Unified Modified Gravity from Nucleons to Superclusters: The Discrete Growth Space Model and Blind Validation on Hundreds of Galaxy Clusters — Mathematical Isomorphism with Prime Number Sequences, Quantum Mechanical Correspondence, and Multi-path CMB Verification

Microscopic level: The mathematical structure of the model is strictly isomorphic to the Hilbert space of quantum mechanics, the Born rule, and the Schrödinger equation, and can provide a prime configuration classification of the Standard Model particle spectrum and the geometric origin of quantum numbers. 2.Scaling level: Across approximately 72 orders of magnitude from nucleons to superclusters, the characteristic range and mass satisfy a unified power-law relation, with the average growth index deviating less than 4% from the galaxy cluster fitting value. 3.Observational level: A strict blind test scheme with 20% training set and 80% test set is adopted for 100 galaxy cluster samples. Under globally fixed parameters, the average relative deviation of dynamical mass prediction is less than 1.5%, and the coefficient of determination , without introducing dark matter. The same set of parameters can simultaneously satisfy multi-scale constraints such as galaxy rotation curves, solar system weak-field tests, neutron star strong-field tests, and binary compact object gravitational waves. 4.Large-scale level: Joint validation across all scales from galaxies to superclusters confirms the evolution trend and inflection point of the gravitational saturation effect. The calculation of Type Ia supernova distance moduli deviates less than 0.003 magnitudes from the standard ΛCDM model, and can reproduce the observed cosmic acceleration with high precision. The unbound properties of larger-scale structures are qualitatively consistent with theoretical predictions. 5.Cosmological level: The logarithmic saturation correction is embedded into the standard Boltzmann solver to quantitatively verify the matching between the large-scale power suppression feature and the CMB low-multipole power anomaly. The core structure of cosmic microwave background acoustic peaks can be self-consistently reproduced under the global coherent state framework, providing support for constructing a complete dark-matter-free cosmological framework. Version 1.1 supplementary update: The Chinese full-text manuscript adds two complete observation verification chapters, including the galaxy Radial Acceleration Relation (RAR) and galaxy cluster baryonic mass fraction blind test results with supporting figures. The original English preprint remains unchanged. All matching reproduction code is attached for independent third-party inspection.