La Profilée On the Necessity of Admissibility Conditions for Global Persistence Laws - A Formal Extension to the Persistence Admissibility Theorem (PAT)

Key Points

• To clarify the necessity of specific conditions for establishing global persistence laws in theoretical frameworks.
• Analyzed the Persistence Admissibility Theorem (PAT) and discussed Conditions 1–7.
• Examined the implications of Conditions 4–7 on the formulation of persistence laws.
• Established structural equivalence in global persistence laws based on these conditions.
• Demonstrated that Conditions 4–7 are necessary for a global persistence law to exist.
• Showed Conditions 1–3 make the persistence problem meaningful but aren't sufficient alone.
• Concluded any claim to a global law must assume Conditions 4–7, leading to a specific structural equation.

Abstract