Universal Spectral Bit–Ratio at Event Horizons

We discover a universal dimensionless ratio (approximately 15.7) that emerges from the interplay between spectral geometry and thermal quantization at event horizons. This ratio characterizes how the energy of the first Laplacian eigenmode relates to the thermal bit energy defined by Hawking temperature and Landauer's information principle. KEY CONTRIBUTION The ratio is universal: it manifests identically across all three canonical horizon types - black holes (Schwarzschild), cosmological horizons (de Sitter), and accelerated observers (Rindler) - independent of mass, size, or acceleration parameter. Numerical verification confirms the theoretical prediction for both stellar-mass black holes and cosmological scales. SIGNIFICANCE This work synthesizes three established frameworks (spectral geometry, KMS thermal states, holographic bounds) into a novel connection revealing a fundamental structural principle. The result suggests that quantum geometric modes and thermal quantization at horizons are not independent but governed by a universal relationship. Implications extend to: - Microscopic structure of black hole entropy - Information theory constraints on quantum gravity - Holographic principle refinement - Connections between different quantum gravity approaches METHODOLOGY The analysis combines rigorous mathematical derivation of Laplacian eigenvalues on three-sphere geometry with thermodynamic quantization via KMS periodicity conditions. Results are verified numerically across multiple physical scales and horizon types. MATERIALS Includes main letter-format paper (2 pages) and comprehensive supplemental material with: - Complete mathematical proofs - Higher-dimensional generalizations - Bekenstein bound analysis - Holographic scaling relationships - Speculative Loop Quantum Gravity connections HONEST ASSESSMENT - Built on well-established components (Hawking, Bekenstein, Unruh frameworks) - Novel synthesis into this specific universal ratio - LQG connection is speculative - Opens questions for future investigation VERIFICATION Solar-mass black hole: computed ratio ≈ 15.77 (theoretical: 15.700556) Cosmological horizon: computed ratio ≈ 15.73 The universality across distinct horizon types with identical ratio is the central finding and the primary novelty of this work.