The Ostrogradskian Instability of Lagrangians with Nonlocality of Finite Extent

TL;DR

This paper defends the position that Lagrangians with finite nonlocality are inherently unstable due to Ostrogradskian instability, countering recent objections.

Contribution

It provides a constructive proof confirming the Ostrogradskian instability in nonlocal Lagrangians of finite extent, addressing recent criticisms.

Findings

Nonlocal Lagrangians of finite extent exhibit Ostrogradskian instability

The constructive proof confirms the instability persists despite objections

Counterarguments to previous claims are addressed and refuted

Abstract

I reply to the objections recently raised by J. Llosa to my constructive proof that Lagrangians with nonlocality of finite extent inherit the full Ostrogradskian instability.