www.kurims.kyoto-u.ac.jp/~motizuki/Inter-universal%20Teichmuller%20Theory%20III.pdf INTER-UNIVERSAL TEICHMULLER THEORY III: ¨ CANONICAL SPLITTINGS OF THE LOG-THETA-LATTICE P153 Theorem 3.11. (Multiradial Algorithms via LGP-Monoids/Frobenioids) Fix a collection of initial Θ-data P159 Proof. The various assertions of Theorem 3.11 follow immediately from the definitions and the references quoted in the statements of these assertions — cf. also the various related observations of Remarks 3.11.1, 3.11.2, 3.11.3, 3.11.4 below. QED P173 Corollary 3.12. (Log-volume Estimates for Θ-Pilot Objects) Suppose that we are in the situation of Theorem 3.11. Write P174 Proof. We begin by observing that, since |log(q)| > 0, P186 This indeterminacy has the effect of rendering meaningless any attempt to perform a precise log-volume computation as in (xi).QED （引用終り） 以上
