselves.

Theorem 2: Open-World Recursive Systems Require Meta-Semantic Constraint Preservation

Key Points

Abstract

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