Abstract
A previously suggested $N$-pion amplitude, constructed from symmetric-group (${\mathrm{S}}_{N}$) considerations, satisfies two desirable factorization properties: (i) There is bootstrap consistency at all internal-pion poles in the $N$-point function. (ii) Using some earlier results of Schwarz, it is possible to prove that a simplified (Gervais-Neveu) version of the model factorizes with finite degeneracy for general $\ensuremath{\rho}$ intercept ${\ensuremath{\alpha}}_{\ensuremath{\rho}}(0)$, and not only for integer values; we except that the full model should share the same property.
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