Functional Foundations of the Shadow Theorem: Analysis of the Observational Loss Functional for the Effective Field Theory of Information Reconstruction (EFIR)
Year: 2026
Type: article
Abstract: This paper provides a rigorous functional-analytic foundation for the Shadow Theorem within the Effective Field Theory of Information Reconstruction (EFIR). The author establishes a formal mathematical structure for the theory by equipping the EFIR phase space with a Banach manifold structure based on Sobolev spaces. The work delivers several key proofs, including the Fréchet differentiability and strict log-concavity of the shadow operator in the Gaussian regime. Furthermore, it provides an explicit computation of the proportionality constant for the decoherence rate and a rigorous Cramér-Rao derivation for the reconstruction tensor. This research upgrades the Shadow Theorem from a conceptually coherent framework to a mathematically complete theory.
Author: Galli, Marco
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140039863
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