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Bulk residual closure and boundary residual reduction for elliptic XYZ-type regular-derivative chains
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DOI：10.1016/j.nuclphysb.2026.117586.png)
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Abstract
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We introduce a two-level residual construction for elliptic XYZ-type regular-derivative chains. The first level places a full two-spin Pauli W-envelope into the ordinary Yang–Baxter residual and closes the bulk sector, inside a nonsingular finite-coefficient leakage chart and a selected equal-orientation component, onto Baxter’s elliptic eight-vertex branch. The second level places a full operator-valued boundary V-envelope into the reflection residual and records a boundary residual-reduction ledger which isolates an explicit boundary-extension candidate carrying an antisymmetric impurity-algebra coupling outside the displayed factorized dressing span. We then insert the closed bulk object and the ledger-retained boundary object into a double-row trace functional and compute its normalized regular derivative, obtaining an algebra-valued XYZ-type regular-derivative operator with a boundary-extension impurity. In physical terms, this object gives a residual-level route from elliptic eight-vertex bulk weights to an open XYZ spin-1/2 chain with an algebra-valued boundary impurity. The construction does not claim a complete reflection-equation certificate for the displayed boundary object; rather, it separates the proven bulk closure, the boundary residual-reduction diagnostic, and the resulting regular-derivative algebraic operator.
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