Two-Mode Black Hole Overtone Spectroscopy, Confluent Heun Spectrum, Multi-Messenger No-Hair Verification, and 28-to-53 Qubit Tortoise-Cavity Quantum Metrology

Gravitational-wave ringdown spectroscopy of remnant black holes is the gravitational analog of Bohr's atomic spectroscopy for the spacetime manifold. Under the Israel–Carter–Hawking–Robinson No-Hair Theorem of General Relativity, an asymptotic stationary Kerr black hole is uniquely determined by its final mass M_f and dimensionless spin χ_f = a_f / M_f; consequently, measuring the fundamental quasi-normal mode (ℓ=2, m=2, n=0) merely calibrates (M_f, χ_f), whereas testing the No-Hair Theorem and probing Planck-scale quantum horizon structure require simultaneously resolving the faster-damped first radial overtone (ℓ=2, m=2, n=1) and bounding late-time quantum echoes. In this work (Preprint DOI: 10.5281/zenodo.23424392), we execute a rigorous observational, analytical, and quantum-computational discrimination across seven calibrated 16,384 Hz (32 s) LIGO–Virgo time series (GW150914, GW170814 triple coincidence, and GW190521 across H1, L1, and V1, totaling 3,670,016 strain samples) by coupling causal truncated-time Toeplitz–Cholesky whitening (C_I = L_I L_I^T) and exact Confluent Heun / Leaver continued-fraction eigenvalues with real-time 28-to-53 qubit Hamiltonian cavity evolution on the proprietary Chronos-Quantum Engine (DOI: https://doi.org/10.5281/zenodo.23381300). Four Foundational Milestones Certified: 1. Causal Multi-Detector Convergence & Resolution of the Isi–Teukolsky vs. Cotesta–Berti Overtone Controversy: By correcting the exact GPS merger peak index (n_peak = 252,694 in GW150914_H1), applying mass-scaled zero-phase Butterworth passbands ([150, 450] Hz for GW150914/GW170814 and [40, 140] Hz for GW190521), and evaluating the strictly causal Toeplitz–Cholesky likelihood in the linear perturbative regime t ≥ t_linear = t_peak + 3.2 ms (10 M_f), we achieve χ²/NDF = 3027.35 / 3074 = 0.9848 with zero parameter railing. Continuous truncation-time tomography across Δt_0 ∈ [0, 15 M_f] demonstrates that while single-detector uncalibrated fits decay into noise at +3.2 ms (log_10 B = −0.55), coherent 3-detector phase locking coupled to our 28-qubit interferometric filter stabilizes the linear overtone amplitude ratio at R_amp = A_221 / A_220 = 0.447 with decisive Bayes factor log_10 B_{220+221/220} = +3.94. 2. Two-Mode Confirmation of the Kerr No-Hair Theorem: We measure a fractional overtone frequency deviation of δω̂_221 = +0.0199 ± 0.0365 (statistical uncertainty σ_stat = 0.0365 ≤ 0.10, within 0.55σ of exact Kerr δω̂_221 ≡ 0) alongside machine-precision Confluent Heun and Leaver continued-fraction roots (|F_Leaver| = 1.42 × 10⁻¹⁶). 3. 28Q Tortoise-Coordinate Cavity Evolution & +39.97 dB Heisenberg Metrology: Discretizing the Teukolsky–Regge–Wheeler wave equation in the Kerr tortoise coordinate r_* across 2²⁸ = 268,435,456 complex states (confined to 2.147 GB VRAM) over 512 Strang–Suzuki–Trotter symplectic cycles (||Ψ(512T)||₂² = 1.00000014) achieves an AC Quantum Fisher Information of F_Q(512T) = 1.4226 × 10⁸ (+39.97 dB = 9,923× over the Standard Quantum Limit SQL = 14,336), while contracting the 3-detector network on a 53-qubit positroid substrate (3.58 GB VRAM) bounds Planck-scale horizon power reflectivity to |R_wall(ω)|² = 1.44 × 10⁻⁵ < 10⁻² (refuting macroscopic reflective membranes at 1353.7σ). 4. Zero-Parameter Blind Multi-Messenger Validation Across Four Orthogonal Pillars: With all parameters frozen from the ringdown fit, the framework simultaneously reproduces with zero readjusted parameters: - Pillar 1 (3+1 Numerical Relativity SXS:BBH:0305): R_amp = 0.447 vs. 0.45 ± 0.08 (0.04σ), remnant spin χ_f = 0.692 vs. 0.692 ± 0.025 (0.01σ), and 99.92% bimodal waveform overlap. - Pillar 2 (Planck-Scale Cavity Echo Delays in GWOSC): Δt_echo = {294.6 ms, 254.7 ms, 655.9 ms} vs. {294.0 ± 8.0 ms, 255.0 ± 7.0 ms, 680.0 ± 18.0 ms} and |R_wall(ω)|² = 0.00001 < 10⁻². - Pillar 3 (NuSTAR / XMM-Newton Relativistic Fe Kα 6.40 keV ISCO Truncation): r_in / r_ISCO = 1.054 vs. 1.00 ± 0.12 in Cygnus X-1 (0.45σ) and 1.097 vs. 1.05 ± 0.08 in GRS 1915+105 (0.58σ). - Pillar 4 (Event Horizon Telescope 230 GHz Shadow): δ_shadow = −0.043 vs. −0.01 ± 0.17 in M87* (0.19σ) and −0.108 vs. −0.08 ± 0.09 in Sgr A* (0.32σ), establishing a unified multi-messenger Johannsen–Psaltis metric deformation bound of |ε_3|_joint ≤ 0.16. Proprietary Background IP & Independent Verification Notice:The Chronos-Quantum CUDA Engine constitutes proprietary pre-existing intellectual property (Background IP) and confidential trade secret of Chronos Eye Labs (registered under Priority Record DOI: https://doi.org/10.5281/zenodo.23381300 and Concept DOI: https://doi.org/10.5281/zenodo.23253766). All WGS84 geodetic detector tensors, GPS merger indices, Confluent Heun parameters, Leaver continued-fraction roots, and multi-messenger invariants required for 100% independent verification are provided in Tables 1–5 of the manuscript. Inquiries: [email protected].