The Finite-Resolution Persistence Theorem (FRPT)

Key Points

• The aim is to establish the Finite-Resolution Persistence Theorem and understand its implications in various systems.
• Formulated the Finite-Resolution Persistence Theorem (FRPT) based on resolution capacity.
• Analyzed the behavior of systems when input variation surpasses local resolution capacity.
• Unified insights across computational, physical, and informational domains.
• Identified that unresolved residue accumulates when input variation exceeds resolution capacity.
• Demonstrated that these accumulations manifest as anomalies in system behavior.

Abstract