\extlabel{II:rw:sec:II-introduction}{1}
\extlabel{II:fl:def:intro-parameter}{1.1}
\extlabel{II:fl:eq:main-full-label}{1.1}
\extlabel{II:rw:thm:II-main}{1.2}
\extlabel{II:rw:sec:earlier-work}{1.2}
\extlabel{II:fl:sec:strategy}{2}
\extlabel{II:rw:fig:geometry-dependencies}{1}
\extlabel{II:rw:sec:dependencies}{2.7}
\extlabel{II:rw:sec:inputs}{3}
\extlabel{II:rw:in:gr}{1}
\extlabel{II:rw:in:hs}{2}
\extlabel{II:rw:in:saito}{3}
\extlabel{II:rw:in:microstalk}{4}
\extlabel{II:rw:sec:from-I}{3.2}
\extlabel{II:fl:sec:parameters-parameters}{4}
\extlabel{II:fl:app:conventions}{4}
\extlabel{II:fl:def:full-excursion-summand}{4.1}
\extlabel{II:rw:sec:geometric-route}{5}
\extlabel{II:rw:eq:curve-pushout-guide}{5.1}
\extlabel{II:rw:eq:valuation-flag-guide}{5.2}
\extlabel{II:rw:eq:hecke-correspondence-guide}{5.3}
\extlabel{II:rw:def:hecke-family}{5.1}
\extlabel{II:fl:sec:punctured-spectral-fibre}{6}
\extlabel{II:rw:setup:auxiliary-curve}{6.1}
\extlabel{II:fl:lem:geometric-centralizer-torus}{6.2}
\extlabel{II:rw:lem:betti-comparison}{6.3}
\extlabel{II:fl:lem:puncture-fibre-model}{6.4}
\extlabel{II:fl:eq:puncture-fibre}{6.1}
\extlabel{II:fl:lem:puncture-compactness}{6.5}
\extlabel{II:fl:eq:puncture-vacuum}{6.2}
\extlabel{II:fl:eq:projected-vacuum-coefficient}{6.3}
\extlabel{II:rw:eq:arithmetic-coefficient-pullback}{6.4}
\extlabel{II:fl:lem:coarse-covariance}{6.6}
\extlabel{II:fl:eq:puncture-family-hecke}{6.5}
\extlabel{II:rw:eq:family-by-spectral-action}{6.6}
\extlabel{II:fl:lem:scalar-coefficient-covariance}{6.7}
\extlabel{II:rw:rem:homotopy-naturality}{6.8}
\extlabel{II:fl:prop:puncture-exact-trace}{6.10}
\extlabel{II:fl:eq:puncture-exact-trace}{6.7}
\extlabel{II:fl:sec:low-rank-example}{6.4}
\extlabel{II:fl:eq:rank-one-centralizer}{6.8}
\extlabel{II:fl:eq:rank-one-nonzero-trace}{6.9}
\extlabel{II:fl:sec:geometrization}{7}
\extlabel{II:fl:sec:marked-parameter-lifting}{7.1}
\extlabel{II:fl:thm:marked-lifting}{7.1}
\extlabel{II:fl:lem:compact-finite-coefficients}{7.2}
\extlabel{II:fl:lem:local-cocycle-approximation}{7.3}
\extlabel{II:fl:lem:finite-local-lift}{7.4}
\extlabel{II:fl:cor:boundary-return-relations}{7.5}
\extlabel{II:fl:lem:weillocal-reversal}{7.6}
\extlabel{II:fl:prop:geometrization-theta}{7.7}
\extlabel{II:fl:eq:integral-composite}{7.1}
\extlabel{II:fl:eq:composite-theta}{7.2}
\extlabel{II:fl:eq:theta-sign}{7.3}
\extlabel{II:rw:eq:t-normalized}{7.4}
\extlabel{II:fl:eq:explicit-smoothing}{7.5}
\extlabel{II:rw:sec:extending-parameter}{7.4}
\extlabel{II:rw:eq:branch-coordinates}{7.6}
\extlabel{II:fl:lem:balanced-parameter-tower}{7.9}
\extlabel{II:rw:eq:node-chart}{7.7}
\extlabel{II:fl:prop:geometrized-parameter}{7.10}
\extlabel{II:rw:sec:example-curve}{7.5}
\extlabel{II:fl:eq:rank-one-section}{7.8}
\extlabel{II:fl:eq:rank-one-smoothing}{7.9}
\extlabel{II:fl:sec:hecke-extension}{8}
\extlabel{II:fl:sec:valued-nodal-family}{8.1}
\extlabel{II:fl:lem:puiseux-algebraic-closure}{8.1}
\extlabel{II:fl:lem:composed-parameter-gluing}{8.2}
\extlabel{II:fl:lem:closed-return-puncture}{8.3}
\extlabel{II:rw:eq:ula-restriction}{8.1}
\extlabel{II:fl:lem:ula-stack-descent}{8.4}
\extlabel{II:fl:lem:relative-satake-kernels}{8.5}
\extlabel{II:fl:lem:hecke-legwise-ula}{8.6}
\extlabel{II:fl:prop:hecke-equivariant-extension}{8.7}
\extlabel{II:fl:thm:compact-automorphic-family}{8.8}
\extlabel{II:fl:sec:noncharacteristic}{9}
\extlabel{II:rw:setup:rank-one}{9.1}
\extlabel{II:fl:thm:noncharacteristic-hecke-comparison}{9.2}
\extlabel{II:fl:eq:total-hecke-input}{9.1}
\extlabel{II:rw:rem:transverse-naturality}{9.3}
\extlabel{II:rw:sec:detectors}{9.2}
\extlabel{II:fl:lem:fixed-maximal-detectors}{9.4}
\extlabel{II:fl:eq:central-detector}{9.2}
\extlabel{II:rw:sec:hecke-geometry}{9.3}
\extlabel{II:rw:def:hecke-chart}{9.5}
\extlabel{II:rw:lem:hecke-cotangent-projections}{9.6}
\extlabel{II:fl:eq:leg-derivative}{9.3}
\extlabel{II:fl:eq:root-hessian}{9.4}
\extlabel{II:rw:lem:hecke-chart-parameters}{9.7}
\extlabel{II:rw:sec:isolation}{9.4}
\extlabel{II:rw:eq:dF-at-base-point}{9.5}
\extlabel{II:rw:lem:isolated-hecke-contribution}{9.8}
\extlabel{II:rw:eq:fibre-cohomology-vanishes}{9.6}
\extlabel{II:rw:sec:stabilization}{9.5}
\extlabel{II:rw:lem:exact-hyperbolic-coordinates}{9.9}
\extlabel{II:fl:eq:exact-quadratic}{9.7}
\extlabel{II:fl:lem:quadric-detection}{9.10}
\extlabel{II:fl:cor:phase-universal-local-acyclicity}{9.11}
\extlabel{II:fl:sec:boundary-whittaker-geometry-section}{9.6}
\extlabel{II:fl:prop:regular-nilpotent-branch}{9.12}
\extlabel{II:fl:sec:graded-morse-chart}{9.7}
\extlabel{II:rw:lem:equivariant-chart-section}{9.13}
\extlabel{II:fl:lem:graded-morse-chart}{9.14}
\extlabel{II:fl:eq:homogeneous-morse-graph}{9.8}
\extlabel{II:rw:rem:grading-obstruction}{9.15}
\extlabel{II:rw:sec:generic-microstalk}{9.8}
\extlabel{II:fl:lem:vacuum-microstalk-comparison}{9.16}
\extlabel{II:fl:eq:generic-microstalk}{9.9}
\extlabel{II:rw:lem:microstalk-classical-reduction}{9.17}
\extlabel{II:rw:lem:positive-weight-contraction}{9.18}
\extlabel{II:rw:lem:weight-two-vanishing-cycles}{9.19}
\extlabel{II:rw:eq:kirillov-kernel}{9.10}
\extlabel{II:rw:lem:twisted-unipotent-chart}{9.20}
\extlabel{II:rw:lem:homogeneous-vanishing-cycles}{9.21}
\extlabel{II:rw:lem:poincare-kernel}{9.22}
\extlabel{II:rw:eq:kernel-comparison}{9.11}
\extlabel{II:fl:sec:conservation}{10}
\extlabel{II:rw:setup:scaling}{10.1}
\extlabel{II:rw:lem:simultaneous-ula-lattice}{10.2}
\extlabel{II:rw:lem:valuation-successive-cycles}{10.3}
\extlabel{II:fl:eq:sign-comparison-triangle}{10.1}
\extlabel{II:fl:thm:scaling-character-conservation}{10.4}
\extlabel{II:fl:lem:sign-square}{10.5}
\extlabel{II:fl:sec:trace-detector}{10.3}
\extlabel{II:rw:lem:inertia-hyperbolic-exchange}{10.6}
\extlabel{II:rw:eq:inertia-trace-factor}{10.2}
\extlabel{II:fl:thm:homogeneous-detector}{10.7}
\extlabel{II:fl:eq:braden-recollement}{10.3}
\extlabel{II:fl:eq:detector-finite-trace}{10.4}
\extlabel{II:fl:sec:morse-geometry}{10.4}
\extlabel{II:fl:prop:composite-trace-nonzero}{10.9}
\extlabel{II:fl:eq:puncture-special-microfunctor}{10.5}
\extlabel{II:fl:sec:arithmetic-trace}{11}
\extlabel{II:rw:setup:trace}{11.1}
\extlabel{II:rw:eq:theta-alpha}{11.1}
\extlabel{II:fl:thm:arithmetic-family-trace}{11.2}
\extlabel{II:fl:eq:trace-empty-map}{11.2}
\extlabel{II:rw:rem:trace-conventions}{11.3}
\extlabel{II:rw:def:coefficient-functions}{11.4}
\extlabel{II:fl:lem:twisted-representation-trace}{11.5}
\extlabel{II:fl:lem:regular-component-selector}{11.6}
\extlabel{II:fl:eq:component-twisted-character}{11.3}
\extlabel{II:fl:eq:family-excursion-selector}{11.4}
\extlabel{II:rw:def:correspondence-kernel}{11.8}
\extlabel{II:fl:eq:trace-relative-Hom}{11.5}
\extlabel{II:fl:eq:trace-six-functor}{11.6}
\extlabel{II:fl:lem:closed-relative-trace}{11.9}
\extlabel{II:fl:lem:closed-weil-transport}{11.10}
\extlabel{II:fl:eq:trace-Weil-edge-square}{11.7}
\extlabel{II:rw:eq:pairing-coefficient}{11.8}
\extlabel{II:rw:fig:two-orders}{2}
\extlabel{II:rw:rem:lafforgue-conditional}{11.11}
\extlabel{II:fl:lem:excursion-selector-contraction}{11.12}
\extlabel{II:fl:cor:arithmetic-family-eigenfunction}{11.13}
\extlabel{II:fl:sec:exceptional-assembly}{12}
\extlabel{II:fl:prop:passive-bundle-restriction}{12.1}
\extlabel{II:rw:eq:fixed-auxiliary-fibre}{12.1}
\extlabel{II:fl:thm:weyl-prime-realization}{12.2}
\extlabel{II:rw:prop:restricted-family}{12.3}
\extlabel{II:rw:rem:convention-robust}{12.4}
\extlabel{II:rw:app:computer}{A}
\extlabel{II:rw:sec:notation}{A}