From Quantum to Cosmos - Fermion Mass Hierarchies Without New Sectors (σₚ = ℓₚ·tₚ = ħG/c⁴ as a covariant two-measure regulator)

Description: We propose a minimal, covariant explanation of the fermion mass and mixing hierarchies based solely on the Planck two-measureσₚ = ℓₚ·tₚ = ħG/c⁴,used as a covariant regulator for composite operators. A σₚ-covariant smearing on local quantized two-surfaces induces a single spurion-like suppression q ∈ (0,1) in Yukawa operators. Assigning integer σ-charges to fermion multiplets yields Froggatt–Nielsen–like textures: Yᵢⱼ ∼ q^{Q_{L i}+Q_{R j}}, with yₜ = O(1) and hierarchical light masses, reproducing CKM scaling |V_us| ∼ q, |V_cb| ∼ q², |V_ub| ∼ q³, and charged-lepton ratios. No new sectors or constants beyond {ħ, c, G, k_B} are introduced; q emerges dynamically from the σ-smeared OPE/anomalous dimensions. We provide sum rules and schematic fits; neutrino patterns follow from lepton σ-charges (e.g. θ₁₃ ∼ q). The construction is covariant and preserves gauge/diffeomorphism symmetries by design. Phenomenologically, q is naturally close to the Cabibbo angle at a reference scale, with mild RG running and testable texture relations. DE: Wir stellen eine minimale, kovariante Erklärung der Fermion-Massen- und Mischungs­hierarchien vor, die allein auf der Planck-Zweimaß σₚ = ℓₚ·tₚ = ħG/c⁴ als kovariantem Regulator für zusammengesetzte Operatoren beruht. Eine σₚ-kovariante Glättung auf lokal quantisierten Zweiflächen erzeugt einen einzigen, spurion-artigen Unterdrückungsfaktor q ∈ (0,1) in den Yukawa-Operatoren. Durch ganzzahlige σ-Ladungen der Fermion-Multiplets entstehen Froggatt–Nielsen-ähnliche Texturen: Yᵢⱼ ∼ q^{Q_{L i}+Q_{R j}}, mit yₜ = O(1) und hierarchischen leichten Massen; Dies reproduziert die CKM-Skalierungen |V_us| ∼ q, |V_cb| ∼ q², |V_ub| ∼ q³ sowie Verhältnisse geladener Leptonen. Keine neuen Sektoren oder Konstanten über {ħ, c, G, k_B} hinaus; q entsteht dynamisch aus der σ-geglätteten OPE/Anomalendimensionen. Wir geben Summenregeln und schematische Fits; Neutrino-Muster folgen aus Lepton-σ-Ladungen (z. B. θ₁₃ ∼ q). Die Konstruktion ist kovariant und erhält Eich-/Diffeomorphie-Symmetrien per Design. Phänomenologisch liegt q natürlich nahe dem Cabibbo-Winkel bei einer Referenzskala; die RG-Laufung ist moderat und liefert testbare Textur-Relationen. Related Works: 10.5281/zenodo.16933270 Zander, A. (2025). From Quantum to Cosmos: The Natural Law of Quantum Fields General Relativity 10.5281/zenodo.15578802 Zander, A. (2025). From Quantum to Cosmos: About Space and Time, Mass and Inertia (Also includes every Paper in an extra Zip in English): 10.5281/zenodo.16925937 Zander, A. (2025). From Quantum Structure to Galactic Rotation: Eliminating Dark Matter with Planck-Covariant Gravity.10.5281/zenodo.16925299 Zander, A. (2025). From Quantum to Cosmos: ZE-Qubit10.5281/zenodo.16925145 Zander, A. (2025). From Quantum to Cosmos - Schrödinger-Zander and Einstein-Zander Equation10.5281/zenodo.16924975 Zander, A. (2025). From Quantum to Cosmos – No Singularities: Planck-Covariant Averaging as Natural Cutoff10.5281/zenodo.16922391 Zander, A. (2025). From Quantum to Cosmos - Planck Two-Measure: Vacuum Catastrophe Fixed, Muon g-2 Consistent10.5281/zenodo.16921499 Zander, A. (2025). From Quantum to Cosmos: Solving the Λ Problem via (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³10.5281/zenodo.16929728 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox -- Full Quantum10.5281/zenodo.16929833 Zander, A. (2025). From Quantum to Cosmos: Defusing the Hubble Tension with Planck-Covariant Spacetime Fine-Structure 10.5281/zenodo.16929899 Zander, A. (2025). From Quantum to Cosmos: Planck-Covariant Flavor: Fermion Mass Hierarchies Without New Sectors10.5281/zenodo.16929940 Zander, A. (2025). From Quantum to Cosmos: A Planck-Covariant, Unitary Solution to the Measurement Problem10.5281/zenodo.16910481 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox Solved (3+1D, No Islands)10.5281/zenodo.16930310 Zander, A. (2025). From Quantum to Cosmos: A Requiem for LCDM - full Scientific + Extra Paper for readers without specialized background Contact & SupportAdrian Zander (Independent Researcher)[email protected]: 0009-0005-2388-5440 Support Scientific Continuation:IBAN: DE73 6149 0150 0132 6850 00BIC: GENODES1AAVReference: Zander Research