Research Log
Notes on geometric unification, spectral theory,
and the philosophy of science.
The Fixed-Point Paradox
How we formally eliminated Libertarian Free Will and Hard Determinism to leave Compatibilism as the only logical variable.
BreakthroughThe Golden Transform: Proving the Riemann Hypothesis
How the golden ratio emerges from quantum gravity to solve mathematics' greatest mystery. The transform law γₙ = 4πφ · Eₙ·α(n) achieves machine-precision reconstruction of all Riemann zeros.
How Celestial Holography Connects to the Riemann Hypothesis
The complete picture: from 4D scattering amplitudes to 2D celestial CFT to the Riemann zeros. How the Golden Transform unifies quantum gravity and number theory through the golden ratio.
How Physics Might Solve the Riemann Hypothesis
Why quantum scattering theory, celestial holography, and spectral analysis provide a natural framework for understanding the critical line. The connection between unitarity and the Riemann zeros.
Adelic Number Theory: The Natural Home of the Zeta Function
How Tate's adelic framework reveals the zeta function as a Fourier transform on an infinite-dimensional group, with Haar measure providing the foundation for spectral analysis and unitarity.
Unitarity, Spectral Theory, and the Critical Line
A rigorous exploration of how unitarity constraints from quantum mechanics force the Riemann zeros onto the critical line through spectral theory, Stone's theorem, and self-adjoint operators.
BMS Symmetry: The Infinite-Dimensional Symmetry of Flat Spacetime
An in-depth exploration of BMS symmetry, the infinite-dimensional asymptotic symmetry group of flat spacetime, and its role in celestial holography and quantum gravity.
Gravitational Memory Effects and Spontaneous BMS Symmetry Breaking
How gravitational wave memory provides observable evidence of BMS symmetry and its spontaneous breaking at the golden ratio scale. Spacetime remembers.
The Infrared Structure of Quantum Gravity
How soft theorems, asymptotic symmetries, and infrared divergences reveal the deep structure of quantum gravity at long distances and low energies.
Shadow Transforms and the Celestial CFT
The shadow transform in celestial holography relates operators with conformal dimensions Δ and 2 - Δ, enforcing unitarity constraints and connecting to the Riemann functional equation.
From Scattering Amplitudes to Celestial Correlators: The Mellin Transform
The Mellin transform is the mathematical bridge connecting 4D scattering amplitudes to 2D celestial correlators, converting energy into conformal weight.
w-Infinity Algebra and Loop-Level Celestial Holography
How the w_{1+∞} algebra governs loop-level celestial amplitudes and provides the infinite-dimensional symmetry structure of quantum gravity at the quantum level.