\makeatletter
\newlabel{cce-cor:quantitative}{{17.23}{151}{Scalar entropy bound at the times $t_m(u)$}{corollary.605}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cce-cor:quantitative@cref}{{[corollary][23][17]17.23}{[1][151][]151}{}{}{}}
\newlabel{ccf-cor:accuracy-cutoff}{{17.6}{118}{Mixing times}{corollary.460}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{ccf-cor:accuracy-cutoff@cref}{{[corollary][6][17]17.6}{[1][117][]118}{}{}{}}
\newlabel{ccf-cor:uniform-envelope}{{17.4}{117}{Uniformity in the gaps}{corollary.456}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{ccf-cor:uniform-envelope@cref}{{[corollary][4][17]17.4}{[1][116][]117}{}{}{}}
\newlabel{ccf-thm:full-profile}{{17.3}{116}{The profile below the critical temperature}{theorem.454}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{ccf-thm:full-profile@cref}{{[theorem][3][17]17.3}{[1][116][]116}{}{}{}}
\newlabel{cd-H-limit}{{18.28}{167}{The mean function}{equation.686}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-H-limit@cref}{{[equation][28][18]18.28}{[1][167][]167}{}{}{}}
\newlabel{cd-angular-functional}{{18.53}{179}{The critical limit process}{equation.740}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-angular-functional@cref}{{[equation][53][18]18.53}{[1][179][]179}{}{}{}}
\newlabel{cd-averaged-tail}{{19.15}{213}{The remaining coordinates at positive times}{lemma.863}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-averaged-tail@cref}{{[lemma][15][19]19.15}{[1][213][]213}{}{}{}}
\newlabel{cd-clipped-picard}{{18.8}{172}{A clipped system and uniqueness}{lemma.713}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-clipped-picard@cref}{{[lemma][8][18]18.8}{[1][172][]172}{}{}{}}
\newlabel{cd-finite-correlation}{{19.20}{220}{Finite semigroup correlations}{lemma.894}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-finite-correlation@cref}{{[lemma][20][19]19.20}{[1][220][]220}{}{}{}}
\newlabel{cd-finite-smoothing}{{19.12}{209}{Finite semigroup smoothing}{lemma.846}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-finite-smoothing@cref}{{[lemma][12][19]19.12}{[1][209][]209}{}{}{}}
\newlabel{cd-functional}{{18.9}{179}{The critical limit process}{theorem.734}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-functional@cref}{{[theorem][9][18]18.9}{[1][179][]179}{}{}{}}
\newlabel{cd-goe-profile}{{19.4}{200}{Critical profiles of the GOE model}{theorem.810}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-goe-profile@cref}{{[theorem][4][19]19.4}{[1][200][]200}{}{}{}}
\newlabel{cd-head-current}{{19.17}{217}{Total variation convergence of the first coordinates}{lemma.879}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-head-current@cref}{{[lemma][17][19]19.17}{[1][217][]217}{}{}{}}
\newlabel{cd-limiting-system}{{18.51}{179}{The critical limit process}{equation.736}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-limiting-system@cref}{{[equation][51][18]18.51}{[1][179][]179}{}{}{}}
\newlabel{cd-mean}{{18.5}{167}{The mean function}{lemma.684}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-mean@cref}{{[lemma][5][18]18.5}{[1][167][]167}{}{}{}}
\newlabel{cd-pin}{{18.12}{191}{The limiting Gibbs law}{corollary.775}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-pin@cref}{{[corollary][12][18]18.12}{[1][191][]191}{}{}{}}
\newlabel{cd-pointwise-profile}{{19.19}{220}{Pointwise convergence of the profile}{proposition.891}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-pointwise-profile@cref}{{[proposition][19][19]19.19}{[1][219][]220}{}{}{}}
\newlabel{cd-profile}{{19.2}{198}{The critical profile along a deterministic sequence}{theorem.803}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-profile@cref}{{[theorem][2][19]19.2}{[1][198][]198}{}{}{}}
\newlabel{cd-quantiles}{{19.3}{198}{Mixing times in the critical window}{corollary.805}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-quantiles@cref}{{[corollary][3][19]19.3}{[1][198][]198}{}{}{}}
\newlabel{cd-stationary-fields}{{19.16}{215}{Stationary bounds for the translation fields}{lemma.870}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-stationary-fields@cref}{{[lemma][16][19]19.16}{[1][215][]215}{}{}{}}
\newlabel{cd-tail-lsi}{{19.14}{210}{Logarithmic Sobolev inequality for the remaining coordinates}{lemma.851}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-tail-lsi@cref}{{[lemma][14][19]19.14}{[1][210][]210}{}{}{}}
\newlabel{cd-vanishing-correlations}{{19.9}{204}{Vanishing spectral correlations}{lemma.830}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cd-vanishing-correlations@cref}{{[lemma][9][19]19.9}{[1][204][]204}{}{}{}}
\newlabel{cg-entrance-lower}{{19.10}{206}{Lower bound at short critical times}{lemma.834}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cg-entrance-lower@cref}{{[lemma][10][19]19.10}{[1][206][]206}{}{}{}}
\newlabel{cl3-density-clock}{{19.11}{207}{Mixing times at every accuracy}{corollary.839}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cl3-density-clock@cref}{{[corollary][11][19]19.11}{[1][207][]207}{}{}{}}
\newlabel{cl3-density-two-time-lower}{{19.6}{202}{Reversible lower bound from two times}{lemma.821}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cl3-density-two-time-lower@cref}{{[lemma][6][19]19.6}{[1][202][]202}{}{}{}}
\newlabel{cor:coldf-top-fraction}{{16.10}{77}{The top fraction under the Gibbs measure}{corollary.297}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cor:coldf-top-fraction@cref}{{[corollary][10][16]16.10}{[1][77][]77}{}{}{}}
\newlabel{cot-deficit}{{21.1}{246}{Scaled eigenvalue gaps and top fraction of the approximations}{lemma.1009}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cot-deficit@cref}{{[lemma][1][21]21.1}{[1][246][]246}{}{}{}}
\newlabel{cot-transfer}{{21.2}{248}{The critical profile far below the critical temperature}{theorem.1018}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cot-transfer@cref}{{[theorem][2][21]21.2}{[1][248][]248}{}{}{}}
\newlabel{cpm-cor:actual-residence}{{17.17}{140}{Residence of the path}{corollary.564}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cpm-cor:actual-residence@cref}{{[corollary][17][17]17.17}{[1][140][]140}{}{}{}}
\newlabel{cpm-cor:killed-collars}{{17.18}{142}{Moments, survival, and the mass where the cutoff may differ from one}{corollary.571}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cpm-cor:killed-collars@cref}{{[corollary][18][17]17.18}{[1][142][]142}{}{}{}}
\newlabel{cpm-lem:finite-seed}{{17.16}{138}{Gaussian approximation of the coordinates at time $\tau $}{lemma.553}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cpm-lem:finite-seed@cref}{{[lemma][16][17]17.16}{[1][138][]138}{}{}{}}
\newlabel{cpm-prop:all-moments}{{17.11}{128}{All fixed-order moment bounds for the uniform start}{proposition.507}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cpm-prop:all-moments@cref}{{[proposition][11][17]17.11}{[1][128][]128}{}{}{}}
\newlabel{cpm-thm:radial-path}{{17.14}{134}{Concentration of the radial part along the path}{theorem.535}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cpm-thm:radial-path@cref}{{[theorem][14][17]17.14}{[1][134][]134}{}{}{}}
\newlabel{cq-full-profile}{{16.1}{64}{Profile at fixed low temperature}{theorem.238}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cq-full-profile@cref}{{[theorem][1][16]16.1}{[1][64][]64}{}{}{}}
\newlabel{cq-hc-head-smoothing}{{16.30}{110}{The second coordinate in total variation}{theorem.431}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{cq-hc-head-smoothing@cref}{{[theorem][30][16]16.30}{[1][110][]110}{}{}{}}
\newlabel{critical-finite-time-positivity}{{19.5}{200}{Exponential lower bound for the critical profile}{corollary.813}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{critical-finite-time-positivity@cref}{{[corollary][5][19]19.5}{[1][200][]200}{}{}{}}
\newlabel{def:coldf-hypotheses}{{16.3}{65}{Hypotheses at low temperature}{definition.242}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{def:coldf-hypotheses@cref}{{[definition][3][16]16.3}{[1][65][]65}{}{}{}}
\newlabel{def:coldm-admissible}{{17.1}{114}{Scaled-gap bounds and separation of $a_3$ from $a_2$}{definition.442}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{def:coldm-admissible@cref}{{[definition][1][17]17.1}{[1][114][]114}{}{}{}}
\newlabel{eq:cproc-scaling}{{18.7}{161}{The rescaled unnormalized process}{equation.642}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:cproc-scaling@cref}{{[equation][7][18]18.7}{[1][161][]161}{}{}{}}
\newlabel{eq:cprof-l2-upper}{{19.28}{208}{Lower bounds on the critical time scale}{equation.844}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:cprof-l2-upper@cref}{{[equation][28][19]19.28}{[1][208][]208}{}{}{}}
\newlabel{eq:cprof-pointwise}{{19.51}{220}{Pointwise convergence of the profile}{equation.892}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:cprof-pointwise@cref}{{[equation][51][19]19.51}{[1][220][]220}{}{}{}}
\newlabel{eq:hotf-constants}{{13.1}{3}{Notation}{equation.5}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:hotf-constants@cref}{{[equation][1][13]13.1}{[1][3][]3}{}{}{}}
\newlabel{eq:hotf-gaussian-tv}{{13.2}{3}{Notation}{equation.6}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:hotf-gaussian-tv@cref}{{[equation][2][13]13.2}{[1][3][]3}{}{}{}}
\newlabel{eq:hotm-geometry}{{14.33}{31}{Hypotheses and constants}{equation.120}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:hotm-geometry@cref}{{[equation][33][14]14.33}{[1][31][]31}{}{}{}}
\newlabel{eq:inf-first-crossing}{{15.7}{47}{Relaxation and cutoff near infinite temperature for the GOE}{equation.187}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{eq:inf-first-crossing@cref}{{[equation][7][15]15.7}{[1][47][]47}{}{}{}}
\newlabel{hp-fixed-profile}{{13.1}{3}{Fixed high temperature}{theorem.9}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{hp-fixed-profile@cref}{{[theorem][1][13]13.1}{[1][3][]3}{}{}{}}
\newlabel{lem:coldf-bounded-head}{{16.16}{85}{The number of retained coordinates}{lemma.331}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-bounded-head@cref}{{[lemma][16][16]16.16}{[1][85][]85}{}{}{}}
\newlabel{lem:coldf-coarse-lsi}{{16.17}{86}{A logarithmic Sobolev inequality on a cap}{lemma.333}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-coarse-lsi@cref}{{[lemma][17][16]16.17}{[1][85][]86}{}{}{}}
\newlabel{lem:coldf-collar}{{16.22}{99}{The region outside which the cutoff equals one}{lemma.384}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-collar@cref}{{[lemma][22][16]16.22}{[1][99][]99}{}{}{}}
\newlabel{lem:coldf-cutoff}{{16.23}{100}{Derivatives of the cutoff}{lemma.388}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-cutoff@cref}{{[lemma][23][16]16.23}{[1][100][]100}{}{}{}}
\newlabel{lem:coldf-goe}{{16.7}{71}{Hypotheses for the GOE}{lemma.278}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-goe@cref}{{[lemma][7][16]16.7}{[1][71][]71}{}{}{}}
\newlabel{lem:coldf-initial-entropy}{{16.27}{104}{Initial entropy}{lemma.403}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-initial-entropy@cref}{{[lemma][27][16]16.27}{[1][104][]104}{}{}{}}
\newlabel{lem:coldf-inverse-gap-lln}{{16.6}{69}{A law of large numbers for the inverse gaps}{lemma.266}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-inverse-gap-lln@cref}{{[lemma][6][16]16.6}{[1][69][]69}{}{}{}}
\newlabel{lem:coldf-renewal}{{16.12}{79}{Renewal estimates}{lemma.306}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldf-renewal@cref}{{[lemma][12][16]16.12}{[1][78][]79}{}{}{}}
\newlabel{lem:coldm-indexed}{{17.2}{115}{Consequences of the indexed bounds}{lemma.448}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldm-indexed@cref}{{[lemma][2][17]17.2}{[1][115][]115}{}{}{}}
\newlabel{lem:coldm-renewal}{{17.8}{122}{Renewal estimates uniform in the top fraction}{lemma.478}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldm-renewal@cref}{{[lemma][8][17]17.8}{[1][122][]122}{}{}{}}
\newlabel{lem:coldm-transfer}{{17.24}{155}{From sequences to uniform bounds}{lemma.624}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:coldm-transfer@cref}{{[lemma][24][17]17.24}{[1][155][]155}{}{}{}}
\newlabel{lem:cproc-joint-law-identification}{{18.11}{180}{Identification from joint laws}{lemma.742}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cproc-joint-law-identification@cref}{{[lemma][11][18]18.11}{[1][180][]180}{}{}{}}
\newlabel{lem:cprof-finite}{{19.21}{223}{Profiles in fixed dimension}{lemma.907}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-finite@cref}{{[lemma][21][19]19.21}{[1][223][]223}{}{}{}}
\newlabel{lem:cprof-limit-continuity}{{19.18}{219}{Continuity of the limiting laws}{lemma.889}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-limit-continuity@cref}{{[lemma][18][19]19.18}{[1][219][]219}{}{}{}}
\newlabel{lem:cprof-measurable}{{19.22}{224}{Measurable dependence of the critical profile}{lemma.911}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-measurable@cref}{{[lemma][22][19]19.22}{[1][224][]224}{}{}{}}
\newlabel{lem:cprof-product-tv}{{19.7}{203}{Total variation on a countable product}{lemma.823}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-product-tv@cref}{{[lemma][7][19]19.7}{[1][203][]203}{}{}{}}
\newlabel{lem:cprof-radius}{{19.13}{210}{Spheres of arbitrary radius}{lemma.850}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-radius@cref}{{[lemma][13][19]19.13}{[1][210][]210}{}{}{}}
\newlabel{lem:cprof-varying-map}{{19.23}{225}{Convergence for varying measurable maps}{lemma.914}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:cprof-varying-map@cref}{{[lemma][23][19]19.23}{[1][225][]225}{}{}{}}
\newlabel{lem:hotf-energy}{{13.9}{13}{The gap on the orthogonal complement of the stationary vector}{lemma.53}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotf-energy@cref}{{[lemma][9][13]13.9}{[1][13][]13}{}{}{}}
\newlabel{lem:hotf-grid}{{13.8}{12}{Semicircle quantiles and rigidity}{lemma.52}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotf-grid@cref}{{[lemma][8][13]13.8}{[1][12][]12}{}{}{}}
\newlabel{lem:hotf-lan-uniform}{{13.2}{4}{A uniform form of the likelihood limit}{lemma.16}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotf-lan-uniform@cref}{{[lemma][2][13]13.2}{[1][4][]4}{}{}{}}
\newlabel{lem:hotf-transfer}{{13.11}{16}{Comparison with the continuum evolution}{lemma.55}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotf-transfer@cref}{{[lemma][11][13]13.11}{[1][16][]16}{}{}{}}
\newlabel{lem:hotf-transient}{{13.10}{14}{Comparison of the decaying parts of two evolutions}{lemma.54}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotf-transient@cref}{{[lemma][10][13]13.10}{[1][14][]14}{}{}{}}
\newlabel{lem:hotm-gradient}{{14.9}{40}{Gradient bounds under the comparison laws}{lemma.151}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:hotm-gradient@cref}{{[lemma][9][14]14.9}{[1][40][]40}{}{}{}}
\newlabel{lem:inf-bulk}{{15.11}{59}{The information when $c\,t$ is bounded}{lemma.226}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:inf-bulk@cref}{{[lemma][11][15]15.11}{[1][58][]59}{}{}{}}
\newlabel{lem:inf-chebyshev}{{15.10}{58}{The compressed multiplication for the semicircle law}{lemma.225}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:inf-chebyshev@cref}{{[lemma][10][15]15.10}{[1][58][]58}{}{}{}}
\newlabel{lem:inf-compressed}{{15.9}{57}{Evolution on vectors with mean zero}{lemma.219}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:inf-compressed@cref}{{[lemma][9][15]15.9}{[1][57][]57}{}{}{}}
\newlabel{lem:inf-goe-elementary}{{15.8}{53}{Norm and traces of the GOE}{lemma.209}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{lem:inf-goe-elementary@cref}{{[lemma][8][15]15.8}{[1][53][]53}{}{}{}}
\newlabel{mc-information}{{14.3}{28}{Information at a smaller scale}{corollary.109}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mc-information@cref}{{[corollary][3][14]14.3}{[1][28][]28}{}{}{}}
\newlabel{mc-measure-theorem}{{14.2}{25}{The rescaled transient measure}{theorem.93}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mc-measure-theorem@cref}{{[theorem][2][14]14.2}{[1][25][]25}{}{}{}}
\newlabel{mc-nu-definition}{{14.16}{25}{The rescaled transient measure}{equation.91}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mc-nu-definition@cref}{{[equation][16][14]14.16}{[1][25][]25}{}{}{}}
\newlabel{mc-proxy-profile}{{14.4}{29}{The comparison law at the times $T_N(u)$}{theorem.111}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mc-proxy-profile@cref}{{[theorem][4][14]14.4}{[1][29][]29}{}{}{}}
\newlabel{mc-renyi-thm}{{17.20}{147}{Density moment bounds for $t\ge \theta ^{-2}$}{theorem.591}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mc-renyi-thm@cref}{{[theorem][20][17]17.20}{[1][147][]147}{}{}{}}
\newlabel{mesocold-prop:stationary-graph}{{16.9}{75}{The Gibbs measure in graph coordinates}{proposition.288}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mesocold-prop:stationary-graph@cref}{{[proposition][9][16]16.9}{[1][75][]75}{}{}{}}
\newlabel{mesocold-thm:weak-profile}{{17.19}{144}{The limit of finitely many coordinates and the lower bound}{theorem.583}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mesocold-thm:weak-profile@cref}{{[theorem][19][17]17.19}{[1][144][]144}{}{}{}}
\newlabel{mgf-all-mesoscopic-profile}{{14.1}{23}{Profile for the approach from above}{theorem.74}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mgf-all-mesoscopic-profile@cref}{{[theorem][1][14]14.1}{[1][23][]23}{}{}{}}
\newlabel{mgf-exact-flow-envelopes}{{14.7}{35}{Coefficient differences along the covariance evolution}{lemma.134}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mgf-exact-flow-envelopes@cref}{{[lemma][7][14]14.7}{[1][35][]35}{}{}{}}
\newlabel{mgf-global-bridge}{{14.10}{41}{Distance to the Bingham comparison law on $[0,C_Td^{-1}\log M]$}{theorem.158}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mgf-global-bridge@cref}{{[theorem][10][14]14.10}{[1][41][]41}{}{}{}}
\newlabel{mgf-weighted-source-transfer}{{14.8}{39}{The initial law weighted by $1/\varphi $}{lemma.149}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{mgf-weighted-source-transfer@cref}{{[lemma][8][14]14.8}{[1][39][]39}{}{}{}}
\newlabel{oc-approximants}{{20.1}{235}{Finite approximations of the limiting scaled half-precisions}{lemma.958}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{oc-approximants@cref}{{[lemma][1][20]20.1}{[1][235][]235}{}{}{}}
\newlabel{oc-derivative-heat}{{20.3}{241}{Decay of the transient part}{lemma.986}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{oc-derivative-heat@cref}{{[lemma][3][20]20.3}{[1][241][]241}{}{}{}}
\newlabel{oc-full-hot}{{20.4}{242}{The critical profile far above the critical temperature}{theorem.992}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{oc-full-hot@cref}{{[theorem][4][20]20.4}{[1][242][]242}{}{}{}}
\newlabel{oc-information-limit}{{20.2}{238}{The limiting information}{lemma.971}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{oc-information-limit@cref}{{[lemma][2][20]20.2}{[1][237][]238}{}{}{}}
\newlabel{part:cold}{{IV}{63}{Proof of the explicit centers}{part.233}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{part:cold@cref}{{[part][4][]IV}{[1][63][]63}{}{}{}}
\newlabel{part:critical}{{V}{159}{Mixing times}{part.626}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{part:critical@cref}{{[part][5][]V}{[1][159][]159}{}{}{}}
\newlabel{part:hot}{{III}{2}{\contentsname \@mkboth {\MakeUppercase \contentsname }{\MakeUppercase \contentsname }}{part.2}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{part:hot@cref}{{[part][3][]III}{[1][2][]2}{}{}{}}
\newlabel{prop:coldf-conditional-entropy}{{16.28}{105}{Conditional relative entropy at the times $t_u$}{proposition.408}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-conditional-entropy@cref}{{[proposition][28][16]16.28}{[1][104][]105}{}{}{}}
\newlabel{prop:coldf-entrance}{{16.13}{80}{Entrance into a cap}{proposition.315}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-entrance@cref}{{[proposition][13][16]16.13}{[1][80][]80}{}{}{}}
\newlabel{prop:coldf-finite-head-tv}{{16.29}{108}{Finitely many coordinates in total variation}{proposition.426}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-finite-head-tv@cref}{{[proposition][29][16]16.29}{[1][108][]108}{}{}{}}
\newlabel{prop:coldf-initial-coordinates}{{16.18}{87}{Gaussian approximation at time $t_{\mathrm p}$}{proposition.338}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-initial-coordinates@cref}{{[proposition][18][16]16.18}{[1][87][]87}{}{}{}}
\newlabel{prop:coldf-normalization}{{16.19}{90}{The squared norm at time $t_u$}{proposition.351}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-normalization@cref}{{[proposition][19][16]16.19}{[1][90][]90}{}{}{}}
\newlabel{prop:coldf-residence}{{16.14}{81}{Residence in a cap}{proposition.317}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:coldf-residence@cref}{{[proposition][14][16]16.14}{[1][81][]81}{}{}{}}
\newlabel{prop:hotf-edge}{{13.7}{10}{Edge asymptotics of the continuum relative errors}{proposition.42}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:hotf-edge@cref}{{[proposition][7][13]13.7}{[1][10][]10}{}{}{}}
\newlabel{prop:hotf-exact}{{13.4}{6}{The continuum covariance evolution}{proposition.27}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{prop:hotf-exact@cref}{{[proposition][4][13]13.4}{[1][6][]6}{}{}{}}
\newlabel{rem:cproc-entrance}{{18.10}{180}{Behavior as $s\downarrow 0$}{remark.741}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{rem:cproc-entrance@cref}{{[remark][10][18]18.10}{[1][180][]180}{}{}{}}
\newlabel{sec:cold-fixed}{{16}{63}{Fixed low temperature}{chapter.234}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:cold-fixed@cref}{{[chapter][16][]16}{[1][63][]63}{}{}{}}
\newlabel{sec:cold-meso}{{17}{113}{Approach to the critical temperature from below}{chapter.437}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:cold-meso@cref}{{[chapter][17][]17}{[1][113][]113}{}{}{}}
\newlabel{sec:coldf-assembly}{{16.11}{110}{Proof of the deterministic theorem}{section.433}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:coldf-assembly@cref}{{[section][11][16]16.11}{[1][110][]110}{}{}{}}
\newlabel{sec:coldf-outline}{{16.1}{66}{Outline of the proof}{subsection*.255}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:coldf-outline@cref}{{[section][1][16]16.1}{[1][66][]66}{}{}{}}
\newlabel{sec:coldm-outline}{{17.1}{118}{Outline of the proof}{subsection*.463}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:coldm-outline@cref}{{[section][1][17]17.1}{[1][118][]118}{}{}{}}
\newlabel{sec:crit-process}{{18}{159}{The critical limit process and the limiting Gibbs law}{chapter.627}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:crit-process@cref}{{[chapter][18][]18}{[1][159][]159}{}{}{}}
\newlabel{sec:crit-profile}{{19}{193}{The critical profile}{chapter.781}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:crit-profile@cref}{{[chapter][19][]19}{[1][193][]193}{}{}{}}
\newlabel{sec:hot-fixed}{{13}{2}{Fixed high temperature}{chapter.3}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:hot-fixed@cref}{{[chapter][13][]13}{[1][2][]2}{}{}{}}
\newlabel{sec:hot-meso}{{14}{21}{Approach to the critical temperature from above}{chapter.65}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:hot-meso@cref}{{[chapter][14][]14}{[1][21][]21}{}{}{}}
\newlabel{sec:infinite}{{15}{45}{The infinite-temperature crossover}{chapter.168}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:infinite@cref}{{[chapter][15][]15}{[1][45][]45}{}{}{}}
\newlabel{sec:outer-cold}{{21}{246}{The critical profile far below the critical temperature}{chapter.1006}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:outer-cold@cref}{{[chapter][21][]21}{[1][246][]246}{}{}{}}
\newlabel{sec:outer-hot}{{20}{231}{The critical profile far above the critical temperature}{chapter.929}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{sec:outer-hot@cref}{{[chapter][20][]20}{[1][231][]231}{}{}{}}
\newlabel{t:outh-choices}{{20.1}{244}{The order of choices in the proof of \cref {oc-full-hot}. No constant in rows 1--5 depends on $N$, and the constants in rows 1--4 do not depend on $\alpha $}{table.caption.1001}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{t:outh-choices@cref}{{[table][1][20]20.1}{[1][243][]244}{}{}{}}
\newlabel{tab:coldf-parameters}{{16.1}{69}{Parameters in the proof of \cref {thm:coldf-deterministic}, in the order in which they are chosen}{table.caption.264}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{tab:coldf-parameters@cref}{{[table][1][16]16.1}{[1][68][]69}{}{}{}}
\newlabel{tab:coldm-parameters}{{17.1}{120}{Parameters in the proof of \cref {ccf-thm:full-profile}, in the order in which they are fixed}{table.caption.464}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{tab:coldm-parameters@cref}{{[table][1][17]17.1}{[1][119][]120}{}{}{}}
\newlabel{tab:cprof-order}{{19.2}{202}{Order of the choices in the proofs of \cref {cd-tail-lsi,cd-averaged-tail,cd-head-current,cd-pointwise-profile}: the conditional logarithmic Sobolev inequality, the bound on the remaining coordinates, total variation convergence of the first coordinates, and pointwise convergence of the full profile. The density is bounded in $L^2(\pi _N)$ at the time $s_0/2$. For convergence of the first coordinates alone, any fixed $J\ge 1$ is allowed}{table.caption.819}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{tab:cprof-order@cref}{{[table][2][19]19.2}{[1][201][]202}{}{}{}}
\newlabel{thm:coldf-deterministic}{{16.5}{66}{Deterministic profile}{theorem.251}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{thm:coldf-deterministic@cref}{{[theorem][5][16]16.5}{[1][66][]66}{}{}{}}
\newlabel{thm:coldf-finite-coordinates}{{16.20}{93}{Finitely many coordinates}{theorem.363}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{thm:coldf-finite-coordinates@cref}{{[theorem][20][16]16.20}{[1][93][]93}{}{}{}}
\newlabel{thm:coldm-goe}{{17.5}{117}{The profile for the GOE}{theorem.459}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{thm:coldm-goe@cref}{{[theorem][5][17]17.5}{[1][117][]117}{}{}{}}
\newlabel{wf-deterministic-theorem}{{15.1}{46}{Small inverse temperature: comparison and information}{theorem.172}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{wf-deterministic-theorem@cref}{{[theorem][1][15]15.1}{[1][46][]46}{}{}{}}
\newlabel{wf-explicit-clocks}{{15.3}{49}{Explicit centers}{theorem.191}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{wf-explicit-clocks@cref}{{[theorem][3][15]15.3}{[1][49][]49}{}{}{}}
\newlabel{wf-goe-classification}{{15.2}{47}{Relaxation and cutoff near infinite temperature for the GOE}{theorem.182}{spherical-sk-dynamics-part-ii.pdf}}
\newlabel{wf-goe-classification@cref}{{[theorem][2][15]15.2}{[1][47][]47}{}{}{}}
\makeatother