Articles
Structural patterns across domains — observed, formalized, verified.
The Proof That Changed Nothing
In 1952, Dyson proved the perturbation series underlying QED diverges. The proof was never retracted or refuted. It changed nothing. An examination of the structural dynamics — threshold cascade, boundary formation, narrative compression — that absorbed it.
The Step That Disappears
Lightning strikes eight million times a day at field strengths an order of magnitude too weak for conventional breakdown. Five candidate triggers compete for the explanation. A pattern-mathematics analysis dissolves the competition and predicts the streamer-to-leader transition mechanism.
The Self-Assembling Cosmos
From stellar nurseries to the cosmic web, the same filamentary geometry appears at every observable scale. Laboratory plasma experiments reveal the self-organizing mechanism that standard cosmology compressed out of view.
The Force You Were Taught to Cancel
Ampère’s original force law contains a longitudinal component that the standard framework treats as exactly zero. It isn’t zero — it was compressed out across four reformulation steps. A formally verified account of the sleeping force.
The Coupling Constant You Stopped Seeing
Four of physics' fundamental force laws share one mathematical skeleton. Maxwell's reformulation hid the structural invariance. A formal verification program is proving it matters.
Three Problems, One Shape
An electrical engineer, an immunologist, and a teacher walk into the same equation. The coupling pattern they share is not metaphor — it is structural identity, verified across 18 domains.