Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation
Abstract
We derive the quasi-normal mode (QNM) spectrum of black hole ringdown from the five axioms {12, π, γ1, ln 2, φ} of Array Cosmology (AC) with zero free parameters.
The Schwarzschild (χ = 0) fundamental mode (l = 2, n = 0) frequency is ω˜R = γ1/(12π) = 0.37494 (GR exact: 0.37367, error 0.34%), and the quality factor is Q = 2 + Znoise = 2.098 (GR: 2.100, error 0.10%). For Kerr black holes,
spin progressively collapses the 12-axis rendering loop to a single Volma stroke (3 axes) via the golden-ratio implosion exponent φ^−2 : the effective axis count is Neff(χ) = 3 + 9(1 − χ) φ−2 , yielding ω˜R(χ) = γ1/[π Neff(χ)] with RMS 2.3% against numerical relativity. The quality factor Q(χ) = (2+Znoise)/(1−χ) 1/2−Znoise achieves RMS 2.2%. The overtone spacing is ∆˜ωI = 2Znoise (0.8% match). Applied to GW150914 (M = 68.5 M⊙, χ = 0.69), the model predicts f = 242 Hz
and τ = 4.41 ms, within 1.1σ and 0.8σ of LIGO observations respectively. All five axioms are employed: 12 (loop topology), π (angular circumference), γ1 (tension anchor), ln 2 (Landauer floor), and φ (spin collapse). This supersedes the previous
AC ringdown paper, correcting the erroneous ×1.699 damping-time scaling
Related
- Analytic Marginalization Over Calibration Uncertainties in Gravitational Wave Inference and Application to Black Hole Ringdown
- Odd-parity ringdown gravitational waves of a spherically symmetric black hole with perfect fluid accretion
- Biases in Ringdown Tests of General Relativity from Gravitational-Wave Microlensing
- The Hubble Ladder: Complete Self-Referential Classification of H0 Measurements and the φ-Rung Spectrum of the R12 Rendering Algebra
- Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence
BibTeX
@misc{lim2026gravitational,
title = {{Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation}},
author = {Han-Jun Lim},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23603865},
url = {https://zenodo.org/records/23603865},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation
AU - Han-Jun Lim
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23603865
UR - https://zenodo.org/records/23603865
AB - We derive the quasi-normal mode (QNM) spectrum of black hole ringdown from the five axioms {12, π, γ1, ln 2, φ} of Array Cosmology (AC) with zero free parameters. The Schwarzschild (χ = 0) fundamental mode (l = 2, n = 0) frequency is ω˜R = γ1/(12π) = 0.37494 (GR exact: 0.37367, error 0.34%), and the quality factor is Q = 2 + Znoise = 2.098 (GR: 2.100, error 0.10%). For Kerr black holes, spin progressively collapses the 12-axis rendering loop to a single Volma stroke (3 axes) via the golden-ratio implosion exponent φ^−2 : the effective axis count is Neff(χ) = 3 + 9(1 − χ) φ−2 , yielding ω˜R(χ) = γ1/[π Neff(χ)] with RMS 2.3% against numerical relativity. The quality factor Q(χ) = (2+Znoise)/(1−χ) 1/2−Znoise achieves RMS 2.2%. The overtone spacing is ∆˜ωI = 2Znoise (0.8% match). Applied to GW150914 (M = 68.5 M⊙, χ = 0.69), the model predicts f = 242 Hz and τ = 4.41 ms, within 1.1σ and 0.8σ of LIGO observations respectively. All five axioms are employed: 12 (loop topology), π (angular circumference), γ1 (tension anchor), ln 2 (Landauer floor), and φ (spin collapse). This supersedes the previous AC ringdown paper, correcting the erroneous ×1.699 damping-time scaling
ER -