Research series. Each opens with its question and its main result, and keeps the hypotheses that were refuted. Appendices give the background, articles give statements and proofs.
✓confirmed✗refuted△partial○pending
Can the geometric structure of a formally checked proof reveal its main argument without requiring the reader to inspect every inference?
739 + 1,359 declarations · 1,277,896 shared nodes
After a geodesic ceases to minimize, where does it focus and how many geodesics reach the same position and heading?
$\operatorname{sn}^2(\psi+p)=r(p)$
Where a physical field forbids a direction of motion, can sub-Riemannian geometry read the field's local structure?
$\delta(\varepsilon)=1-\tfrac{2}{\pi}K(2\varepsilon),\quad \varepsilon<\tfrac12$
Appendices
Articles
Is the orientation-lifted geometry of visual completion a better instrument for finding cosmic filaments, or even part of the physics that builds them?
mean transport error 4.98 → 4.52 voxels · 3 held-out seeds
How does the visual cortex complete contours that are not there, and what exactly are the optimal curves it draws?
$\dot x=u_1\cos\theta,\quad \dot y=u_1\sin\theta,\quad \dot\theta=u_2$
