\extlabel{III:rw:sec:III-introduction}{1}
\extlabel{III:fl:def:intro-parameter}{1.1}
\extlabel{III:fl:eq:main-full-label}{1.1}
\extlabel{III:rw:thm:III-main}{1.2}
\extlabel{III:rw:sec:earlier-work}{1.2}
\extlabel{III:rw:sec:descent-route}{2}
\extlabel{III:rw:sec:inputs}{3}
\extlabel{III:rw:in:llafforgue}{1}
\extlabel{III:rw:in:descent}{2}
\extlabel{III:rw:sec:from-I}{3.2}
\extlabel{III:fl:sec:parameters-parameters}{4}
\extlabel{III:fl:app:conventions}{4}
\extlabel{III:fl:def:central-period-lattice}{4.1}
\extlabel{III:fl:def:full-excursion-summand}{4.2}
\extlabel{III:fl:sec:classical-descent}{5}
\extlabel{III:fl:sec:parameters}{5}
\extlabel{III:fl:lem:prelim-form}{5.1}
\extlabel{III:fl:prop:prelim-block}{5.2}
\extlabel{III:fl:lem:prelim-pole}{5.4}
\extlabel{III:fl:lem:prelim-coeff}{5.5}
\extlabel{III:fl:prop:prelim-full-parameter}{5.6}
\extlabel{III:fl:sec:type-a}{5.4}
\extlabel{III:fl:lem:central-torus-lift}{5.7}
\extlabel{III:fl:thm:type-a-realization}{5.8}
\extlabel{III:fl:sec:odd-tools}{5.5}
\extlabel{III:fl:lem:odd-exchange}{5.9}
\extlabel{III:fl:lem:odd-averaging}{5.10}
\extlabel{III:fl:cor:jacquet-coset-decomposition}{5.10}
\extlabel{III:fl:sec:common-descent}{6}
\extlabel{III:fl:sec:gl-whittaker}{6.1}
\extlabel{III:fl:lem:gl-whittaker}{6.1}
\extlabel{III:fl:lem:gl-induced-whittaker}{6.2}
\extlabel{III:fl:lem:regularized-eisenstein-family}{6.3}
\extlabel{III:fl:lem:residual-image-square-integrable}{6.4}
\extlabel{III:fl:cor:residual-image-irreducible}{6.5}
\extlabel{III:fl:lem:residual-analytic}{6.6}
\extlabel{III:fl:sec:orthogonal-descent}{7}
\extlabel{III:fl:prop:uniform-b-jacquet}{7.1}
\extlabel{III:rw:eq:descent-roots}{7.1}
\extlabel{III:rw:eq:jacquet-criterion}{7.2}
\extlabel{III:rw:lem:jacquet-double-coset}{7.2}
\extlabel{III:rw:eq:blocks-increase}{7.3}
\extlabel{III:rw:lem:jacquet-intersection}{7.3}
\extlabel{III:rw:lem:jacquet-locus}{7.4}
\extlabel{III:rw:lem:jacquet-characters}{7.5}
\extlabel{III:rw:lem:jacquet-two-parabolics}{7.6}
\extlabel{III:rw:sec:smallest-case}{7.3}
\extlabel{III:fl:lem:uniform-row-separation}{7.8}
\extlabel{III:fl:lem:uniform-interleave}{7.9}
\extlabel{III:rw:fig:interleave}{1}
\extlabel{III:fl:prop:uniform-b-nonzero}{7.10}
\extlabel{III:rw:fig:siegel-exchange}{2}
\extlabel{III:rw:rem:odd-descent-computer}{7.11}
\extlabel{III:fl:sec:odd-symplectic}{8}
\extlabel{III:fl:sec:even-residual}{8.1}
\extlabel{III:fl:sec:even-jacobi}{8.2}
\extlabel{III:fl:lem:even-jacobi-nonzero}{8.1}
\extlabel{III:rw:lem:jacobi-embedding}{8.2}
\extlabel{III:rw:fig:even-groups}{3}
\extlabel{III:fl:eq:even-corrected-period}{8.1}
\extlabel{III:fl:lem:even-period-to-generic}{8.3}
\extlabel{III:rw:tab:even-descent-route}{1}
\extlabel{III:fl:lem:descent-vanishing-and-period}{8.4}
\extlabel{III:fl:prop:even-generic-nonzero}{8.5}
\extlabel{III:fl:sec:char2-d}{9}
\extlabel{III:fl:lem:cartier-character-formula}{9.1}
\extlabel{III:fl:eq:cartier-character}{9.1}
\extlabel{III:fl:lem:char2-cartier}{9.2}
\extlabel{III:fl:eq:cartier-frequency-translation}{9.2}
\extlabel{III:fl:lem:char2-row-iteration}{9.3}
\extlabel{III:fl:eq:char2-root-commutator}{9.3}
\extlabel{III:fl:prop:char2-direct-generic}{9.4}
\extlabel{III:rw:tab:char2-route}{2}
\extlabel{III:rw:fig:char2-cross}{4}
\extlabel{III:rw:eq:terminal-commutator}{9.4}
\extlabel{III:rw:eq:terminal-conjugation}{9.5}
\extlabel{III:fl:cor:char2-descent-split}{9.5}
\extlabel{III:rw:rem:two-frequencies}{9.6}
\extlabel{III:rw:sec:orthogonal-realization}{10}
\extlabel{III:fl:lem:orthogonal-descent-cuspidality}{10.1}
\extlabel{III:fl:thm:orthogonal-realization}{10.2}
\extlabel{III:fl:thm:odd-orthogonal-spin-realization}{10.3}
\extlabel{III:fl:cor:char2-odd-orthogonal-realization}{10.4}
\extlabel{III:fl:sec:odd-theta}{11}
\extlabel{III:fl:eq:quadratic-levi}{11.1}
\extlabel{III:fl:eq:quadratic-unipotent}{11.2}
\extlabel{III:fl:eq:quadratic-fourier}{11.3}
\extlabel{III:fl:lem:theta-jacquet-module}{11.1}
\extlabel{III:fl:eq:quadratic-whittaker-transform}{11.4}
\extlabel{III:rw:lem:whittaker-hecke}{11.2}
\extlabel{III:fl:eq:universal-whittaker-hecke}{11.5}
\extlabel{III:fl:eq:quadratic-interlacing}{11.6}
\extlabel{III:rw:prop:theta-spherical}{11.3}
\extlabel{III:fl:eq:quadratic-lattice-value}{11.7}
\extlabel{III:fl:prop:odd-theta-Whittaker}{11.5}
\extlabel{III:fl:eq:quadratic-global-unfolding}{11.8}
\extlabel{III:fl:cor:odd-theta-moment}{11.6}
\extlabel{III:fl:sec:classical-double-line}{12}
\extlabel{III:fl:lem:generic-double-line-obstruction}{12.1}
\extlabel{III:fl:lem:generic-cuspidal-support}{12.2}
\extlabel{III:fl:prop:classical-doubled-line-extraction}{12.4}
\extlabel{III:fl:thm:symplectic-realization}{12.5}
\extlabel{III:fl:sec:CLA-proof}{13}
\extlabel{III:fl:thm:classical-realization}{13.1}
\extlabel{III:rw:app:computer}{A}
\extlabel{III:rw:sec:notation}{A}