#title-block-header{display:none}
/* Quarto propagates page-columns through ancestors of an aside. Keep its
   named page grid outside this self-contained application layout. */
.lqg.page-columns{display:block!important}
.lqg .page-columns>*{grid-column:auto!important;grid-row:auto!important}
.lqg .lqg-layout.page-columns{display:grid!important;grid-template-columns:252px minmax(0,1fr)!important}
.lqg-bootstrap{position:absolute;width:1px;height:1px;overflow:hidden;clip-path:inset(50%)}
.lqg{--bg:#101922;--panel:#182630;--line:#344853;--ink:#eff8fa;--muted:#b2c5ce;--teal:#64ddd0;--gold:#f2cc84;--pink:#f1a4d1;--green:#a1e2af;color:var(--ink);background:radial-gradient(ellipse at 85% 0,rgba(58,151,141,.13),transparent 48%),var(--bg);font-size:16px;line-height:1.6;min-height:85vh;padding:24px clamp(16px,4vw,64px) 64px}
.lqg *{box-sizing:border-box}.lqg [hidden]{display:none!important}.lqg a{color:var(--teal);text-underline-offset:4px}.lqg a:hover{color:#fff}.lqg button,.lqg select,.lqg input{font:inherit}.lqg button,.lqg select{min-height:42px;border:1px solid var(--line);border-radius:6px;background:#20333f;color:var(--ink);padding:7px 12px}.lqg button{cursor:pointer}.lqg button:hover{border-color:var(--teal);background:#294550}.lqg button[aria-pressed=true],.lqg .primary{border-color:var(--teal);background:#24514e}.lqg button:disabled{opacity:.5;cursor:default}.lqg :focus-visible{outline:3px solid var(--gold);outline-offset:3px}.lqg input[type=search]{width:100%;background:#101c25;color:var(--ink);border:1px solid var(--line);border-radius:6px;padding:9px 12px}.lqg input[type=range]{width:100%;accent-color:var(--teal)}.lqg input[type=checkbox]{accent-color:var(--teal);width:18px;height:18px;vertical-align:middle}.lqg label{display:block;font-size:14px;color:var(--muted)}.lqg label select{display:block;width:100%;margin-top:5px}.lqg h1{font-size:clamp(30px,4vw,48px);font-weight:650;letter-spacing:-.035em;line-height:1.15;margin:10px 0 14px}.lqg h2{font-size:24px;margin:0 0 12px;border:0}.lqg h3{font-size:18px;margin:0}.lqg p{margin:8px 0 16px}.lqg small,.lqg .muted{color:var(--muted)}.lqg .eyebrow{color:var(--teal);font-size:13px;text-transform:uppercase;letter-spacing:.14em;font-weight:650;margin:0}.lqg .lede{max-width:850px;color:var(--muted)}
.lqg-nav{display:flex;gap:8px;flex-wrap:wrap;border-bottom:1px solid var(--line);padding-bottom:14px;margin-bottom:26px}.lqg-nav a{padding:7px 13px;color:var(--muted);text-decoration:none;border-radius:5px;font-size:15px}.lqg-nav a[aria-current=page]{background:#26433f;color:var(--teal)}.lqg-header{display:flex;align-items:flex-end;justify-content:space-between;gap:24px;margin-bottom:22px}.lqg-header .lede{margin-bottom:0}.lqg-layout{display:grid;grid-template-columns:252px minmax(0,1fr);gap:22px;align-items:start}.lqg-controls{background:var(--panel);border:1px solid var(--line);border-radius:10px;padding:18px;position:sticky;top:80px;max-height:calc(100vh - 105px);overflow:auto}.lqg-controls>*+*{margin-top:17px}.lqg-control-row{display:flex;gap:8px;align-items:center;flex-wrap:wrap}.lqg-control-row>*{flex:1}.lqg-control-row label{min-width:130px}.lqg-buttons{display:flex;gap:7px;flex-wrap:wrap}.lqg-buttons button{font-size:14px}.lqg-level-label{display:flex;justify-content:space-between;gap:8px;color:var(--teal);font-size:14px;margin:8px 0}.lqg-stage{min-width:0}.lqg-breadcrumbs{display:flex;gap:8px;align-items:center;flex-wrap:wrap;min-height:42px;margin-bottom:12px}.lqg-breadcrumbs button{font-size:14px}.lqg-status{font-size:14px;color:var(--muted);min-height:24px;margin:10px 0}.lqg-card{border:1px solid var(--line);background:var(--panel);border-radius:10px;margin-bottom:16px;padding:20px;min-width:0}.lqg-card-head{display:flex;gap:10px;justify-content:space-between;align-items:start}.lqg-card-head small{font-size:13px}.lqg-card-head h2{font-size:20px;margin:2px 0}.lqg-card-id{font-family:monospace;color:var(--teal);font-size:14px}.lqg-equation{overflow-x:auto;overflow-y:hidden;padding:12px 5px;font-size:1.05rem;scrollbar-color:var(--line) transparent}.lqg-equation mjx-container[display=true]{margin:12px 0!important;min-width:min-content}.lqg-equation mjx-container{color:inherit}.lqg-card-note{color:var(--muted);font-size:15px}.lqg-card-actions{display:flex;gap:7px;flex-wrap:wrap;margin-top:12px}.lqg-card-actions button{font-size:14px;min-height:36px}.lqg-expansions{border-left:2px solid var(--teal);padding:6px 0 0 16px;margin-top:18px}.lqg-expansions .lqg-card{background:#14212a}.lqg-child-links{display:flex;gap:7px;flex-wrap:wrap;margin:8px 0}.lqg-child-links button{font-size:14px;text-align:left}.lqg details{font-size:14px;margin-top:12px}.lqg summary{cursor:pointer;color:var(--muted);padding:4px 0}.lqg details a{display:inline-block;margin:8px 0}.lqg pre{white-space:pre-wrap;overflow-wrap:anywhere;color:var(--ink);background:#0d1820;padding:14px;font-size:13px}.lqg .scope{border-left:3px solid var(--gold);padding:10px 16px;background:#292c29;color:#e6d8b7;font-size:14px;margin:16px 0}.lqg-grid{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:18px}.lqg-entry{display:block;border:1px solid var(--line);border-radius:10px;padding:24px;text-decoration:none!important;background:var(--panel)}.lqg-entry p{color:var(--muted)}.lqg-entry h2{color:var(--ink)}.lqg-section{margin-top:36px}.lqg-start-equations{display:grid;grid-template-columns:1fr;gap:0;margin-top:22px}.lqg-start-equations .lqg-card{border-left:3px solid var(--teal)}.lqg .lqg-notation{display:grid;grid-template-columns:repeat(auto-fit,minmax(180px,1fr));gap:12px}.lqg-notation div{border:1px solid var(--line);border-radius:6px;padding:12px}.lqg-notation dt{color:var(--gold)}.lqg-notation dd{font-size:14px;color:var(--muted);margin:4px 0 0}.lqg.colour .lqg-card[data-route=canonical]{border-left:3px solid var(--gold)}.lqg.colour .lqg-card[data-route=covariant]{border-left:3px solid var(--pink)}.lqg.colour .lqg-card[data-route=both]{border-left:3px solid var(--teal)}.lqg .lqg-key{display:flex;gap:18px;flex-wrap:wrap;font-size:14px}.lqg-key span:nth-child(1){color:var(--teal)}.lqg-key span:nth-child(2){color:var(--gold)}.lqg-key span:nth-child(3){color:var(--pink)}
.lqg-diagram-panel{border:1px solid var(--line);border-radius:10px;background:var(--panel);padding:16px;margin:16px 0}.lqg-diagram-grid{display:grid;grid-template-columns:minmax(0,1.3fr) minmax(240px,1fr);gap:24px;align-items:start}.lqg-svg-wrap{background:#fff;border-radius:8px;color:#192d32}.lqg-simplex{display:block;width:100%;height:auto;max-height:75vh}.lqg-wire-line{fill:none;stroke:#222;stroke-width:1.7}.lqg-wire-hit{fill:none;stroke:transparent;stroke-width:18}.lqg-wire{cursor:pointer}.lqg-wire.is-bulk .lqg-wire-line{stroke:#a21c79;stroke-width:2.7}.lqg-wire:hover .lqg-wire-line,.lqg-wire:focus .lqg-wire-line,.lqg-wire.is-selected .lqg-wire-line{stroke:#007e89;stroke-width:4}.lqg-simplex text{fill:#192d32;font-family:Georgia,serif;font-size:17px}.lqg-wire-label{paint-order:stroke;stroke:#fff;stroke-width:5px;stroke-linejoin:round}.lqg-node{cursor:pointer}.lqg-node rect{fill:#def4f5;stroke:#26747a;stroke-width:1.5}.lqg-node circle{fill:#222}.lqg-node:hover rect,.lqg-node:focus rect,.lqg-node.is-selected rect{stroke:#007e89;stroke-width:4}.lqg-intertwiner{fill:none;stroke:#176635;stroke-width:2}.lqg-simplex .lqg-intertwiner-label{fill:#176635;font-size:16px}.lqg-wire-editor{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:10px}.lqg-wire-editor label{border:1px solid var(--line);padding:10px;border-radius:6px}.lqg table{width:100%;font-size:14px;border-collapse:collapse}.lqg td,.lqg th{padding:8px;border-bottom:1px solid var(--line);text-align:left}.lqg-lab-output{font-size:20px;color:var(--teal);margin:12px 0}.lqg-bar{height:6px;border-radius:4px;background:var(--teal);margin:8px 0 14px;max-width:100%}.lqg-steps{display:flex;gap:8px;flex-wrap:wrap;margin:20px 0}.lqg-step{flex:1;min-width:90px;font-size:14px!important}.lqg-guide-copy{max-width:900px}.lqg-fallback{padding:24px;border:1px solid var(--line);border-radius:8px}.lqg-download{display:inline-block;padding:8px 12px;border:1px solid var(--line);border-radius:6px}.lqg-glue{width:100%;height:200px;background:white;border-radius:6px}.lqg-glue text{fill:#162e34;font-size:16px}.lqg-glue line,.lqg-glue path{stroke:#a21c79;fill:none;stroke-width:2}.lqg-glue rect{fill:#def4f5;stroke:#26747a}
@media(min-width:1500px){.lqg{padding-left:max(40px,calc((100vw - 1500px)/2));padding-right:max(40px,calc((100vw - 1500px)/2))}}
@media(max-width:1000px){.lqg .lqg-layout.page-columns{grid-template-columns:220px minmax(0,1fr)!important}}
@media(max-width:720px){.lqg .lqg-layout.page-columns{display:block!important}}
@media(max-width:1000px){.lqg-layout{grid-template-columns:220px minmax(0,1fr)}.lqg-grid{grid-template-columns:1fr}.lqg-diagram-grid{grid-template-columns:1fr}.lqg-header{display:block}}
@media(max-width:720px){.lqg{padding:16px 12px 40px}.lqg-layout{display:block}.lqg-controls{position:static;max-height:none;display:grid;grid-template-columns:1fr 1fr;gap:14px;margin-bottom:18px;padding:14px}.lqg-controls>*+*{margin:0}.lqg-controls .wide{grid-column:1/-1}.lqg-card{padding:14px}.lqg-expansions{padding-left:8px}.lqg-card-head h2{font-size:18px}.lqg-equation{font-size:.95rem}.lqg-nav{gap:2px}.lqg-nav a{padding:7px 9px;font-size:14px}.lqg-wire-editor{grid-template-columns:1fr 1fr}}
@media(prefers-reduced-motion:reduce){.lqg *{scroll-behavior:auto!important}}
@media print{.lqg{background:white;color:black}.lqg-controls,.lqg-card-actions,.lqg-nav{display:none}.lqg-layout{display:block}.lqg-card{break-inside:avoid;background:white;color:black}.lqg-card-note,.lqg small{color:#333}}