Brahim QFT Operator

The provided workbook details the Brahim Quantum Field Theory (QFT) framework, a mathematical system designed to derive fundamental physical constants without external parameters. Using Axiom Zero, which establishes core inputs like color charge and spacetime dimensions, the system calculates critical values such as Euler’s number and the QCD confinement scale. Central to this framework is the Ψ formula, a discrete encoding method that predicts 14 distinct observables, including dark matter density and the strong coupling constant, with high precision. By partitioning residues into specific class structures, the model bypasses traditional continuous running approximations to bridge the gap between theoretical scales and experimental data. Statistical analysis suggests these results reach a 6σ significance level, indicating a non-random correlation with established physical benchmarks. Ultimately, the sources describe a self-referential operator landscape where mathematical identities directly manifest as the building blocks of particle physics and cosmology. The core of the Brahim QFT Operator Workbook is a parameter-free framework that derives 14 fundamental physical observables from a single mathematical starting point called Axiom Zero. The workbook demonstrates that cosmological parameters and particle physics constants can be calculated as discrete structural encodings rather than being fitted as free parameters. The essential components that form the "core" of this system include: 1. Axiom Zero: The Three Inputs The entire framework is built upon three axiomatic inputs, with zero free parameters and zero fitting: Nc (Color Charge): 3 Nₒₓ (Spacetime Dimensions): 4 K (Framework Prime): 107 (the 28th prime). 2. The Master Formula At the heart of the workbook's predictive power is the (r; class) formula, which derives values for physical constants based on their mathematical "residue class": (r; class) = (m) (m/K) (r/ (e K) ) (m): A normalization constant defined as 1 + m/K. Mode envelope: A K-centered sinusoidal mode where m is determined by the residue class (m \10, 14, 28\). Residue probe: Uses the framework-derived Euler's number (e 3311/1218) and the Brahim residue r. 3. Discrete Encoding Levels The workbook posits that physical constants are encoded at three different levels of the formula: Level 1 (Direct): (r) predicts cosmological parameters like Dark Matter density (c) and the Hubble constant (h). Level 2 (Product): (r₁) (r₂) predicts couplings like the QCD strong coupling ₛ (MZ) and CKM mixing elements. Level 3 (Ratio): (r₁) / (r₂) predicts angles and ratios like the Weinberg angle (²W) and primordial helium fraction (Yₚ). 4. B-Scheme Operators and the "Running Gap" The workbook introduces the B-scheme, which defines an infrared confinement wall (B) and a running coupling (B) derived entirely from internal identities (e. g. , B = Tc 100/K). A key breakthrough highlighted is using the formula to close the 38. 7% gap between standard one-loop running and the experimental value of ₛ (MZ).