Research & Publications

Andrew M. Brilliant is Director of Computational Physics at Applied Dynamics Research, an aerodynamics and CFD consultancy, and an independent researcher in fundamental physics based in Sapporo, Japan. He is also the founder of AMB Aero, and a member of the Institute of Electrical and Electronics Engineers (IEEE) and the International Association of Engineers (IAENG). The engineering practice (race-car aerodynamics, wind-tunnel testing, high-fidelity simulation) funds and informs the physics, and the same discipline (pre-registration, seeded reproducibility, adversarial self-audit) runs through both. Why motorsport? Because it's physics, with money.

The physics program has two strands. The first is empirical: the geometry of fermion mass relations, the Koide relation for the charged leptons read as a Descartes circle configuration, its outer-Soddy completion, and the light-fermion mass values found by rigorous mathematical exploration of the resulting map. The second is methodological: how to tell structure from coincidence when a pattern is found before its test, via Monte Carlo null models, pre-registered protocols, and validation criteria for machine-learning pattern discovery in physics.

The program started by accident, in engineering. I was building a coupled solver for condensed-matter problems and needed fermion masses as a calculation, not a lookup table: something that could improve as the input data improved, without waiting for the underlying theory to be settled. That requirement led to the Koide formula: a partial empirical relation from 1982, published by Yoshio Koide, a maverick working in western Japan, in a journal that no longer exists, which then predicted the tau mass and has only converged as lepton masses became precision quantities. The original paper survives mostly as lore: when I went to read the 1982 Lettere al Nuovo Cimento article itself, the only obtainable copy was a scanned fax, retrieved from KEK's preprint archive with Alejandro Rivero's help. One writer called it "the mystery that launched a thousand papers." I only needed a closure; I got a problem I couldn't put down.

There is a prior question under all of this: why mass, at all? For most Standard Model work the masses are simply filled in from experiment, handed to the Lagrangian through the Yukawa couplings, and for most situations that is fine. But the line between "Standard Model" and "condensed matter," or between a quark mass and an entry in the periodic table, is not a line that exists in nature. If you want to write a quantum fluid solver you build up from the roots, and the Yukawa sector is no help there: it is unsettled, and it drags structure into the calculation that does not matter for the mathematics you actually need. Worse, the masses themselves are not stable objects. They run. At M_Z they take values far from their low-energy ones. A colleague once put it to me memorably: "But aren't the masses just nonsense anyway? At M_Z it's some wild number compared to anywhere else." The point stands: mass is not a stable thing you can write down once. Why can adding energy change mass, in a way that is coupled and not obvious on its face? The intuitions I had imported from cosmology broke down exactly here, and a place where familiar thinking breaks is usually where the secrets are hiding. Somewhere in those years I came across the lazier version of this resignation, a messageboard post, long since lost, asking "maybe the masses are just random?" Something in me lit up at that. No. The universe does not roll dice; it is math mathing itself, and that is exactly why it is so beautiful. This program is that conviction, made methodical.

The formula is clearly geometric, so the question became: what geometry? Kocik had pointed at Descartes circle configurations, and computing the fourth circle of the lepton configuration produced a number that landed on the strange-quark mass, evaluated at the lepton-sum scale I had just written down, to 0.06σ. That result became the Descartes–Soddy preprint. Normalizing the mass spectrum to the lepton sum then exposed the familiar light-quark ratios, including the one flagged year after year in the FLAG lattice review, and the geometric-mean structure that became the MPLA paper. And because none of this could be certified as structure rather than coincidence by anyone, not me and not a referee, the first paper I actually finished was the philosophy one, proposing a repository for pre-theoretical patterns instead of crowding the literature with pattern hunts. Everything since has followed that discipline: pre-register first, survive one cycle of new PDG data, and only then write the paper.

Every numerical claim in the papers below is backed by public, pre-registered code with committed result artifacts. Where a result is a candidate rather than a conclusion, the papers say so.