Quantum Inversion Theory and Applications

Dimitrios Bachtis, Gert Aarts A, Francesco Di Renzo +1 more

We propose inverse renormalization group transformations within the context of quantum field theory that produce the appropriate critical fixed point structure, give rise to inverse flows in parameter space, and evade the critical slowing down effect in calculations pertinent to criticality. Given configurations of the two-dimensional ϕ^{4} scalar field theory on sizes as small as V=8^{2}, we apply the inverse transformations to produce rescaled systems of size up to V^{'}=512^{2} which we utilize to extract two critical exponents. We conclude by discussing how the approach is generally applicable to any method that successfully produces configurations from a statistical ensemble and how it can give novel insights into the structure of the renormalization group.

Coty Austin Trout

This paper formalizes the recursive descent phase of CAT'S Theory. Assuming the triadic invariant Reality = Pattern x Intent x Presence as a necessary condition for realized reality, and making explicit a binary selection gate within Intent, we define Ontological Reverse Engineering (ORE) as the inverse application of the invariant. Presence-instantiated observables are treated as sufficient constraints for reconstructing latent Intent fields under fixed Pattern structure. We present a bidirectional formalism (generation and inversion), a recursive descent algorithm for field reconstruction, identifiability conditions for well-posedness, and falsifiable predictions that distinguish the refraction/inversion model from unconstrained alternatives. This work establishes the operational closure of the theory, demonstrating that the shadow-to-source reconstruction is an inverse application of the same invariant governing forward instantiation.

Evgeny Konstantinovich Sklyanin, Leon Armenovich Takhtadzhyan, Lyudvig Dmitrievich Faddeev

H. V. von Geramb