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MQ→RG: Essay on Four Domains and Four Validable Mathematical Proofs

Denis Grenier

Published Jun 9, 2026• 0 citations
Publisher

Abstract

This essay presents four independent mathematical proofs, each associated with a distinct domain: quantum mechanics (MQ), propagation (RL), renormalization (RG), and structural coherence (ESCT). The proofs are formulated in a strictly mathematical, falsifiable, and testable manner, without external assumptions or reliance on any proprietary theoretical framework. The main objective is to provide an official timestamp for these proofs and to establish a public basis for their future validation, whether experimental or computational. The French and English PDF versions are both provided in this deposit.

DOI
10.5281/zenodo.20822431

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This essay presents four independent mathematical proofs, each associated with a distinct domain: quantum mechanics (MQ), propagation (RL), renormalization (RG), and structural coherence (ESCT). The proofs are formulated in a strictly mathematical, falsifiable, and testable manner, without external assumptions or reliance on any proprietary theoretical framework. The main objective is to provide an official timestamp for these proofs and to establish a public basis for their future validation, whether experimental or computational. The French and English PDF versions are both provided in this deposit.
This record establishes the theory priority for the Φ-Modulated Quantum Context Theory (Φ-QCT), a minimal extension of quantum mechanics introducing conscious selection of quantum measurement contexts via the structural quantity Φ_Q and a dimensionless coupling constant β. The deposit includes the full axiomatized theoretical framework, experimental predictions, falsifiability conditions, and core computational methods. This DOI serves as the official timestamped priority reference for future peer-reviewed publications.
In this note, we present a table with a summary of recent developments in quantum mechanics. If you not have studied our papers carefully already [1–4], then this paper will not make much sense and the equations could easily be misunderstood, so we strongly encourage the reader to become familiar with this material first. We will possibly write a long paper on this topic later, but it may be helpful to present the essence of both old and new QM, as we understand it today. This is useful for both tracing the history of ideas related to QM in mathematical form and for creating an opportunity to compare equations and analyze their similarities and differences.
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Phase XI: The Observable Bridge — Physical Interface, Validation, and Experimental Architecture This release presents Phase XI of the AAIS (Artificial Asymptotic Information Structure) framework. Its primary objective is to establish a rigorous and transparent pathway from theoretical constructs to experimentally testable interfaces. The central contribution is the Observable Bridge methodology: a structured framework that connects mathematical assumptions → operational mappings → measurable signatures → falsifiable experimental criteria. Key elements of this phase include: • A formal inheritance registry that preserves the epistemological status of all previously introduced AAIS mathematical structures. • Candidate physical interface models linking information-dynamical quantities to concrete laboratory observables. • A multi-channel validation architecture with primary emphasis on quantum coherence experiments (cQED / transmon systems), complemented by precision metrology pathways. • A bias-resistant secondary statistical compatibility protocol (Appendix E) designed for independent evaluation of AAIS phenomenological extensions against publicly available experimental datasets. Appendix E provides a structured Standard Operating Procedure (SOP) featuring: – mandatory pre-registration and cryptographic timestamping, – clear separation of matched-acquisition (Tier 1) and legacy (Tier 2) datasets, – parameter identifiability constraints, – conservative AIC/BIC interpretation rules, – secondary Bayesian evidence assessment, and – out-of-sample predictive validation requirements. All models, parameters, and numerical benchmarks are explicitly classified according to their epistemological status (e.g., inherited structure, phenomenological parameter, or simulation prior). The included simulations serve solely to evaluate theoretical consistency, parameter sensitivity, and possible observable consequences; they do not constitute evidence of physical realization. Phase XI is therefore presented as an experimentally oriented validation framework that prioritizes reproducibility, falsifiability, transparent model comparison, and explicit separation between theoretical assumptions and empirical evidence. Keywords: AAIS, experimental validation, quantum coherence, cQED, transmon, model selection, AIC, BIC, Bayesian analysis, open quantum systems, falsifiability, precision measurement, Observable Bridge