Short note proves the existence of continuant residues in endpoint-compression word fibers, indicating their irreducibility and smoothness.
This short note identifies the continuant residue hidden inside endpoint walls of endpoint-compression word fibers. It proves that the inherited endpoint branch is governed by a non-adjacent continuant Km K_mKm, shows that this residue is irreducible and smooth on the relevant generic branch, and separates positive-chamber terminal collapse from signed/complex continuant cancellation.
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Hiroyuki Shioiri (2026) studied this question.
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