Prescribing the Zeros of a Linear Recurrence
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.
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✦ Notes & Essays
When Two Singularities Merge: Variational Relic Geometry
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.
Stress Degeneracy, Collinearity Flags, and Three-Dimensional Body–Pin Rigidity
Stress degeneracy and collinearity flags establish the Euclidean three-dimensional body–pin partition criterion, resolving a conjecture that remained open for nearly two decades.
The Bland–Jensen Conjecture Through Quotient Geometry
Nine parity equations, Rado’s theorem, and quotient geometry of fixed dimension resolve the 1987 conjecture nearly four decades after it was posed.