Andrew A. Schoen

An improved lower bound for the distortion of a knotted curve

We prove that every non-trivial rectifiable tame knot embedding K ⊂ R³ has distortion δ(K) > 6.5321. Consequently, the infimum within every non-trivial tame knot type is at least 6.5321. This improves the 6.32 bound in version 1.0 by 0.2121. The proof combines essential-secant pr...

Equivalence Principle Extension: Universal Non-Minimal Matter–Metric Coupling

The weak equivalence principle is traditionally stated as universal gravitational free fall, tested by composition-dependent experiments to fractional precision 10^-15. In minimally coupled point-particle limits this is closely related to universal kinetic propagation, but canoni...