MathOverflow

Definitive documentation and rigorous derivations are archived in the repository for review: SO-HMS Core Mathematical Framework
Formal Theoretical Statement
We formalize a boundary-free, invariant stabilization criteria for multi-objective functional paths acting on an infinite-dimensional Hilbert space $\mathcal{H} = L^2(\mathcal{M})$, where $\mathcal{M}$ is a globally connected, compactly supported Riemannian...

In Jain–Kravitz, Relative Lonely Runner spectra, for an integer velocity vector$v=(v_1,\dots,v_n)$ the maximal-loneliness deficit is$$D(v)=\tfrac12-\max_{t\in\mathbb R}\ \min_{i:\,v_i\neq0}\ \|v_i t\|,\qquad \|x\|=\operatorname{dist}(x,\mathbb Z),$$and...

Alice and Bob take turns colouring the edges of a complete graph $K_n$ red and blue respectively, with Alice going first. They continue until the graph is fully coloured.
Next, they take turns removing vertices until a triangle $K_3$ remains. Alice wins if it is monochrome red, Bob wins if it is monochrome blue, otherwise it is a draw....

Let $M$ be a manifold. Let $G$ be a Lie group and $\mathfrak{g}$ be its Lie algebra.
Let $P(M,G)$ be a principal bundle. Recall that, a connection on $P(M,G)$ is a distribution $\mathcal{H}\subseteq TP$ satisfying certain conditions. Equivalently, a $\mathfrak{g}$-valued differential forms on $P$ satisfying certain conditions....