Groundbreaking contributions?

Breakthroughs of which I am most proud:

1. Armstrong, E.  Colonel Mustard in the Aviary with the Candlestick: a limit cycle attractor transitions to a stable focus via supercritical Andronov-Hopf bifurcation. https://arxiv.org/abs/1803.11559, 2018 April 1; PDF

2. Armstrong, E. A Neural Networks Approach to Predicting How Things Might Have Turned Out Had I Mustered the Nerve to Ask Barry Cottonfield to the Junior Prom Back in 1997. https://arxiv.org/abs/1703.10449, 2017 April 1; PDF

3. Armstrong, E. Pipe-cleaner Model of Neuronal Network Dynamics. https://arXiv:1603:09723, 2016 April 1; PDF

4. Armstrong, E. Non-detection of the Tooth Fairy at Optical Wavelengthshttps://arxiv.org/abs/1204.0492?context=astro-ph, 2012 April 1; Journal of Irreproducible Results 52, 3: 22-25, 2014; PDF

 

And here are suggested qualifying exam questions for physics graduate students at UC San Diego, which I wrote while studying for my own.