On modelling hard combinatorial optimisation problems as linear programs: Refutations of the 'unconditional impossibility' claims

There has been a series of developments in the recent literature (by essentially a same 'circle' of authors) with the absolute/unconditioned (implicit or explicit) claim that there exists no abstraction of an NP-complete combinatorial optimisation problem in which the defining combinatorial configurations [such as 'tours' in the case of the travelling salesman problem (TSP) for example] can be modelled by a polynomial-sized system of linear constraints. The purpose of this paper is to provide general as well as specific refutations for these recent claims.