\newcommand{\R}{\mathbb R} \newcommand{\C}{\mathbb C} \newcommand{\Z}{\mathbb Z} \newcommand{\N}{\mathbb N} \newcommand{\SU}{\mathrm{SU}(2)} \newcommand{\su}{\mathfrak{su}(2)} \newcommand{\SL}{\mathrm{SL}(2,\C)} \newcommand{\Id}{I} \newcommand{\Torus}{\mathbb T_L^3} \newcommand{\Lat}[1]{\Lambda_{#1}} \newcommand{\Links}[1]{\mathcal E_{#1}} \newcommand{\Faces}[1]{\mathcal P_{#1}} \newcommand{\LatticeGauge}[1]{\mathcal G_{#1}} \newcommand{\Conf}[1]{\mathcal U_{#1}} \newcommand{\Haar}{H} \newcommand{\dH}{\,dH} \newcommand{\dvol}{\,d\mathrm{vol}} \newcommand{\dd}{\,d} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\Ad}{Ad} \DeclareMathOperator{\ad}{ad} \DeclareMathOperator{\Log}{Log} \DeclareMathOperator{\Hol}{Hol} \DeclareMathOperator{\sinc}{sinc} \DeclareMathOperator{\supp}{supp} \DeclareMathOperator{\dist}{dist} \DeclareMathOperator{\Var}{Var} \DeclareMathOperator{\Cov}{Cov} \DeclareMathOperator{\Ent}{Ent} \DeclareMathOperator{\Lip}{Lip} \DeclareMathOperator{\Law}{Law} \DeclareMathOperator{\TV}{TV} \DeclareMathOperator{\Sym}{Sym} \DeclareMathOperator{\diam}{diam} \DeclareMathOperator{\Hom}{Hom} \newcommand{\E}{\mathbb E} \newcommand{\Prob}{\mathbb P} \newcommand{\Pp}{\mathbb P} \newcommand{\one}{\mathbf 1} \newcommand{\qfun}{q} \newcommand{\groupdist}{\rho_G} \newcommand{\norm}[1]{\lVert #1\rVert} \newcommand{\abs}[1]{\lvert #1\rvert} \newcommand{\ip}[2]{\langle #1,#2\rangle} \newcommand{\mesh}[1]{a_{#1}} \newcommand{\hnum}[1]{h_{#1}} \newcommand{\gnum}[1]{g_{#1}} \newcommand{\Depth}{d} \newcommand{\PriorDepth}{d_0} \newcommand{\Block}{T_M} \newcommand{\Macro}{T_M^J} \newcommand{\MacroFactor}{B} \newcommand{\COconstraint}{\mathsf C} \newcommand{\RawRecon}{\mathscr C_{\mathrm{raw}}} \newcommand{\RepMap}{\widehat{\mathscr R}} \newcommand{\PhysFree}{z} \newcommand{\White}{w} \newcommand{\Rec}{b_{\mathrm{rec}}} \newcommand{\WilsonLaw}[2]{\mu_{#1,#2}} \newcommand{\Selected}[3]{S_{#1,#2,#3}} \newcommand{\SelectedLaw}[3]{\nu_{#1,#2,#3}} \newcommand{\StoppedLaw}{\widehat\nu} \newcommand{\OrbitLaw}{\lambda_{L,\gamma,[n_*]}} \newcommand{\RGAction}[1]{E_{#1}} \newcommand{\RGResidual}[1]{R_{#1}} \newcommand{\ScalarLedger}{\Lambda} \newcommand{\rsupp}{r} \newcommand{\ran}{\rho} \newcommand{\rcl}{\rho_{\mathrm{cl}}} \newcommand{\Rraw}{R_{\mathrm{raw}}} \newcommand{\Rbuf}{R_{\mathrm{buf}}} \newcommand{\Rcell}{R_{\mathrm{cell}}} \newcommand{\Rwhite}{R_W} \newcommand{\Ren}{R_{\mathrm{en}}} \newcommand{\rrecord}{\beta_{\mathrm{rec}}} \newcommand{\erode}{s_{\mathrm{er}}} \newcommand{\asp}{a_{\mathrm{sp}}} \newcommand{\awall}{\alpha_{\mathrm{bd}}} \newcommand{\Tree}{\mathsf t} \newcommand{\Profile}{\phi} \newcommand{\WideProfile}{\psi_{\mathrm{prof}}} \newcommand{\InflatedProfile}{\widehat\phi} \newcommand{\SmallChart}[1]{B_{#1}} \newcommand{\SatChart}[1]{D_{#1}} \newcommand{\Anorm}[3]{\mathcal B_{#1,#2}(#3)} \newcommand{\Wallnorm}[3]{\mathcal X_{#1}^{#2}(#3)} \newcommand{\WhiteCut}[1]{p_{\mathrm w}(#1)} \newcommand{\WhiteProduct}{\Omega_p} \newcommand{\Activity}{\mathfrak z} \newcommand{\Polymer}{\mathfrak X} \newcommand{\Heat}[2]{P_{#1}^{#2}} \newcommand{\Duhamel}[1]{\mathcal Q_{#1}} \newcommand{\Polarized}[1]{\mathcal B_{#1}} \newcommand{\Flowcov}{\Phi} \newcommand{\Flowlat}[1]{\Psi^{(#1)}} \newcommand{\SpaceA}{\mathcal A_L} \newcommand{\SpaceG}{\mathcal G_L} \newcommand{\OrbitSpace}{\mathcal X_L} \newcommand{\WilsonTopology}{\mathcal T_W} \newcommand{\CoordMetric}{d_c} \newcommand{\EnergyL}{E_L} \newcommand{\BLdist}{d_{\mathrm{BL}}} \newcommand{\alpflow}{\alpha_{\mathrm{fl}}} \newcommand{\betflow}{\beta_{\mathrm{fl}}} \newcommand{\kapflow}{\kappa_{\mathrm{fl}}} \newcommand{\kapterm}{\kappa_{\mathrm{term}}} \newcommand{\qanc}{q_{\mathrm{anc}}} \newcommand{\Xnorm}[2]{\mathsf X_{#1}^{#2}} \newcommand{\Ynorm}[2]{\mathsf Y_{#1}^{#2}} \newcommand{\Hnorm}[2]{\mathsf H_{#1}^{#2}} \newcommand{\Vnorm}[2]{\mathsf V_{#1}^{#2}} \newcommand{\Toron}{\bm\vartheta} \newcommand{\CommMan}{\mathcal M} \newcommand{\NormalFiber}[1]{\mathcal N_{#1}} \newcommand{\NormalCov}{\Sigma_\theta} \newcommand{\Quartic}{Q} \newcommand{\CoreRadius}{r_\gamma} \newcommand{\CoreMeasure}{m_Q} \newcommand{\BGMMeasure}{\mu_{13}} \newcommand{\ObsA}{A_{\mathrm{obs}}} \newcommand{\ObsB}{B_{\mathrm{obs}}} \newcommand{\SchurStat}{\mathscr C_\gamma} \newcommand{\WardStat}{\mathcal S_{\gamma,P}}