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INTER-UNIVERSAL TEICHMULLER THEORY III: ¨
CANONICAL SPLITTINGS OF THE LOG-THETA-LATTICE
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Theorem 3.11. (Multiradial Algorithms via LGP-Monoids/Frobenioids)
Fix a collection of initial Θ-data
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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
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Corollary 3.12. (Log-volume Estimates for Θ-Pilot Objects) Suppose
that we are in the situation of Theorem 3.11. Write
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Proof. We begin by observing that, since |log(q)| > 0,
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This indeterminacy has the effect of rendering
meaningless any attempt to perform a precise log-volume computation as in (xi).QED
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