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\newcommand{\VectSp}{{ \VectSp }} \newcommand{\VectBun}{{ \VectBundle }} \newcommand{\Bung}{{ \Bun\qty{G}}} \newcommand{\Alg}{\mathsf{Alg}} \newcommand{\Hopf}{\mathsf{Hopf}} \newcommand{\alg}{\Alg} \newcommand{\scalg}{\mathsf{sCAlg}} \newcommand{\cAlg}{{\mathsf{cAlg}}} \newcommand{\calg}{\mathsf{CAlg}} \newcommand{\liegmod}{{\mathfrak{g}\dash\mathsf{Mod}}} \newcommand{\liealg}{{\mathsf{Lie}\dash\Alg}} \newcommand{\Lie}{\mathsf{Lie}} \newcommand{\kalg}{{}_{k} \Alg} \newcommand{\kAlg}{\kalg} \newcommand{\falg}{{}_{\FF} \Alg} \newcommand{\ralg}{{}_{R} \Alg} \newcommand{\rAlg}{\ralg} \newcommand{\zalg}{{}_{\ZZ} \Alg} \newcommand{\CCalg}{{}_{\CC} \Alg} \newcommand{\dga}{{\mathsf{dg\Alg}}} \newcommand{\cdga}{{ \mathsf{c}\dga }} \newcommand{\FMP}{\mathsf{FMP}} \newcommand{\dgla}{\dg\Lie\Alg} \newcommand{\DGLA}{\dgla} \newcommand{\Poly}{{\mathsf{Poly}}} \newcommand{\Hk}{{\mathsf{Hk}}} \newcommand{\Asm}{{\mathsf{Asm}}} \newcommand{\kSch}{{\mathsf{Sch}_{/k}}} \newcommand{\Grpd}{{\mathsf{Grpd}}} 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\newcommand{\Sh}{{\mathsf{Sh}}} \newcommand{\Stacks}{{\mathsf{St}}} \newcommand{\Var}{{\mathsf{Var}}} \newcommand{\Vark}{{ \Var_{/k}}} \newcommand{\Open}{{\mathsf{Open}}} \newcommand{\CW}{{\mathsf{CW}}} \newcommand{\ssets}{\mathsf{sSet}} \newcommand{\hoTop}{{\mathsf{hoTop}}} \newcommand{\hoType}{{\mathsf{hoType}}} \newcommand{\ho}{{\mathsf{ho}}} \newcommand{\SHC}{{\mathsf{SHC}}} \newcommand{\SH}{{\mathsf{SH}}} \newcommand{\Spaces}{{\mathsf{Spaces}}} \newcommand{\Spectra}{{\mathsf{Sp}}} \newcommand{\Sp}{{\mathsf{Sp}}} \newcommand{\Top}{{\mathsf{Top}}} \newcommand{\Bord}{{\mathsf{Bord}}} \newcommand{\TQFT}{{\mathsf{TQFT}}} \newcommand{\Kc}{{\mathsf{K^c}}} \newcommand{\triang}{{\mathsf{triang}}} \newcommand{\TTC}{{\mathsf{TTC}}} \newcommand{\dchrmod}{{\derivedcat{\Ch(\rmod)}}} \newcommand{\Finset}{{\mathsf{FinSet}}} \newcommand{\Cat}{\mathsf{Cat}} \newcommand{\Fun}{{\mathsf{Fun}}} \newcommand{\Kan}{{\mathsf{Kan}}} \newcommand{\Monoid}{\mathsf{Mon}} \newcommand{\Arrow}{\mathsf{Arrow}} \newcommand{\quasiCat}{{ \mathsf{quasiCat}}} \newcommand{\inftycat}{{ \underset{\infty}{ \Cat} }} \newcommand{\core}{{ \mathsf{core}}} \newcommand{\Indcat}{\mathsf{Ind}} \newcommand{\Prism}{\mathsf{Prism}} \newcommand{\Solid}{\mathsf{Solid}} \newcommand{\WCart}{\mathsf{WCart}} \newcommand{\Quadform}{{\mathsf{QuadForm}}} \newcommand{\HI}{{\mathsf{HI}}} \newcommand{\DM}{{\mathsf{DM}}} \newcommand{\hoA}{{\mathsf{ho}_*^{\scriptstyle \AA^1}}} \newcommand{\Tw}{\mathsf{Tw}} \newcommand{\SB}{\mathsf{SB}} \newcommand{\CSA}{\mathsf{CSA}} \newcommand{\CSS}{{ \mathsf{CSS}}} \newcommand{\FGL}{\mathsf{FGL}} \newcommand{\FI}{{\mathsf{FI}}} \newcommand{\CE}{{\mathsf{CE}}} \newcommand{\Fuk}{{\mathsf{Fuk}}} \newcommand{\Lag}{{\mathsf{Lag}}} \newcommand{\Mfd}{{\mathsf{Mfd}}} \newcommand{\Riem}{\mathsf{Riem}} \newcommand{\Wein}{{\mathsf{Wein}}} \newcommand{\deltaring}{{\delta\dash\mathsf{Ring}}} \newcommand{\terminal}{{ 0_{\scriptscriptstyle \uparrow}}} \newcommand{\initial}{{ \mathscr 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\newcommand{\gset}[1]{\gsetsleft{#1}} \newcommand{\gsets}[1]{\gset{#1}} \newcommand{\VectBundlerk}[1]{{ \Bun\qty{\GL_{#1}}}} \newcommand{\VectBunrk}[1]{{ \VectBundlerk{#1}}} \newcommand{\algs}[1]{{ {}_{#1} \Alg }} \newcommand{\inftycatn}[1]{{ \underset{(\infty, {#1})}{ \Cat} }} \newcommand{\GSpaces}{{G\dash\mathsf{Spaces}}} \newcommand{\gspaces}[1]{{#1}\dash{\mathsf{Spaces}}} \newcommand{\Torsor}[1]{{\mathsf{#1}\dash\mathsf{Torsor}}} \newcommand{\Torsorleft}[1]{{\mathsf{#1}\dash\mathsf{Torsor}}} \newcommand{\Torsorright}[1]{{\mathsf{Torsor}\dash\mathsf{#1}}} \newcommand{\adj}[4]{#1 \mathrel{\underset{#4}{\overset{#3}{\rightleftarrows}}} #2} \newcommand{\tmf}{\mathrm{tmf}} \newcommand{\taf}{\mathrm{taf}} \newcommand{\TAF}{\mathrm{TAF}} \newcommand{\TMF}{\mathrm{TMF}} \newcommand{\String}{\mathrm{String}} \newcommand{\BO}{{\B \Orth}} \newcommand{\EO}{{\mathsf{E} \Orth}} \newcommand{\BSO}{{\B\SO}} \newcommand{\ESO}{{\mathsf{E}\SO}} \newcommand{\BG}{{\B G}} \newcommand{\EG}{{\mathsf{E} G}} \newcommand{\BP}{{\operatorname{BP}}} \newcommand{\BU}{\B{\operatorname{U}}} \newcommand{\MO}{{\operatorname{MO}}} \newcommand{\MSO}{{\operatorname{MSO}}} \newcommand{\MSpin}{{\operatorname{MSpin}}} \newcommand{\MString}{{\operatorname{MString}}} \newcommand{\MU}{{\operatorname{MU}}} \newcommand{\KO}{{\operatorname{KO}}} \newcommand{\KU}{{\operatorname{KU}}} \newcommand{\ku}{{\operatorname{ku}}} \newcommand{\smashprod}{\wedge} \newcommand{\hofib}{{\operatorname{hofib}}} \newcommand{\cofib}{{\operatorname{cofib}}} \newcommand{\hocofib}{{\operatorname{hocofib}}} \newcommand{\Loop}{{\Omega}} \newcommand{\Loops}{\Loop} \newcommand{\Suspend}{{\Sigma}} \newcommand{\Suspendpinf}{\operatorname{{\Sigma_+^\infty}}} \newcommand{\Loopinf}{\operatorname{{\Omega^\infty}}} \newcommand{\Loopsinf}{\Loopinf} \)

Writing

Categorical and arithmetic foundations

Algebraic structure

Forms, lattices, and Witt theory

Reference

Coble surfaces

Lattice theory

The Coble lattice

Moduli spaces and period domains

Reflection groups and compactifications

Degenerations

The cusp correspondence

Stable limits

Results for \(F_{\mathrm{En},2}\)

Computational methods

Computed results

Open problems and research programs

Reference