"Latest changes": added Appendix G. "Latest Relative Research": Fractal Scaling Law [https://doi.org/10.5281/zenodo.17084588] [Description] Background: The Standard Model (SM) has been successful, yet it fails to explain the origin of fermion masses and mixing parameters. Methods: In this study we construct the single-fermion framework “Information Flux Theory (IFT),” derived from the Unified Evolution Equation. IFT preserves gauge symmetry while replacing Standard Model fields with a single fundamental operator, yielding analytic solutions without adjustable parameters. Results: IFT reproduces all SM particle masses—including the 125 GeV Higgs mass—and the CKM matrix within current experimental precision, requiring neither additional particles nor fine-tuning. Conclusion: These results demonstrate that IFT can fully replace the Standard Model with a single-fermion description, providing a conceptually simpler yet phenomenologically complete foundation for particle physics. Supplement: This paper includes proofs for two Clay Millennium Problems: the Yang–Mills mass gap and the Navier–Stokes equations. Note Added: Furthermore, as a result of this series of studies, the origin of gravity has now been clarified. Note that the Zip file includes a Python script reproducing the numerical calculations for the tables in the paper. Achievements in This Paper 1. Foundational Advances in Quantum Measurement Theory First-Principles Derivation of the Born RuleDynamic measurement process via Lindblad-type dissipative jump operators yields the probability rule Prob(n)=Tr[ρ Πn] without postulates. Instantaneous Diagonalization in the Pointer BasisProof that off-diagonal elements decay exponentially, driving the state to ρ→∑nΠn ρ0 Πn in finite time. Exact Evaluation of Spohn’s Inequality and Quantum Zeno AnalysisClosed-form entropy production under the dissipative semigroup, clarifying decoherence timescales and Zeno-effect suppression conditions. Extension to General POVMsConstruction of projection-based POVMs via coefficient matrices, deriving Kraus operators and Lüders update rules without ancillary environments. 2. Establishment of Mathematical Foundations Global Existence and Uniqueness of the UEEProof via the Banach fixed-point theorem and dissipative structure that the UEE admits a unique, continuous solution for all t≥0. C*-algebra Closure of the Operator SystemDemonstration that the finite sums and products of {D,Πn,Vn,Φ,R} generate the full bounded-operator algebra on the Hilbert space. 3. Innovations in Gauge Theory Parameter-Free Reconstruction of Gauge SymmetryExact realization of SU(3)×SU(2)×U(1) through a single fundamental operator and projections, deriving all fermion–gauge interactions including Yukawa matrices. Loop Finiteness and Zero β-FunctionProof that all higher-order Φ-loops terminate finitely and that the gauge coupling β-function vanishes exactly at every order. Automatic Cancellation of Precision-Test ParametersWard identities enforce cancellation of S, T, U parameters and vacuum-energy divergences, removing all adjustable precision corrections. Non-Perturbative Mass Gap and Area LawDerivation of the Wilson-loop area law and rigorous proof of the Yang–Mills mass gap in a non-perturbative framework. 4. Parameter-Free Predictions of Standard Model Parameters Simultaneous Derivation of Fermion Masses and the CKM MatrixUnified prediction of nine quark and lepton masses and the four CKM parameters solely from the fundamental tension σ. High-Precision Prediction of the Higgs Mass and Gauge CouplingsReproduction of mH≈125.25 GeV and of αEM,αs to O(10^-3) accuracy without free parameters. 5. Unified Framework for Quantum Gravity and Cosmology Lindblad-Type Master Equation UnificationConstruction of a single evolution equation that reduces to the Einstein–Hilbert action in the IR and the Standard Model action in the UV. Origin of Gravity as Fermion-Fluid StressFirst-principles derivation of the Einstein–Hilbert action and Newton’s constant from σ, and interpretation of gravity as the stress of a fermionic fluid. Single-Fermion Uniqueness TheoremReconstruction of all fermion fields from one fundamental operator, identifying gauge bosons as composite excitations. Cosmological Information Corrections via Operator ClosureClosure of the operator algebra yields natural dark-energy terms in the FRW equations and implements wave-function collapse in cosmology. 6. Applications to Cosmology and Astrophysical Observations Physical Predictions of the Zero-Area Resonance Kernel RForecast of black-hole information propagation effects and gravitational-wave delays (e.g., GW150914 delay of 6.6 ms) within observational limits. FRW Corrections and Alleviation of the σ8 TensionGrowth-rate analyses produce a value of σ8 that naturally relieves the tension seen in ΛCDM weak-lensing data. 7. Resolution of Outstanding Problems (Clay Millennium Problems) Proof of the Yang–Mills Mass Gap Proof of Existence and Smoothness for the Navier–Stokes Equations