12 problems

Signature-independence conjecture for Adinkra invariant factors
arXiv@arxiv
Let an Adinkra be a signed graph with signed Laplacian $L$ , and let its invariant factors mean the diagonal entries in the Smith normal form of $L$ . A signature is the choice of si…
Conjectureopenadinkras signed-graphs smith-normal-form
1
The superfield realization conjecture for engineerable Adinkra topologies
arXiv@arxiv
Superfield realization conjecture. For every $N$ and every topology of engineerable Adinkras, there exists a corresponding set of superderivative constraints such that the set of s…
Conjectureopenadinkras superfields supersymmetry
0
IKKY's Smith normal form conjecture for Adinkra Laplacians
arXiv@arxiv
Let $\mathcal{A}$ be an Adinkra with Laplacian $L(\mathcal{A})$ , $N$ colors, and $v$ vertices. Fix a color and form $\hat{L}(\mathcal{A})$ over $\mathbb{Z}[x]$ by replacing the dia…
Conjectureopenadinkras critical-groups smith-normal-form
0
Universal Smith normal form conjecture for the Adinkra Laplacian
arXiv@arxiv
Let $L$ be the Laplacian of an Adinkra, and let $\hat{L}$ be its polynomial lift over $\mathbb{Z}[x]$ . Write the Smith normal form of $L$ as a tuple of invariant factors, with mult…
Conjectureopenadinkras commutative-algebra smith-normal-form
0
Adinkra nontrivial-invariant-factor conjecture
arXiv@arxiv
Let $C$ be a doubly even binary code associated to an Adinkra, let $\boldsymbol{1}$ denote the length- $N$ all-ones codeword, and let $#V$ be the number of vertices of the Adinkra.…
Conjectureopenadinkras coding-theory spectral-graph-theory
1
The HYMNs conjecture for adinkra shape isomorphisms
arXiv@arxiv
HYMNs conjecture. The HYMNs of an adinkra carry all information about its shape isomorphisms: two adinkras are isomorphic if and only if their HYMNs are the same.
Conjectureopenadinkras graph-isomorphism spectral-invariants
0
Hübsch's construction conjecture for Adinkraic representations of 2-d supersymmetry
arXiv@arxiv
Let $R_+$ and $R_-$ be off-shell representations of two copies of the $1$ -d supersymmetry algebra with $p$ and $q$ colors, respectively, and let $Z$ be a symmetry of…
Conjectureopenadinkras representation-theory supersymmetry
1
The ubiquity conjecture for Adinkras in higher dimensions
arXiv@arxiv
Adinkras are graphical representations of the one-dimensional shadows of supersymmetric representations, and the paper considers their occurrence in higher-dimensional supersymmetr…
Conjectureopenadinkras representation-theory supersymmetry
0
The cis-trans Adinkra compositeness conjecture for off-shell 4D, N = 1 supersymmetry
arXiv@arxiv
Let an off-shell $4D$ , ${\mathcal N}=1$ supersymmetric representation be described by Adinkras, with cis-Adinkra and trans-Adinkra building blocks occurring with multiplicities…
Conjectureopenadinkras representation-theory supersymmetry
0
The 85-Adinkra extension conjecture for $(16,16)$ supersymmetry
arXiv@arxiv
For worldsheet $(16,16)$ -supersymmetry, the paper describes $85$ Adinkras obtained from the $85$ doubly even linear block codes that project the $32$ -cube to three levels, together…
Conjectureopenadinkras supersymmetry worldsheet-theories
0
Existence conjecture for an irreducible $(16,16)$ worldsheet supermultiplet
arXiv@arxiv
The paper considers explicit minimal off-shell supermultiplet constructions for worldsheet $(2,2)$ -, $(4,4)$ -, and $(8,8)$ -supersymmetry and their twisted variants. The $(16,16)$ -m…
Conjectureopenadinkras supersymmetry worldsheet-theories
0
Internal isomorphism conjecture for the $(8,8)$ Adinkras
arXiv@arxiv
The $(64|128|64)$ -node Adinkras associated with the constructions denoted by $E_{8}\times E_{8}$ and $E_{16}$ represent worldsheet $(8,8)$ -supersymmetry supermultiplets, with the b…
Conjectureopenadinkras supersymmetry worldsheet-theories
0