\( \def\<#1>{\left<#1\right>} \newcommand{\aba}{\A({\bf A})} \newcommand{\abs}[1]{\lvert#1\rvert} \newcommand{\ab}{\text{ab}} %abelianisation \newcommand{\Acal}{\mathcal{A}} \newcommand{\ad}{{\mathop{\rm ad}}} \newcommand{\Ad}{{\mathop{\rm Ad}}} \newcommand{\Ad}{{\mathop{\rm Ad}}} \newcommand{\Aff}{{\mathop{\rm Aff}}} \newcommand{\aff}{\text{aff}} \newcommand{\AGrAut}{AGrAut} \newcommand{\AGrIso}{AGrIso} \newcommand{\Ai}{Ai} \newcommand{\al}{\alpha} \newcommand{\alc}{\alpha\spcheck} \newcommand{\AlgAut}{AlgAut} \newcommand{\Ann}{\mathop{\rm Ann}} \newcommand{\asexp}{{\mathop{\rm \AE}}} \newcommand{\Aut}{Aut} \newcommand{\authorised}{inconsequential} \newcommand{\Authorised}{Inconsequential} \newcommand{\Aut}{\mathop{\rm Aut}} \newcommand{\ba}{{\bf a}} \newcommand{\bA}{{\bf A}} \newcommand{\bap}{{\bf A\!'}} \newcommand{\bar}{\overline} % these first commands were renewcommand \newcommand{\barp}{\bar\partial} \newcommand{\bb}{{\bf b}} \newcommand{\bB}{{\bf B}} \newcommand{\bC}{{\bf C}} \newcommand{\bcC}{\boldsymbol{\mathcal{C}}} \newcommand{\bcMB}{{\boldsymbol{\mathcal{M}}}_\text{B}} \newcommand{\bcM}{{\boldsymbol{\mathcal{M}}}} \newcommand{\bcO}{\boldsymbol{\mathcal{O}}} \newcommand{\bd}{{\bf d}} \newcommand{\bD}{{\bf D}} \newcommand{\bdp}{{\bf d'}} \newcommand{\be}{\beta} \newcommand{\Betti}{\text{B}} \newcommand{\bfa}{{\bf a}} \newcommand{\bfb}{{\bf b}} \newcommand{\bfc}{{\bf c}} \newcommand{\bfd}{{\bf d}} \newcommand{\bfe}{{\bf e}} \newcommand{\bff}{{\bf f}} \newcommand{\bF}{\mathbf{F}} \newcommand{\bfx}{{\bf x}} \newcommand{\bfy}{{\bf y}} \newcommand{\bfz}{{\bf z}} \newcommand{\bG}{{\bf G}}\newcommand{\bg}{{\bf g}} \newcommand{\bH}{{\bf H}}\newcommand{\bh}{{\bf h}} \newcommand{\bi}{{\bf i}} \newcommand{\Bi}{Bi} \newcommand{\bI}{{\text{\bf I}}} \newcommand{\bj}{{\bf j}} \newcommand{\bJ}{{\text{\bf J}}} \newcommand{\bk}{{\bf k}} \newcommand{\bK}{{\text{\bf K}}} \newcommand{\bLa}{{\bf \Lambda}} \newcommand{\bla}{{\pmb{\lambda}}} %is there better??? \newcommand{\bL}{{\bf\Lambda}} \newcommand{\bm}{{\bf m}} \newcommand{\bM}{{\bf M}} \newcommand\bmx{\left(\begin{matrix}} \newcommand\bmxnp{\begin{matrix}} \newcommand{\Bonn}{\mathcal{B}onn} \newcommand{\bp}{{\bf p}} \newcommand{\bP}{{\bf P}} \newcommand{\bpfms}{\noindent {\em Proof }} \newcommand{\bPI}{{$\text{\bf P}_{\text{\bf I}}$}} \newcommand{\bPP}{\mathop{\rm\bf PP}} \newcommand{\bq}{{\bf q}} \newcommand{\bQ}{{\bf Q}} \newcommand{\bs}{{\bf S}} \newcommand{\bS}{{\bf S}} \newcommand{\bSi}{{\bf \Si}} \newcommand\bsmx{\left(\begin{smallmatrix}} \newcommand\bsmxnp{\begin{smallmatrix}} \newcommand{\bt}{{\bf t}} \newcommand{\bT}{{\bf T}} \newcommand{\bth}{{\pmb{\theta}}} \newcommand{\bTh}{{\pmb{\Theta}}} \newcommand{\bu}{{\bf u}} \newcommand{\bU}{{\bf U}} \newcommand{\Bun}{\text{Bun}} \newcommand{\bv}{{\bf v}} \newcommand{\bV}{{\bf V}} \newcommand{\bw}{{\bf w}} \newcommand{\bW}{{\bf W}} \newcommand{\bwcMs}{{\boldsymbol{\widetilde{\mathcal{M}}^*}}} \newcommand{\bwcMso}{\widetilde{\boldsymbol{\mathcal{M}}}^*} \newcommand{\bwMB}{ \widetilde{\boldsymbol{\mathcal{M}}}_\text{B}} \newcommand{\bx}{{\bf x}} \newcommand{\bZ}{{\bf Z}} \newcommand{\cA}{\mathcal{A}} \newcommand{\can}{\text{can}} \newcommand{\Can}{\text{Can}} \newcommand{\Card}{Card} \newcommand{\cB}{\mathcal{B}} \newcommand{\Ccal}{\mathcal{C}} \newcommand{\cCF}{\mathcal{C}\!\mathcal{F}} %compble framings \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\ceiling}[1]{\lceil#1\rceil} \newcommand{\ceil}{\ceiling} \newcommand{\cE}{\mathcal{E}} \newcommand{\cF}{\mathcal{F}} \newcommand{\cG}{\mathcal{G}} \newcommand{\ch}{\eta} %{\hslash} %\hbar, hslash..mathcal fails \newcommand{\cH}{\mathcal{H}} \newcommand{\chO}{\check{O}} \newcommand{\cI}{\mathcal{I}} \newcommand{\cir}[1]{\< #1 \>} \newcommand{\cJ}{\mathcal{J}} \newcommand{\cK}{\mathcal{K}} \newcommand{\cL}{\mathcal{L}} \newcommand{\clp}{(\!\{} \newcommand{\Cl}{\rm Cl} \newcommand{\cM}{\mathcal{M}} \newcommand{\cN}{\mathcal{N}} \newcommand{\cOB}{\mathcal{O}_{\!B}} \newcommand{\cOH}{\mathcal{O}_{\!H}} \newcommand{\Coker}{\mathop{\rm Coker}} \newcommand{\col}{{\mkern2mu:\mkern2mu}} \newcommand{\cO}{\mathcal{O}} \newcommand{\Conn}{\mathcal{C}onn} \newcommand{\conn}{{\rm conn}} \newcommand{\Connrs}{\mathcal{C}onn_{\rm rs}} \newcommand{\const}{{\mathop{\rm Const}}} \newcommand{\cp}{\mathcal{P}} \newcommand{\cP}{\mathcal{P}} \newcommand{\cQ}{\mathcal{Q}} \newcommand{\cRD}{\mathcal{R}\cD} \newcommand{\cR}{\mathcal{R}} \newcommand{\CR}{\mathop{\rm CR}} \newcommand{\crp}{\}\!)} \newcommand{\csan}{\overline\Delta_r} \newcommand{\Cscr}{\mathscr{C}} \newcommand{\cS}{\mathcal{S}} \newcommand{\CSO}{{\mathop{\rm CSO}}} \newcommand{\cSto}{{\cS}to} \newcommand{\cT}{\mathcal{T}} \newcommand{\cU}{\mathcal{U}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cW}{\mathcal{W}} \newcommand{\cX}{\mathcal{X}} \newcommand{\cY}{\mathcal{Y}} \newcommand{\cZ}{\mathcal{Z}} \newcommand{\dbar}{\overline \partial} \newcommand{\db}{\bar\partial} \newcommand{\Dcal}{\mathcal{D}} \newcommand{\dd}{{\text{\bf d}}} \newcommand{\de}{\delta} \newcommand{\De}{\Delta} \newcommand{\deg}{\text{deg}} \newcommand{\diag}{{\mathop{\rm diag}}} \newcommand{\diagonals}{{\mathop{\rm diagonals}}} \newcommand{\diags}{{{\rm diagonals}}} \newcommand{\Diff}{\mathop{\rm Diff}} \newcommand{\disc}{\Delta} \newcommand{\Dol}{{\text{Dol}}} \newcommand{\d}{\partial} \newcommand{\Drop}{\text{Drop}} \newcommand{\DR}{\text{DR}} \newcommand{\Ds}{\Delta^{\!*}} \newcommand{\dunion}{\amalg} \newcommand{\ef}{exponential factor} \newcommand{\efs}{exponential factors} \newcommand{\eMB}{\wt{\mathcal{M}}_{\text{B}}} \newcommand{\eMDol}{\wt{\mathcal{M}}_{\text{Dol}}} \newcommand{\eMDR}{\wt{\mathcal{M}}_{\text{DR}}} \newcommand\emx{\end{matrix}\right)} \newcommand\emxnp{\end{matrix}} \newcommand{\End}{End} \newcommand{\epf}{\end{proof}} \newcommand{\epfms}{\end{bpfms}\hfill$\square$\\} \newcommand{\epii}{\varepsilon^{-1}_\infty} \newcommand{\epi}{\varepsilon_\infty} \newcommand{\epsi}{\varepsilon^{-1}} \newcommand{\Eps}{\mathcal{E}} \newcommand{\eps}{\varepsilon} \newcommand\esmx{\end{smallmatrix}\right)} \newcommand\esmxnp{\end{smallmatrix}} \newcommand{\even}{\text{even}} \newcommand{\ev}{\text{ev}} \newcommand{\Ext}{\rm Ext} \newcommand{\Fcal}{\mathcal{F}} \newcommand{\fH}{\mathfrak{H}} \newcommand{\flb}{\lbrack\!\lbrack} \newcommand{\fl}{{\mathop{\footnotesize\rm {f}l} }} \newcommand{\FLocSys}{\mathcal{FL}oc\mathcal{S}ys} \newcommand{\FLogConn}{\mathcal{FL}og\mathcal{C}onn} \newcommand{\floor}[1]{\lfloor#1\rfloor} \newcommand{\flp}{(\!(} \newcommand{\flt}{{\rm flat}} \newcommand{\F}{\mathcal{F}} \newcommand{\FMeroConn}{\mathcal{FM}ero\mathcal{C}onn} \newcommand{\fM}{\mathfrak{M}} \newcommand{\frb}{\rbrack\!\rbrack} \newcommand{\frkt}{\mathfrak{t}} \newcommand{\frkz}{\mathfrak{z}} \newcommand{\from}{\leftarrow} \newcommand{\frp}{)\!)} \newcommand{\FSLocSys}{\mathcal{FSL}oc\mathcal{S}ys} \newcommand{\fth}{\flb \th \frb} \newcommand{\fullconfig}{\mathbf{\wb B}} \newcommand{\fulllwmcg}{\wb \Ga} \newcommand{\Fun}{\mathop{\rm Fun}} \newcommand{\fus}{\circledast} \newcommand{\fusion}[1]{\underset{#1}{\circledast}} \newcommand{\GaAut}{\Ga\!\Aut} \newcommand{\ga}{\gamma} \newcommand{\Ga}{\Gamma} \newcommand{\gahr}{\papk{G}{H}{r}} \newcommand{\Gal}{\mathop{\rm Gal}} \newcommand{\gA}{ \mathfrak{A} } \newcommand{\gatr}{\papk{G}{T}{r}} \newcommand{\gc}{\mathfrak{g}_{\IC}} \newcommand{\GConn}{\mathcal{GC}onn} \newcommand{\gki}{ \mathfrak{g}_{k_i}} \newcommand{\gkis}{ \mathfrak{g}_{k_i}^* } \newcommand{\gk}{ \mathfrak{g}_k } \newcommand{\gks}{ \mathfrak{g}_k^* } \newcommand{\gl}{ \mathfrak{gl} } \newcommand{\GL}{{\mathop{\rm GL}}} \newcommand{\glue}[1]{\underset{#1}{\strictiff}} \newcommand{\glu}{\strictiff} \newcommand{\glu}{\asymp} \newcommand{\glue}{\asymp} \newcommand{\g}{ \mathfrak{g} } \newcommand{\gMB}{\mathfrak{M}_{\text{B}}} \newcommand{\gMDol}{\mathfrak{M}_{\text{Dol}}} \newcommand{\gMDR}{\mathfrak{M}_{\text{DR}}} \newcommand{\gm}{ \mathfrak{m} } \newcommand{\gM}{ \mathfrak{M} } \newcommand{\GMPConn}{\mathcal{GMPC}onn} \newcommand{\gN}{ \mathfrak{N} } \newcommand{\go}{\mathfrak{go}} \newcommand{\gP}{ \mathfrak{P} } \newcommand{\gQ}{ \mathfrak{Q} } \newcommand{\GrAut}{GrAut} \newcommand{\GrIso}{GrIso} \newcommand{\Gr}{{\rm Gr}} \newcommand{\gr}{\text{gr}} \newcommand{\gs}{ \mathfrak{g}^* } \newcommand{\Herm}{\text{Herm}} \newcommand{\hh}{\mathop{\rm H}} \newcommand{\HH}{\text{H}} \newcommand{\Hilb}{\text{Hilb}} \newcommand{\hkq}{/\!\!/\!\!/} \newcommand{\hkqa}[1]{\underset{#1}{/\!\!/\!\!/}} \newcommand{\h}{\mathfrak{h}} \newcommand{\Hm}{{\text{H}({\bf m})}} \newcommand{\Hn}{{\text{H}({\bf n})}} \newcommand{\Hol}{Hol} \newcommand{\hol}{{\mathop{\footnotesize\rm hol}}} \newcommand{\Hom}{Hom} \newcommand{\hPIV}{{$\text{hP}_{\text{IV}}$ }} \newcommand{\hPIVn}{{$\text{hP}^n_{\text{IV}}$ }} \newcommand{\hPV}{{$\text{hP}_{\text{V}}$ }} \newcommand{\hPVI}{{$\text{hP}_{\text{VI}}$ }} \newcommand{\hPVIn}{{$\text{hP}^n_{\text{VI}}$ }} \newcommand{\hPVn}{{$\text{hP}^n_{\text{V}}$ }} \newcommand{\iA}{{^i\!A}} \newcommand{\IA}{\mathbb{A}} \newcommand{\iAo}{{^i\!A^0}} \newcommand{\IBir}{{\IB}ir} \newcommand{\IB}{\mathbb{B}} \newcommand{\iBo}{{^i\!B^0}} \newcommand{\Ical}{\mathcal{I}} \newcommand{\IC}{\mathbb{C}} \newcommand{\idLj}{{^i\!\dot\Lambda_j}} \newcommand{\ID}{\mathbb{D}} \newcommand{\idRj}{{^i\!\dot R_j}} \newcommand{\iDSP}{i\text{DSP}} \newcommand{\id}{\text{Id}} \newcommand{\Id}{\text{Id}} \newcommand{\IE}{\mathbb{E}} \newcommand{\IF}{\mathbb{F}} \newcommand{\IG}{\mathbb{G}} \newcommand{\igo}{{^i\!g_0}} \newcommand{\Ih}{\mathbb{h}} \newcommand{\IH}{\mathbb{H}} \newcommand{\II}{\mathbb{I}} \newcommand{\i}{\iota} \newcommand{\iL}{{^i\!\Lambda}} \newcommand{\IL}{\mathbb{L}} \newcommand{\iLo}{{^i\!\Lambda^{\!0}}} \newcommand{\iLp}{{^i\!\Lambda'}} \newcommand{\Image}{\mathop{\rm Im}} \newcommand{\I}{\mathfrak{I}} \newcommand{\IM}{\mathbb{M}} \newcommand{\im}{\text{Im}} \newcommand{\Im}{\text{Im}} \newcommand{\Inc}{\text{Inc}} \newcommand{\IN}{\mathbb{N}} \newcommand{\Inn}{\text{Inn}} \newcommand{\into}{\hookrightarrow} \newcommand{\Io}{\mathbb{1}} \newcommand{\IO}{\mathbb{O}} \newcommand{\ip}{\int_{\IP^1}} \newcommand{\IP}{\mathbb{P}} \newcommand{\iQ}{{^i\!Q}} \newcommand{\IQ}{\mathbb{Q}} \newcommand{\IR}{\mathbb{R}} \newcommand{\irr}{\text{irr}} \newcommand{\Irr}{\text{Irr}} \newcommand{\ISect}{\IS\text{ect}} \newcommand{\isj}{{^i\si_j}} \newcommand{\IS}{\mathbb{S}} \newcommand{\IsoAE}{\rm Iso\AE} \newcommand{\iso}{{^i\si_0}} \newcommand{\Iso}{Iso} \newcommand{\Isom}{Isom} \newcommand{\ISto}{{\IS}to} \newcommand{\IT}{\mathbb{T}} \newcommand{\IU}{\mathbb{U}} \newcommand{\IV}{\mathbb{V}} \newcommand{\iwAod}{{^i\!\wt A^0_\Delta}} \newcommand{\iwAo}{{^i\!\wt A^0}} \newcommand{\iwbj}{{^i\wt b_j}} \newcommand{\iwbo}{{^i\wt b_0}} \newcommand{\iwg}{{^i\wh{g}}} %beware hats not tildes \newcommand{\IW}{\mathbb{W}} \newcommand{\IX}{\mathbb{X}} \newcommand{\IY}{\mathbb{Y}} \newcommand{\IZ}{\mathbb{Z}} \newcommand{\Jac}{\text{Jac}} \newcommand{\Jcal}{\mathcal{J}} \newcommand{\JJ}{\mathbb{J}} \newcommand{\ka}{\kappa} \newcommand{\Katz}{\text{Katz}} \newcommand{\Ker}{Ker} \newcommand{\ker}{\mathop{\rm Ker}} \newcommand{\Ker}{\mathop{\rm Ker}} \newcommand{\labelitemi}{$\bullet$} \newcommand{\la}{\lambda} \newcommand{\La}{\Lambda} \newcommand{\Lambdareplacement}{L} \newcommand{\Lbb}{\mathbb{L}} \newcommand{\lbki}{ \mathfrak{b}_{k_i} } \newcommand{\lbkis}{ \mathfrak{b}_{k_i}^* } \newcommand{\lbk}{ \mathfrak{b}_k } \newcommand{\lbks}{ \mathfrak{b}_k^* } \newcommand{\lb}{ \mathfrak{b} } \newcommand{\lbra}{{(\!(}} \newcommand{\Lcal}{\mathcal{L}} \newcommand{\lcm}{\text{lcm}} \newcommand{\ld}{\mathfrak{d}} \newcommand{\levels}{\text{Levels}} \newcommand{\Levels}{\text{Levels}} \newcommand{\lev}{\mathop{lev}} \newcommand{\lh}{\mathfrak{h}} \newcommand{\Lia}{{\mathop{Lie}}} \newcommand{\liea}{\mathfrak{a}} \newcommand{\LieB}{\mathcal L} %used for Lie bracket \newcommand{\Lie}{{\mathop{Lie}}} \newcommand{\lien}{\mathfrak{n}} \newcommand{\lieo}{\mathfrak{o}} \newcommand{\lieu}{\mathfrak{u}} \newcommand{\Lift}{\text{Lift}} \newcommand{\lk}{\mathfrak{k}} \newcommand{\lln}{\mathfrak{ln}} \newcommand{\llp}{\wp} \newcommand{\lm}{\mathfrak{m}} \newcommand{\LocSys}{{\mathcal{L}oc\,\monesp\monesp\mathcal{S}ys}} \newcommand{\LogConn}{\mathcal{L}og\mathcal{C}onn} \newcommand{\LogConnP}{\mathcal{L}og\mathcal{C}onn\mathcal{P}} \newcommand{\Lo}{{\Lambda^{\!0}}} \newcommand{\lp}{\mathfrak{p}} \newcommand{\lsl}{ \mathfrak{sl} } \newcommand{\ls}{\mathfrak{s}} \newcommand{\lt}{\mathfrak{t}} \newcommand{\lu}{\mathfrak{u}} \newcommand{\lz}{\mathfrak{z}} \newcommand{\mAo}{{^m\!A^0}} \newcommand{\Map}{Map} \newcommand{\MBetti}{\mathcal{M}_{\text{Betti}}} \newcommand{\Mb}{\mathcal{M}'} \newcommand\MB{\mathcal{M}_{\text{B}}} \newcommand{\Mcal}{\mathcal{M}} \newcommand{\mc}{{\rm Mod}_{0,\{4\}}} \newcommand{\mdiagonals}{{\setminus\mathop{diagonals}}} \newcommand{\MDol}{\mathcal{M}_{\text{Dol}}} \newcommand{\MDR}{\mathcal{M}_{\text{DR}}} \newcommand{\MeroConn}{\mathcal{M}ero\mathcal{C}onn} \newcommand{\MeroConnP}{\mathcal{M}ero\mathcal{C}onn\mathcal{P}} \newcommand{\mit}{pointed irregular type} \newcommand{\mits}{pointed irregular types} \newcommand{\mki}{{k_i}} \newcommand{\mk}{{k}} \newcommand{\mko}{{k_1}} \newcommand{\M}{\mathcal{M}} \newcommand{\model}{{\text{mod}}} \newcommand{\mod}{{\text{mod}}} \newcommand{\monesp}{\;\!\!} \newcommand{\Mon}{\mathop{Mon}} \newcommand{\mon}{mon} \newcommand{\MPConn}{\mathcal{MPC}onn} \newcommand{\MR}{\mathop{\rm MR}} \newcommand{\msc}{\M_S({\bf C})} \newcommand{\muc}{\mu_\IC} \newcommand{\Mult}{\mathop{Mult}} \newcommand{\mult}{\text{mult}} \newcommand{\mur}{\mu_\IR} \newcommand{\myboxed}[1]{{\boxed{\phantom{\bmx 0 \\ 0 \emx} #1\ \ \ \ \ }}} \newcommand{\N}{\mathbb{N}} \newcommand{\n}{\mathfrak{n}} \newcommand{\nonpure}{full} \newcommand{\Nonpure}{Full} \newcommand{\norm}[1]{\lVert#1\rVert} \newcommand{\nt}{\text{nt}} \newcommand{\oa}{{^0\!\!\A}} \newcommand{\oAo}{{^1\!A^0}} \newcommand{\oBo}{{^1\!B^0}} \newcommand{\oc}{{^0C}} \newcommand{\odd}{\text{odd}} \newcommand{\og}{{^0\!\G}} \newcommand{\ogo}{{^1\!g_0}} \newcommand{\omegac}{\omega\spcheck} \newcommand{\ominfo}{{\Omega^1_{C^\infty}}} \newcommand{\om}{\omega} \newcommand{\Om}{\Omega} \newcommand{\omu}{\overline\mu} \newcommand{\onesp}{\:\!} \newcommand{\onto}{\twoheadrightarrow} \newcommand{\onto}{\twoheadrightarrow} \newcommand{\oom}{\overline\omega} \newcommand{\opi}{\overline\pi} \newcommand{\op}{{\mathop{\rm op}}} \newcommand{\orbit}{O} \newcommand{\ord}{ord} \newcommand{\O}{{{\rm O}}} \newcommand{\Out}{\mathop{\rm Out}} \newcommand{\ov}{\overline} \newcommand{\owAod}{{^1\!\wt A^0_\Delta}} \newcommand{\owc}{{^0\wt C}} \newcommand{\owg}{{^1\wh g}} \newcommand{\owm}{{^0\Omega}} \newcommand{\owmd}{{^0\Omega^\bullet}} \newcommand{\owmn}{{^0\Omega^0}} \newcommand{\owmo}{{^0\Omega^1}} \newcommand{\owmt}{{^0\Omega^2}} \newcommand{\pair}[2]{\langle#1,#2\rangle} \newcommand{\pairg}[2]{g\!\left(#1,#2\right)} \newcommand{\pairh}[2]{h\!\left(#1,#2\right)} \newcommand{\pairhh}[2]{\left(\!\left(#1,#2\right)\!\right)} \newcommand{\pap}[2]{{\,_{#1}\cA_{#2}}} \newcommand{\papk}[3]{\,_{#1}^{\phantom{#3}}\cA_{#2}^{#3} } \newcommand{\papt}[2]{{\,_{#1}^{\phantom{2}}\cA_{#2}^2}} \newcommand{\pardeg}{\text{pardeg}} \newcommand{\Pbb}{\mathbb{P}} \newcommand{\Pcal}{\mathcal{P}} \newcommand{\pdeg}{\text{pdeg}} \newcommand{\Perm}{Perm} \newcommand{\pf}{\begin{proof}} \newcommand{\pfms}{\begin{bpfms}} \newcommand{\PGL}{{\mathop{\rm PGL}}} \newcommand{\PGL}{{\mathop{\rm PGL}}} \newcommand{\PI}{{$\text{P}_{\text{I}}$ }} \newcommand{\pibm}{{^i\!\,b_-}} \newcommand{\pibp}{{^i\!\,b_+}} \newcommand{\pibpm}{{^i\!\,b_\pm}} \newcommand{\Pic}{\mathop{\rm Pic}} \newcommand{\PII}{{$\text{P}_{\text{II}}$ }} \newcommand{\PIII}{{$\text{P}_{\text{III}}$ }} \newcommand{\PIIIp}{{$\text{P$'$}_{\text{III}}$ }} \newcommand{\PIIIpp}{{$\text{P$''$}_{\text{III}}$ }} \newcommand{\pii}{\pi_{\hbox{\footnotesize\rm irr}}} \newcommand{\pir}{\pi_{\hbox{\footnotesize\rm res}}} \newcommand{\PIV}{{$\text{P}_{\text{IV}}$ }} \newcommand{\PP}{{\rm PP}} \newcommand{\Prod}{\prod} \newcommand{\proj}{\mathop{\rm Proj}} \newcommand{\Proj}{\mathop{\rm Proj}} \newcommand{\proofname}{Proof} \newcommand{\pr}{pr} \newcommand{\prsmall}{\mathop{\footnotesize\rm pr}} \newcommand{\PSL}{{\mathop{\rm PSL}}} \newcommand{\PSU}{\mathop{\rm PSU}} \newcommand{\Ptwo}{{$\text{P}_{\text{II}}$ }} \newcommand{\pureconfig}{\mathbf{B}} \newcommand{\purelwmcg}{\Ga} \newcommand{\PV}{{$\text{P}_{\text{V}}$ }} \newcommand{\PVI}{{$\text{P}_{\text{VI} }$ }} \newcommand{\PVIs}{{$\text{P}_{\text{VI\ }}$}} \newcommand\qchoose[2]{\left[\begin{matrix} #1 \\ #2 \end{matrix}\right]} \newcommand{\Q}{\mathbb{Q}} \newcommand{\Rad}{\text{Rad}} \newcommand{\ram}{Ram} \newcommand{\Ram}{Ram} \newcommand{\ram}{\text{Ram}} \newcommand{\Ram}{\text{Ram}} \newcommand{\range}{\operatorname{Im}} \newcommand{\>}{\rangle} \newcommand{\rank}{\mathop{\rm rank}} \newcommand{\Rank}{Rank} \newcommand{\Rat}{\mathop{\rm Rat}} \newcommand{\rbra}{{)\!)}} \newcommand{\rdeg}{\text{rdeg}} \newcommand{\RD}{\mathcal{R}\cD} \newcommand{\Real}{{\mathop{\rm Re}}} \newcommand{\reg}{{\mathop{\footnotesize\rm reg}}} \newcommand{\rel}{{\mathop{\footnotesize\rm Rel}}} \newcommand{\re}{\mathop{\rm Re}} \newcommand{\Re}{\mathop{\rm Re}} \newcommand{\Rep}{\rm Rep} \newcommand{\res}{{\mathop{\rm Res}}} \newcommand{\Res}{{\mathop{\rm Res}}} \newcommand{\RH}{\text{RH}} \newcommand{\rk}{\mathop{\rm rk}} \newcommand{\Rk}{\mathop{\rm Rk}} \newcommand{\R}{\mathbb{R}} \newcommand{\R}{\mathcal{R}} \newcommand{\roof}[1]{\lceil#1\rceil} \newcommand{\Roots}{\mathop{\rm Roots}} \newcommand{\rpair}[2]{\left(#1,#2\right)} \newcommand{\rs}{{\rm rs}} \newcommand{\rvline}{\hspace*{-\arraycolsep}\vline\hspace*{-\arraycolsep}} \newcommand{\SB}{\mathop{\rm SB}} \newcommand{\sdp}{{\rtimes}} \newcommand{\sD}{\slashed{D}} \newcommand{\Sect}{\text{Sect}} \newcommand{\SFLS}{\mathcal{SFLS}} \newcommand{\SGLS}{\mathcal{SGLS}} \newcommand{\ShaB}{\Sh_{\text{B}}} \newcommand{\ShaDol}{\Sh_{\text{Dol}}} \newcommand{\ShaDR}{\Sh_{\text{DR}}} \newcommand{\Sha}{\Sh} \newcommand{\Sif}{\Sigma_i(\wh F)} \newcommand{\sign}{\text{\it sgn}} \newcommand{\si}{\sigma} \newcommand{\Si}{\Sigma} \newcommand{\Sjf}{\Sigma_j(\wh F)} \newcommand{\sl}{\mathfrak{sl}} \newcommand{\SL}{{\mathop{\rm SL}}} \newcommand{\SLocSys}{{\mathcal{S}\monesp\monesp\mathcal{L}oc\,\monesp\monesp\mathcal{S}ys}} \newcommand{\slope}{\text{slope}} \newcommand{\SLS}{\mathcal{SLS}} \newcommand{\SolAE}{\rm Sol\AE} \newcommand{\Sol}{Sol} \newcommand{\so}{ \mathfrak{so} } \newcommand{\SO}{{\mathop{\rm SO}}} \newcommand{\spec}{\mathop{\rm Spec}} \newcommand{\Spec}{\mathop{\rm Spec}} \newcommand{\Spin}{\mathop{\rm Spin}} \newcommand{\Splits}{{\rm Splits}} \newcommand{\sp}{{\mathfrak{sp}}} \newcommand{\Sp}{{\mathop{\rm Sp}}} \newcommand{\spm}{{\mathop{\rm Spm}}} \newcommand{\spq}{/\!\!/} \newcommand{\spqa}[1]{\underset{#1}{/\!\!/}} \newcommand{\sqmo}{\sqrt{-1}} \newcommand{\sqpa}[1]{\underset{#1}{\setminus\!\!\setminus}} \newcommand{\sqp}{\setminus\monesp\monesp\!\!\setminus\,} \newcommand{\Ssect}{\wh {\mathop{\rm Sect}}} \newcommand{\sslash}{\mathbin{/\mkern-6mu/}} \newcommand{\Stab}{{\mathop{\rm Stab}}} \newcommand{\st}{\ \bigl\vert\ } \newcommand{\st}{\ \bigl\vert\ } \newcommand{\Sto}{{\cS}to} \newcommand{\su}{ \mathfrak{su} } \newcommand{\SU}{{\mathop{\rm SU}}} \newcommand{\sym}{Sym} \newcommand{\Sym}{Sym} \newcommand{\Syst}{\mathop{\rm Syst}} \newcommand{\tame}{\text{tame}} \newcommand{\TAut}{TAut} \newcommand{\THom}{THom} \newcommand{\th}{\theta} \newcommand{\Th}{\Theta} \newcommand{\TIso}{TIso} \newcommand{\T}{\mathcal{T}} \newcommand{\tq}{\ \bigl\vert\ } \newcommand{\Trip}{\text{Trip}} \newcommand{\tr}{{\mathop{\rm Tr}}} \newcommand{\Tr}{{\mathop{\rm Tr}}} \newcommand{\twosp}{\onesp\onesp} \newcommand{\ug}{\mathfrak{Ug}} \newcommand{\u}{\mathfrak{u}} \newcommand{\um}{{\Undertilde{\bf m}}} \newcommand{\Union}{\bigcup} \newcommand{\union}{\cup} \newcommand{\unt}{\text{nt}} \newcommand{\un}{{\Undertilde{\bf n}}} \newcommand{\U}{{\rm {U}}} \newcommand{\var}{\text{var}} \newcommand{\Var}{\text{Var}} \newcommand{\Vect}{{\mathop{\rm Vect}}} \newcommand{\vol}{\mathop{\rm vol}} \newcommand{\wAf}{{\wt \A_\fl}} \newcommand{\wA}{{\wt \A}} \newcommand{\wcc}{\widetilde \cC} \newcommand{\Wedge}{{\bigwedge\!}} \newcommand{\wh}{\fixwidehat} \newcommand{\whth}{{\widehat\theta}} \newcommand{\wh}{\widehat} \newcommand{\wMB}{\wt{\mathcal{M}}_{\text{B}}} \newcommand{\wmc}{\wt {\mathop{\rm M}}_{0,4}} \newcommand{\wMDol}{\wt{\mathcal{M}}_{\text{Dol}}} \newcommand{\wMDR}{\wt{\mathcal{M}}_{\text{DR}}} \newcommand{\wtMB}{\wt{\mathcal{M}}_{\text{B}}} \newcommand{\wtMDol}{\wt{\mathcal{M}}_{\text{Dol}}} \newcommand{\wtMDR}{\wt{\mathcal{M}}_{\text{DR}}} \newcommand{\wt}{\widetilde} \newcommand{\zAo}{{^0\!A^0}} \newcommand{\zbar}{\overline z} \newcommand{\zec}{\zeta_\IC} \newcommand{\zer}{\zeta_\IR} \newcommand{\zetac}{\zeta_\IC} \newcommand{\zetar}{\zeta_\IR} \newcommand{\ze}{\zeta} \newcommand{\zgo}{{^0\!g_0}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\zwg}{{^0\wh g}} \)