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The encoding is executed by a small virtual machine comprising a sparse hypergraph, a circular doubly-linked list (CDLL) of node references, and $k$ traversal pointers, where $k$ bounds the hyperedge arity. Instructions either move a pointer through the CDLL or insert a hyperedge, optionally together with new nodes, into the hypergraph. Every string over $\\Sigma_{\\mathrm{HG}}$ decodes to a valid hypergraph; the alphabet is closed. A greedy \\emph{HypergraphToString} (h2s) algorithm encodes any connected hypergraph into a string; a backtracking variant seeded at nodes of lexicographically maximal structural tuple produces a \\emph{canonical string} $w^{*}$, which we conjecture to be a complete isomorphism invariant. Canonical-string equality then d","title":"Instruction Set and Language for Hypergraphs","url":"https://arxiv.org/abs/2607.10194","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.10194v1 Announce Type: cross \nAbstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\\Sigma_{\\mathrm{HG}}$. The encoding is executed by a small virtual machine comprising a sparse hypergraph, a circular doubly-linked list (CDLL) of node references, and $k$ traversal pointers, where $k$ bounds the hyperedge arity. Instructions either move a pointer through the CDLL or insert a hyperedge, optionally together with new nodes, into the hypergraph. Every string over $\\Sigma_{\\mathrm{HG}}$ decodes to a valid hypergraph; the alphabet is closed. A greedy \\emph{HypergraphToString} (h2s) algorithm encodes any connected hypergraph into a string; a backtracking variant seeded at nodes of lexicographically maximal structural tuple produces a \\emph{canonical string} $w^{*}$, which we conjecture to be a complete isomorphism invariant. 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