\extlabel{I:fl:sec:introduction}{1}
\extlabel{I:fl:def:intro-parameter}{1.1}
\extlabel{I:fl:eq:main-full-label}{1.1}
\extlabel{I:fl:thm:semisimple-elliptic}{A}
\extlabel{I:rw:cor:intro-hecke}{1.2}
\extlabel{I:rw:rem:characteristic-restriction}{1.3}
\extlabel{I:rw:sec:coverage}{1.2}
\extlabel{I:rw:thm:intro-geometric}{1.4}
\extlabel{I:rw:thm:intro-classical}{1.5}
\extlabel{I:rw:sec:general-parameters}{1.3}
\extlabel{I:fl:thm:main}{B}
\extlabel{I:fl:thm:central-period-realization}{C}
\extlabel{I:rw:sec:earlier-work}{1.5}
\extlabel{I:rw:sec:inputs}{2}
\extlabel{I:rw:in:llafforgue}{1}
\extlabel{I:rw:in:vlafforgue}{2}
\extlabel{I:rw:in:xue}{3}
\extlabel{I:rw:in:function-field-forms}{4}
\extlabel{I:fl:sec:parameters-parameters}{3}
\extlabel{I:fl:app:conventions}{3}
\extlabel{I:rw:sec:satake-convention}{3.2}
\extlabel{I:rw:eq:source-bound}{3.1}
\extlabel{I:rw:eq:satake-loop}{3.2}
\extlabel{I:rw:lem:satake-label}{3.1}
\extlabel{I:fl:def:central-period-lattice}{3.2}
\extlabel{I:fl:def:full-excursion-summand}{3.3}
\extlabel{I:rw:sec:chevalley-involution}{3.5}
\extlabel{I:fl:sec:common-arithmetic}{4}
\extlabel{I:fl:sec:arithmetic-purity}{4}
\extlabel{I:fl:lem:arithmetic-finite-coefficients}{4.1}
\extlabel{I:fl:lem:torus-geometric-image}{4.2}
\extlabel{I:fl:lem:finite-centralizer-algebra}{4.3}
\extlabel{I:fl:lem:arithmetic-monodromy-quotient}{4.4}
\extlabel{I:fl:prop:arithmetic-finite-determinants}{4.5}
\extlabel{I:rw:rem:centre-after-extension}{4.6}
\extlabel{I:fl:def:strong-purity}{4.7}
\extlabel{I:fl:thm:arithmetic-strong-purity}{4.8}
\extlabel{I:fl:sec:common-central-normalization}{4.4}
\extlabel{I:fl:eq:two-central-maps}{4.1}
\extlabel{I:fl:def:constant-field-central-homomorphism}{4.10}
\extlabel{I:fl:lem:finite-coefficients}{4.11}
\extlabel{I:fl:sec:compact-foundations}{5}
\extlabel{I:fl:sec:canonical-compact}{5}
\extlabel{I:rw:rem:nonempty-level}{5.1}
\extlabel{I:fl:lem:central-hecke-units}{5.2}
\extlabel{I:fl:lem:central-degree-stacks}{5.3}
\extlabel{I:fl:eq:exact-degree-central-quotient}{5.1}
\extlabel{I:fl:lem:graded-central-period}{5.4}
\extlabel{I:fl:eq:degree-recentering}{5.2}
\extlabel{I:fl:prop:classical-one-place-finiteness}{5.5}
\extlabel{I:fl:rem:deep-periods}{5.6}
\extlabel{I:fl:def:weil-excursion-datum}{5.7}
\extlabel{I:fl:eq:star-label}{5.3}
\extlabel{I:fl:lem:unperiodized-specialization}{5.8}
\extlabel{I:rw:rem:xue-drinfeld}{5.9}
\extlabel{I:fl:prop:canonical-compact}{5.10}
\extlabel{I:fl:prop:compact-excursion-transpose}{5.11}
\extlabel{I:fl:eq:full-transpose}{5.4}
\extlabel{I:fl:def:function-excursion-action}{5.12}
\extlabel{I:fl:eq:function-action}{5.5}
\extlabel{I:fl:eq:chevalley-functional}{5.6}
\extlabel{I:fl:prop:compact-central-twists}{5.13}
\extlabel{I:fl:eq:canonical-finite-twist}{5.7}
\extlabel{I:rw:sec:function-spaces-section}{6}
\extlabel{I:fl:def:finite-hecke-model}{6.1}
\extlabel{I:fl:eq:finite-hecke-quotient}{6.1}
\extlabel{I:fl:lem:finite-module-weil-extension}{6.2}
\extlabel{I:fl:thm:finite-integral-excursion}{6.3}
\extlabel{I:fl:eq:finite-model-unramified-action}{6.2}
\extlabel{I:fl:prop:finite-model-duality}{6.5}
\extlabel{I:fl:eq:periodic-annihilator-dual}{6.3}
\extlabel{I:fl:sec:function-spaces}{6.2}
\extlabel{I:fl:def:finite-integral-orbit}{6.6}
\extlabel{I:fl:lem:all-place-stable-lattice}{6.7}
\extlabel{I:fl:lem:parameter-satake-integrality}{6.8}
\extlabel{I:fl:def:parameter-independent-spaces}{6.9}
\extlabel{I:fl:eq:periodic-function-space}{6.4}
\extlabel{I:fl:eq:continuous-centre-space}{6.5}
\extlabel{I:fl:thm:function-space}{6.10}
\extlabel{I:fl:eq:transported-full-action}{6.6}
\extlabel{I:fl:prop:one-place-automorphicity}{6.11}
\extlabel{I:fl:cor:excursion-space-automorphicity}{6.12}
\extlabel{I:rw:rem:not-all-duals}{6.13}
\extlabel{I:fl:eq:generalized-block}{6.7}
\extlabel{I:fl:cor:weil-to-galois-nonzero}{6.14}
\extlabel{I:rw:sec:example-gm}{6.3}
\extlabel{I:fl:sec:constant-terms-cuspidality}{7}
\extlabel{I:fl:sec:constant-term}{7}
\extlabel{I:fl:thm:normalized-ct}{7.1}
\extlabel{I:fl:eq:normalized-ct-excursion}{7.1}
\extlabel{I:fl:lem:constant-term-haar-measure}{7.2}
\extlabel{I:fl:eq:geometric-test-haar}{7.2}
\extlabel{I:fl:lem:constant-term-arithmetic-restriction}{7.3}
\extlabel{I:fl:eq:geometric-test-satake}{7.3}
\extlabel{I:rw:sec:ct-partial-frobenius}{7.2}
\extlabel{I:fl:lem:constant-term-frobenius-normalization}{7.4}
\extlabel{I:rw:sec:ct-completion}{7.3}
\extlabel{I:fl:lem:finite-row-testing}{7.5}
\extlabel{I:fl:cor:finite-model-ct}{7.6}
\extlabel{I:rw:lem:ct-spherical}{7.7}
\extlabel{I:fl:sec:arithmetic-cuspidality}{8}
\extlabel{I:fl:def:unit-satake-support}{8.1}
\extlabel{I:fl:lem:faithful-satake-model}{8.2}
\extlabel{I:fl:lem:minimal-cuspidal-support}{8.3}
\extlabel{I:fl:def:locally-generalized-weil-label}{8.4}
\extlabel{I:rw:lem:noncuspidal-levi-parameter}{8.5}
\extlabel{I:rw:eq:levi-hecke-equations}{8.1}
\extlabel{I:rw:eq:twisted-satake-values}{8.2}
\extlabel{I:fl:prop:full-label-cuspidality}{8.6}
\extlabel{I:fl:sec:hecke-moment-extraction}{8.3}
\extlabel{I:fl:lem:hecke-moment-extraction}{8.8}
\extlabel{I:fl:sec:arithmetic-excursion}{8.4}
\extlabel{I:fl:prop:cuspidal-excursion-character}{8.10}
\extlabel{I:fl:eq:functional-excursion}{8.3}
\extlabel{I:rw:lem:chevalley-dual-summand}{8.11}
\extlabel{I:fl:sec:unitary-extraction}{9}
\extlabel{I:fl:lem:unitary-admissible-semisimplicity}{9.1}
\extlabel{I:fl:prop:restricted-tensor-unitary-image}{9.3}
\extlabel{I:fl:sec:arithmetic-central}{10}
\extlabel{I:fl:eq:central-twist-operator}{10.1}
\extlabel{I:fl:lem:arithmetic-central-pullback}{10.1}
\extlabel{I:fl:prop:cuspidal-products}{10.2}
\extlabel{I:fl:lem:central-envelope-invariants}{10.3}
\extlabel{I:fl:lem:cuspidal-central-quotient}{10.4}
\extlabel{I:fl:prop:connected-central-character}{10.5}
\extlabel{I:fl:eq:extended-centre-label}{10.2}
\extlabel{I:fl:lem:cuspidal-zero-extension}{10.6}
\extlabel{I:fl:lem:derived-extension}{10.7}
\extlabel{I:fl:cor:generic-derived-extension}{10.8}
\extlabel{I:fl:thm:arithmetic-central-bridge}{10.9}
\extlabel{I:fl:eq:central-envelope}{10.3}
\extlabel{I:fl:eq:dual-central-envelope}{10.4}
\extlabel{I:fl:cor:simple-group-reduction}{10.11}
\extlabel{I:fl:sec:minimal-levi}{11}
\extlabel{I:fl:prop:reductive-centralizer}{11.1}
\extlabel{I:fl:eq:minimal-centralizer}{11.1}
\extlabel{I:fl:eq:minimal-ellipticity}{11.2}
\extlabel{I:fl:cor:elliptic-minimal-levi-parameter}{11.2}
\extlabel{I:fl:eq:minimal-factorization}{11.3}
\extlabel{I:fl:ex:minimal-levi-gl}{11.3}
\extlabel{I:fl:eq:root-bound-values}{11.4}
\extlabel{I:fl:eq:proper-levi-bound}{11.5}
\extlabel{I:fl:prop:levi-root-bound}{11.4}
\extlabel{I:fl:eq:levi-bound-monotonicity}{11.6}
\extlabel{I:fl:eq:product-proper-bound}{11.7}
\extlabel{I:fl:rem:proper-bound-scope}{11.5}
\extlabel{I:fl:sec:eisenstein}{12}
\extlabel{I:fl:thm:eisenstein-full-label}{12.1}
\extlabel{I:fl:eq:eisenstein-full-label}{12.1}
\extlabel{I:fl:lem:eisenstein-relation-specialization}{12.2}
\extlabel{I:rw:lem:compact-cusp-tests}{12.4}
\extlabel{I:rw:lem:eisenstein-relation-mod-cusp}{12.5}
\extlabel{I:fl:lem:faithful-finite-character-fibre}{12.6}
\extlabel{I:fl:sec:semisimple-proof}{13}
\extlabel{I:fl:sec:reductive-proof}{13}
\extlabel{I:rw:sec:proof-semisimple}{13.1}
\extlabel{I:rw:app:partial-frobenius}{A}
\extlabel{I:fl:lem:constant-term-rotation-square}{A.1}
\extlabel{I:fl:eq:ct-framed-rotation-square}{A.1}
\extlabel{I:fl:lem:constant-term-rotation-trace}{A.2}
\extlabel{I:fl:eq:ct-finite-flat-coefficient-trace}{A.2}
\extlabel{I:rw:eq:ct-local-frobenius}{A.3}
\extlabel{I:rw:eq:ct-local-iso}{A.4}
\extlabel{I:rw:eq:ct-coefficient-map}{A.5}
\extlabel{I:fl:eq:ct-coefficient-rotation-identity}{A.6}
\extlabel{I:rw:rem:signed-satake}{A.4}
\extlabel{I:rw:rem:ct-normalization-check}{A.5}
\extlabel{I:rw:sec:notation}{A.2}