https://dongzhezheng.com/blog/ Research notes on geometric analysis, rigidity theory, matroid theory, mathematical physics, scientific machine learning, and formal proof. en-us Sun, 04 Oct 2026 03:32:27 GMT https://denzelzheng.com/blog/recurrence-zero-patterns/ https://denzelzheng.com/blog/recurrence-zero-patterns/ Sun, 04 Oct 2026 03:32:27 GMT A construction over one fixed field resolves Derksen’s inverse conjecture: every p-normal set occurs as the exact zero set of a linear recurrence, with a companion Lean 4 proof. https://denzelzheng.com/blog/variational-relic-geometry/ https://denzelzheng.com/blog/variational-relic-geometry/ Sat, 26 Sep 2026 12:00:00 GMT A variational framework for relics with multiplicity connects the construction of local minimizing models to global control of singular-set measures. It resolves Fujioka’s 33-year-old classification problem for minimizing projective cones (1993) and answers Mazowiecka–Miśkiewicz–Schikorra’s question on stability beyond sphere targets for every complex projective space. https://dongzhezheng.com/blog/body-pin-rigidity-collinearity-flags/ https://dongzhezheng.com/blog/body-pin-rigidity-collinearity-flags/ Thu, 20 Aug 2026 12:00:00 GMT A stress-codimension theorem and a recursive system of collinearity flags yield the Euclidean three-dimensional body–pin partition criterion. https://dongzhezheng.com/blog/bland-jensen-conjecture/ https://dongzhezheng.com/blog/bland-jensen-conjecture/ Fri, 07 Aug 2026 12:00:00 GMT We explore a proof strategy for the Bland–Jensen conjecture using nine parity equations, Rado’s theorem, and fixed-dimensional quotient geometry.