Australian Guitar Maker Posts Controversial Whitepaper

The MIA Research Foundation has released a constructive operator-theoretic framework for L-functions in the Selberg class, authored by Trent Palelei. The paper aims to resolve the longstanding Berry-Keating domain specification problem using Stone's Theorem (1932) and a unique "multiplicative sieve" boundary condition.

Beyond Additive Barriers

The core of the controversy lies in Palelei’s assertion that traditional additive operators—like those used in the Epstein zeta counterexamples—fail to account for the multiplicative symmetry inherent in the primes. By shifting the focus from geometric boundary data to arithmetic averaging over units modulo n, the framework establishes a "spectral wall" that enforces the critical line.

Key technical highlights include:

• Unconditional Operator Theory: Utilizing Stone's Theorem to construct a unique self-adjoint generator (H = πA²) where A = -ix(d/dx).
• The Multiplicative Boundary: A boundary condition derived from φ(n)-averaging that selects only functions with Euler product structure.
• Spectral Wall Inequality: A proof-sketch demonstrating that any off-critical-line zero incurs a strictly positive "unitarity defect," effectively barring zeros from existing anywhere but Re(s) = 1/2.

Addressing the "Hilbert-Pólya" Dream

For decades, the mathematical community has sought a self-adjoint operator whose spectrum corresponds to the Riemann zeros. Palelei argues that previous attempts failed not because such an operator doesn't exist, but because they were modeled on additive physics (Hamiltonians) rather than multiplicative spectral theory.

The framework has been tested across extensive computational models, including non-abelian Artin representations and the icosahedral A5 case, showing zero deviation from theoretical predictions.