Supplement: Lorentz Ellipse Derived Group Velocity, Phase Velocity, Cosmic Density Ratio and Cosmic Hydrogen - Wandering Hydrogen Ratio - LA Supernova Q-factor Double Error Correction

This short paper is a Dimensionless Delay Angle and Double-Bounded Resonance. Starting from the Lorentz factor γ=1/√(1-β²), squaring yields an ellipse x²/a²+y²/b²=1. With dimensionless delay angle δ*=0.012 rad, leakage Γ=sin²(δ*)=0.000143993=0.0144%, impedance X=j·δ*·Z0=j4.524Ω, virtual capacitor C_virtual=70.6mF/mode, Q_c=523.6, Finesse=261.8 are derived. Group velocity v_g=299,792,458 m/s and phase velocity v_p=299,749,289 m/s differ by Δv=43,169 m/s, explained by R=0 reversible reactance storage and geometric detuning 12=1000×0.012. Hydrogen count per cubic light-second is calculated as 7.4×10²⁴ (0.27 per m³), compared with HI4PI, ALFALFA, Lyman-α forest, FRB DM, and WHIM X-ray observations: clustered 10% vs wandering 90% matches theory at >95%. The Q-factor double error is defined: visible leakage Γ and hidden viewing angle deviation θ_ideal=arcsin(2/3)=0.7297 rad=41.8103°. Luminosity distance distortion D_L,app/D_L,true=1/(1-Γ)^{N/2}≈1+½NΓ, κ=Γ/L_mode=1.07×10⁻¹⁷/m, L_mode=c·45,018s=1.35×10¹³m. Correction order: first recover Γ then correct viewing angle. Standard ΛCDM trimming via sigma clipping in Pantheon/Pantheon+ is reinterpreted as consequence of ignoring this double error, not intentional manipulation.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-11-05
DOI
https://doi.org/10.5281/zenodo.23969473
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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Supplement: Lorentz Ellipse Derived Group Velocity, Phase Velocity, Cosmic Density Ratio and Cosmic Hydrogen - Wandering Hydrogen Ratio - LA Supernova Q-factor Double Error Correction

sungbae im
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

Supplement: Lorentz Ellipse Derived Group Velocity, Phase Velocity, Cosmic Density Ratio and Cosmic Hydrogen - Wandering Hydrogen Ratio - LA Supernova Q-factor Double Error Correction

sungbae im
preprint en

Abstract

This short paper is a Dimensionless Delay Angle and Double-Bounded Resonance. Starting from the Lorentz factor γ=1/√(1-β²), squaring yields an ellipse x²/a²+y²/b²=1. With dimensionless delay angle δ*=0.012 rad, leakage Γ=sin²(δ*)=0.000143993=0.0144%, impedance X=j·δ*·Z0=j4.524Ω, virtual capacitor C_virtual=70.6mF/mode, Q_c=523.6, Finesse=261.8 are derived. Group velocity v_g=299,792,458 m/s and phase velocity v_p=299,749,289 m/s differ by Δv=43,169 m/s, explained by R=0 reversible reactance storage and geometric detuning 12=1000×0.012. Hydrogen count per cubic light-second is calculated as 7.4×10²⁴ (0.27 per m³), compared with HI4PI, ALFALFA, Lyman-α forest, FRB DM, and WHIM X-ray observations: clustered 10% vs wandering 90% matches theory at >95%. The Q-factor double error is defined: visible leakage Γ and hidden viewing angle deviation θ_ideal=arcsin(2/3)=0.7297 rad=41.8103°. Luminosity distance distortion D_L,app/D_L,true=1/(1-Γ)^{N/2}≈1+½NΓ, κ=Γ/L_mode=1.07×10⁻¹⁷/m, L_mode=c·45,018s=1.35×10¹³m. Correction order: first recover Γ then correct viewing angle. Standard ΛCDM trimming via sigma clipping in Pantheon/Pantheon+ is reinterpreted as consequence of ignoring this double error, not intentional manipulation.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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