17 problems

Let $G$ be a graph that is p-logarithmic in $d=4$ dimensions and whose vertices all have degree at most $4$; call such a graph a $\phi^4$ graph. Let $\mathcal{P}(G)$ denote its per…

For a $phi^4$ graph $G$, let $P_G$ denote its Feynman period and let $H_G$ denote its Hepp bound, a combinatorial invariant of $G$. Panzer's Hepp-bound conjecture. Two $phi^4$ grap…

Non-crossing chord diagram conjecture. The regions contributing to $A_n^{phi^4}$ are in bijection with the $C_{n/2-1}$ possible non-crossing chord diagrams. The region associated w…

The minimally subtracted $\phi^4$ theory has a beta function whose primitive contribution is considered at increasing loop order. Folklore dominance conjecture. The primitive contr…

Let $P_{l,n}$ denote the Feynman period indexed by loop order $l$ and graph number $n$ in the notation of the cited census. Loop-order-eight period conjecture. The first examples o…

Let $L$ denote loop order, and let the four-dimensional primitive beta function be the contribution of primitive graphs to the beta function in four-dimensional scalar $c6^4$ theor…

Primitive beta-function asymptotic conjecture. The leading growth of the primitive beta function satisfies

Cachazo's H-function conjecture. The contributing regions, each corresponding to a polyhedral cone of dimension $n/2-1$ in $cmathbb{R}^{n-3}$, are exactly the solutions to $H(x)=0$…

Let $n$ be even, let $x=(x_0,cldots,x_{n-3})cincmathbb{R}^{n-2}$, and define … A non-crossing chord diagram is a perfect matching of $n-2$ ordered points, with chords $ctheta_{ab}$…

Period-determines-extended-graph-permanent conjecture. If $G$ and $H$ have equal periods, then they have equal extended graph permanents.

Period-determines-$c_2$ conjecture. If $G$ and $H$ have equal periods, then they have equal $c_2$ invariants.

Schnetz's cosmic Galois closure conjecture. The space $V$ is itself closed under the action of the cosmic Galois group $\mathcal{C}_{0,0}$.

Common critical parameter conjecture. The two constants coincide,

Let $G_1$ and $G_2$ be primitive-divergent graphs in $\phi^4$ theory. For a graph $G$, let $\widehat G$ be its completion, obtained by adjoining a vertex to the four three-valent v…

Let $G_1$ and $G_2$ be primitive-divergent graphs in $phi^4$ theory, let $I_{G_i}$ denote their residues, and let $c_2(G_i)$ be their graph invariants. Period-determines-$c_2$ conj…

Let $G$ be a primitive-divergent graph in $phi^4$ theory, and let $c_2(G)$ denote its graph invariant. The completion relation identifies graphs whose completions are isomorphic; w…

Unbounded Tate-defect conjecture. There exists a sequence of primitive-divergent graphs $G_i$ in $\phi^4$ such that