arXiv:2611.08687v1 Announce Type: new Abstract: We combine McShane's identity for a once-punctured torus with the length-spectrum identity of Wang and Xue. An exact identity in each primitive homology class yields a finite limit for the difference of two divergent length-spectrum sums over self-intersecting hyperbolic geodesics. The limit is $\frac18$ and is equivalent to McShane's identity. We also derive higher-iteration identities governed by integer divisors.
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