:root,:root[data-theme=light]{--bg: #dcdbd2;--bg-elev: #e7e6dd;--bg-sunken: #cecdc3;--ink: #1b1a17;--ink-soft: #4c4944;--ink-muted: #615d53;--rule: #bbb9ae;--rule-soft: #d0cec3;--accent: #a83e06;--accent-soft: #f6e0cf;--link: var(--accent);--link-hover: #c2510c;--code-bg: var(--bg-sunken);--shadow: 0 1px 2px rgba(40, 30, 20, .06);--shadow-lg: 0 6px 24px rgba(40, 30, 20, .1);--ok: #2c7138;--warn: #8a6000;--bad: #b32424;--signal: var(--ink-soft);--serif: "Iowan Old Style", "Charter", "Source Serif Pro", "STIX Two Text", Georgia, serif;--sans: ui-sans-serif, system-ui, -apple-system, "Segoe UI", Roboto, sans-serif;--mono: "JetBrains Mono", ui-monospace, "SFMono-Regular", Menlo, Consolas, monospace}:root[data-theme=dark]{--bg: #161517;--bg-elev: #1e1d20;--bg-sunken: #100f11;--ink: #ece7df;--ink-soft: #bab4a9;--ink-muted: #8a8377;--rule: #2c2a30;--rule-soft: #201f23;--accent: #f59042;--accent-soft: #3a2410;--link: var(--accent);--link-hover: #ffab63;--code-bg: var(--rule-soft);--shadow: 0 1px 2px rgba(0, 0, 0, .4);--shadow-lg: 0 6px 24px rgba(0, 0, 0, .5);--ok: #6dd28a;--warn: #e8c14a;--bad: #f06363}*,*:before,*:after{box-sizing:border-box}html,body{min-height:100%}:root{--header-h: 2.85rem}body{margin:0;background:var(--bg);color:var(--ink);font-family:var(--sans);font-size:15px;line-height:1.55;-webkit-font-smoothing:antialiased;text-rendering:optimizeLegibility}a{color:var(--link);text-decoration:none}a:hover,a:focus-visible{color:var(--link-hover);text-decoration:underline}code,kbd,pre{font-family:var(--mono);font-size:.92em}code{background:var(--code-bg);padding:.1em .35em;border-radius:3px}hr{border:none;border-top:1px solid var(--rule);margin:2rem 0}button{font:inherit;color:var(--ink);background:var(--bg-elev);border:1px solid var(--rule);border-radius:4px;padding:.3rem .7rem;cursor:pointer}button:hover{border-color:var(--accent);color:var(--accent)}:focus-visible{outline:2px solid var(--accent);outline-offset:2px}.ar5iv-header{display:flex;align-items:center;justify-content:space-between;padding:.65rem 1.5rem;border-bottom:1px solid var(--rule);background:var(--bg-elev);position:sticky;top:0;z-index:10}.ar5iv-logo{font-family:var(--serif);font-size:1.15rem;font-weight:600;letter-spacing:.01em;color:var(--ink)}.ar5iv-logo:hover{text-decoration:none;color:var(--accent)}.ar5iv-header nav{display:flex;gap:1.1rem;align-items:center}.ar5iv-header nav a{color:var(--ink-soft);font-size:.92rem;letter-spacing:.02em}.ar5iv-header nav a:hover{color:var(--accent);text-decoration:none}body[data-page=editor] .ar5iv-header nav a[href="/editor"],body[data-page=upload] .ar5iv-header nav a[href="/upload"],body[data-page=vscode] .ar5iv-header nav a[href="/vscode"],body[data-page=schemas] .ar5iv-header nav a[href="/schemas"],body[data-page=validate] .ar5iv-header nav a[href="/validate"],body[data-page=about] .ar5iv-header nav a[href="/about"],body[data-page=help] .ar5iv-header nav a[href="/help"]{font-weight:700;color:var(--ink)}.ar5iv-header nav #theme-toggle{min-width:5.5rem;display:inline-flex;align-items:center;justify-content:center;gap:.4rem;line-height:1}.theme-toggle__glyph,.theme-toggle__label{display:inline-flex;align-items:center;height:1em;line-height:1}.landing{max-width:64rem;margin:0 auto;padding:3rem 1.5rem 4rem}.landing-hero{margin-bottom:2.5rem}.landing-hero h1{font-family:var(--serif);font-weight:600;font-size:clamp(2rem,4vw,2.75rem);margin:0 0 .6rem;letter-spacing:-.01em}.landing-hero .lead{font-family:var(--serif);font-size:1.15rem;color:var(--ink-soft);max-width:42rem;margin:0}.service-grid{list-style:none;margin:0;padding:0;display:grid;grid-template-columns:repeat(auto-fit,minmax(18rem,1fr));gap:1rem}.service-card{background:var(--bg-elev);border:1px solid var(--rule);border-radius:6px;padding:1.25rem 1.4rem;transition:border-color .12s ease,box-shadow .12s ease,transform .12s ease}.service-card:hover{border-color:var(--accent);box-shadow:var(--shadow-lg);transform:translateY(-1px)}.service-card h2{font-family:var(--serif);font-size:1.15rem;font-weight:600;margin:0 0 .5rem;display:flex;align-items:baseline;gap:.6rem}.service-card h2 a{color:var(--ink)}.service-card h2 a:hover{color:var(--accent);text-decoration:none}.service-card p{margin:0;color:var(--ink-soft);font-size:.94rem}.service-card--disabled{opacity:.65}.service-card--disabled:hover{border-color:var(--rule);box-shadow:none;transform:none}.badge{display:inline-block;font-family:var(--mono);font-size:.68rem;text-transform:uppercase;letter-spacing:.08em;color:var(--accent);background:var(--accent-soft);padding:.15em .5em;border-radius:3px;vertical-align:middle}.upload-page{display:flex;flex-direction:column;min-height:calc(100vh - var(--header-h))}.upload-intro{max-width:64rem;width:100%;margin:0 auto;padding:3rem 1.5rem 1.5rem}.upload-intro h1{font-family:var(--serif);font-weight:600;font-size:clamp(1.8rem,3.5vw,2.5rem);margin:0 0 .5rem;letter-spacing:-.01em}.upload-intro .lede{font-family:var(--serif);font-size:1.1rem;color:var(--ink-soft);margin:0 0 1.6rem}.upload-form{margin:0}.upload-drop{display:flex;flex-direction:column;align-items:center;justify-content:center;gap:.4rem;padding:2.4rem 1.5rem;border:2px dashed var(--rule);border-radius:8px;background:var(--bg-elev);color:var(--ink-soft);cursor:pointer;text-align:center;transition:border-color .12s ease,background-color .12s ease}.upload-drop:hover,.upload-drop:focus-visible{border-color:var(--accent);outline:none}.upload-drop--over{border-color:var(--accent);background:color-mix(in srgb,var(--accent) 10%,var(--bg-elev))}.upload-drop__primary{font-family:var(--serif);font-size:1.1rem;font-weight:600;color:var(--ink)}.upload-drop__hint{font-size:.9rem;color:var(--ink-muted)}.upload-input{position:absolute;width:1px;height:1px;padding:0;margin:-1px;overflow:hidden;clip:rect(0,0,0,0);white-space:nowrap;border:0}.upload-status{display:flex;align-items:center;flex-wrap:wrap;column-gap:.75rem;margin-top:1rem;font-family:var(--mono);font-variant-numeric:tabular-nums;font-size:.78rem;color:var(--ink-muted)}.upload-status .caption{text-transform:uppercase;letter-spacing:.08em;font-family:var(--sans);font-size:.66rem;color:color-mix(in oklab,var(--ink-soft) 75%,var(--accent))}.upload-status #status{color:var(--ink-soft)}.prose{max-width:42rem;margin:3rem auto;padding:0 1.5rem;font-family:var(--serif);font-size:1.05rem;line-height:1.65}.prose h1{font-weight:600;font-size:2rem;margin:0 0 .4rem;letter-spacing:-.01em}.prose .lede{font-size:1.15rem;color:var(--ink-soft);margin:0 0 1.4rem;letter-spacing:0}.prose .prose-footer{margin-top:2.4rem;padding-top:1rem;border-top:1px solid var(--rule);font-size:.85rem;color:var(--ink-muted)}.prose .prose-footer a{color:var(--ink-muted)}.prose .prose-footer a:hover{color:var(--link-hover)}.prose .prose-table{width:100%;border-collapse:collapse;margin:1rem 0 1.6rem;font-size:.95rem}.prose .prose-table th,.prose .prose-table td{text-align:left;vertical-align:top;padding:.55rem .8rem;border-bottom:1px solid var(--rule-soft)}.prose .prose-table thead th{font-weight:600;color:var(--ink-soft);border-bottom:1px solid var(--rule);font-size:.82rem;letter-spacing:.04em;text-transform:uppercase}.prose .prose-table tbody th{font-weight:500;white-space:nowrap;width:1%}.prose h2{font-weight:600;font-size:1.4rem;margin-top:2rem}.prose p{margin:.9em 0}.prose ul{padding-left:1.4em}.prose li+li{margin-top:.3em}.prose a{border-bottom:1px solid currentColor}.prose a:hover{text-decoration:none;border-bottom-color:var(--link-hover)}main{display:flex;flex-direction:column;min-height:calc(100vh - var(--header-h))}.ar5iv-editor-shell{display:grid;grid-template-columns:var(--w-files, 16rem) 4px var(--w-source, 32rem) 4px minmax(0,1fr);align-items:start;flex:1}.pane{display:flex;flex-direction:column;min-width:0;background:var(--bg-elev)}.pane-files,.pane-source{position:sticky;top:var(--header-h);height:calc(100vh - var(--header-h))}.pane-files{border-right:1px solid var(--rule);background:var(--bg-sunken);transition:background .12s ease,box-shadow .12s ease}.pane-files--drop{background:color-mix(in srgb,var(--accent) 12%,var(--bg-sunken));box-shadow:inset 0 0 0 2px var(--accent)}.pane-source{border-right:1px solid var(--rule)}.pane-preview{min-height:calc(100vh - var(--header-h))}.resizer{cursor:col-resize;background:var(--rule);position:sticky;top:var(--header-h);height:calc(100vh - var(--header-h))}.resizer:before{content:"";position:absolute;top:0;right:-3px;bottom:0;left:-3px;background:transparent}.resizer:hover,.resizer--dragging,.resizer:focus-visible{background:var(--accent)}.resizer:focus-visible{outline:none}.resizer{position:relative}.resizer__toggle{position:absolute;top:50%;left:50%;transform:translate(-50%,-50%);width:14px;height:36px;padding:0;border:1px solid var(--rule);border-radius:3px;background:var(--bg-elev);color:var(--ink-soft);font-family:var(--mono);font-size:11px;line-height:1;cursor:pointer;display:flex;align-items:center;justify-content:center;z-index:2;opacity:.55;transition:opacity .12s ease,color .12s ease,border-color .12s ease,background-color .12s ease}.resizer:hover .resizer__toggle,.resizer__toggle:focus-visible,.resizer__toggle--collapsed{opacity:1}.resizer__toggle:hover{color:var(--accent);border-color:var(--accent);background-color:color-mix(in srgb,var(--accent) 10%,var(--bg-elev))}.resizer__toggle:focus-visible{outline:none;border-color:var(--accent);box-shadow:0 0 0 2px color-mix(in srgb,var(--accent) 28%,transparent)}@media(prefers-reduced-motion:reduce){.resizer__toggle{transition:none}}.ar5iv-editor-shell--files-collapsed .pane-files,.ar5iv-editor-shell--source-collapsed .pane-source{overflow:hidden;border-right:none}.pane-title{text-transform:uppercase;letter-spacing:.08em;font-family:var(--sans);font-size:.72rem;color:var(--ink-soft)}.pane-actions{display:inline-flex;gap:.4rem;align-items:center;flex:1;justify-content:flex-end}.pane-actions button{background:transparent;border:1px solid var(--rule);border-radius:3px;color:var(--ink-soft);padding:.12rem .42rem;font-family:var(--mono);font-size:.72rem;letter-spacing:.02em;line-height:1.15;cursor:pointer;white-space:nowrap;transition:border-color .12s ease,color .12s ease,background-color .12s ease}.pane-actions button:not(:disabled):hover{color:var(--accent);border-color:var(--accent);background-color:color-mix(in srgb,var(--accent) 8%,transparent)}.pane-actions button:not(:disabled):focus-visible{outline:none;border-color:var(--accent);box-shadow:0 0 0 2px color-mix(in srgb,var(--accent) 28%,transparent)}.pane-actions button:not(:disabled):active{background-color:color-mix(in srgb,var(--accent) 16%,transparent)}.pane-actions button:disabled{opacity:.45;cursor:not-allowed}.pane-actions button.pane-action--destructive:not(:disabled):hover{color:var(--bad);border-color:var(--bad);background-color:color-mix(in srgb,var(--bad) 8%,transparent)}.pane-actions button.pane-action--destructive:not(:disabled):active{background-color:color-mix(in srgb,var(--bad) 16%,transparent)}.pane-actions button.pane-action--destructive:not(:disabled):focus-visible{border-color:var(--bad);box-shadow:0 0 0 2px color-mix(in srgb,var(--bad) 28%,transparent)}@media(prefers-reduced-motion:reduce){.pane-actions button{transition:none}}.file-tree{flex:1;min-height:0;overflow:auto;padding:.3rem .2rem .6rem;font-family:var(--sans);font-size:.85rem;color:var(--ink-soft)}.file-tree:empty:before{content:"(empty)";display:block;padding:.6rem;color:var(--ink-muted);font-style:italic;font-size:.82rem}.ftree-root,.ftree-sublist{list-style:none;margin:0;padding:0}.ftree-row{display:flex;align-items:center;gap:.25rem;position:relative}.ftree-button{flex:1;display:flex;align-items:baseline;gap:.45rem;background:transparent;border:none;padding:.2rem .4rem;text-align:left;color:var(--ink-soft);font-family:var(--mono);font-size:.78rem;letter-spacing:.01em;cursor:pointer;min-width:0}.ftree-button:hover{color:var(--accent)}.ftree-row--active>.ftree-button{background:var(--accent-soft);color:var(--accent)}.ftree-icon{flex:0 0 auto;width:.9em;text-align:center;color:var(--ink-muted);font-size:.7em}.ftree-row--dir>.ftree-button:hover>.ftree-icon{color:var(--accent)}.ftree-label{flex:1 1 auto;overflow:hidden;text-overflow:ellipsis;white-space:nowrap}.ftree-delete{flex:0 0 auto;margin-left:auto;background:transparent;border:0;cursor:pointer;color:var(--bad);font-family:var(--mono);font-size:.85rem;line-height:1;padding:.15rem .45rem;border-radius:3px;opacity:0;transition:opacity .12s ease,background-color .12s ease}.ftree-row:hover .ftree-delete,.ftree-row:focus-within .ftree-delete,.ftree-delete:focus-visible{opacity:1}.ftree-delete:hover{background:color-mix(in srgb,var(--bad) 18%,transparent)}.ftree-delete:focus-visible{outline:2px solid var(--bad);outline-offset:1px}@media(prefers-reduced-motion:reduce){.ftree-delete{transition:none}}.binary-stub{flex:1;min-height:0;display:flex;flex-direction:column;align-items:center;justify-content:center;padding:2rem 1.5rem;background:var(--bg-elev);color:var(--ink-soft);text-align:center;gap:1rem}.binary-stub[hidden]{display:none}.binary-stub__title{font-family:var(--mono);font-size:1rem;color:var(--ink);word-break:break-all;max-width:38rem}.binary-stub__meta{display:grid;grid-template-columns:auto auto;gap:.15rem .8rem;margin:0;font-family:var(--mono);font-size:.82rem;color:var(--ink-muted)}.binary-stub__meta dt{text-transform:uppercase;letter-spacing:.06em;font-size:.72rem;text-align:right}.binary-stub__meta dd{margin:0;color:var(--ink-soft)}.binary-stub__hint{font-family:var(--serif);font-size:.95rem;color:var(--ink-soft);max-width:36rem}.binary-stub__hint code{background:var(--code-bg);padding:.15em .4em;border-radius:3px}.binary-stub__download{display:inline-block;padding:.4rem 1rem;border:1px solid var(--rule);border-radius:4px;color:var(--accent);font-size:.88rem;text-decoration:none}.binary-stub__download:hover{background:var(--bg-sunken);border-color:var(--accent)}.preview-version{margin-left:auto;font-family:var(--mono);font-size:.72rem;letter-spacing:.01em;color:var(--ink-muted);text-decoration:none;white-space:nowrap;padding:0 .15rem}.preview-version:hover{color:var(--accent);text-decoration:underline}.diag-badge{margin-left:.5rem;background:transparent;border:1px solid transparent;color:var(--ink-muted);font-size:.95rem;padding:0 .3rem;border-radius:50%;cursor:pointer;line-height:1.6}.diag-badge:hover{background:var(--bg-elev);color:var(--accent)}.diag-badge--warn{color:var(--warn)}.diag-badge--error{color:var(--bad)}.diag-popup{position:fixed;z-index:90;max-width:min(36rem,calc(100vw - 2rem));max-height:50vh;overflow:auto;background:var(--bg-elev);border:1px solid var(--rule);border-radius:4px;box-shadow:var(--shadow-lg);padding:.5rem;font-family:var(--sans);font-size:.85rem}.diag-popup__row{padding:.4rem .55rem;border-radius:3px}.diag-popup__row+.diag-popup__row{margin-top:.2rem}.diag-popup__row--error,.diag-popup__row--fatal{border-left:3px solid var(--bad);padding-left:.45rem}.diag-popup__row--warning{border-left:3px solid var(--warn);padding-left:.45rem}.diag-popup__row--info{border-left:3px solid var(--rule);padding-left:.45rem}.diag-popup__sev{text-transform:uppercase;font-family:var(--mono);font-size:.72rem;letter-spacing:.05em;color:var(--ink-muted)}.diag-popup__cat{font-family:var(--mono);color:var(--ink);font-weight:600}.diag-popup__msg{margin-top:.2rem;white-space:pre-wrap;color:var(--ink-soft);font-size:.82rem}.toast-stack{position:fixed;bottom:1rem;right:1rem;display:flex;flex-direction:column;gap:.45rem;z-index:100;max-width:min(30rem,calc(100vw - 2rem))}.toast{background:var(--bg-elev);border:1px solid var(--rule);border-left:3px solid var(--accent);padding:.55rem .85rem;border-radius:4px;box-shadow:var(--shadow-lg);font-family:var(--sans);font-size:.86rem;color:var(--ink);cursor:pointer;animation:toast-in .22s ease-out}.toast--warn{border-left-color:var(--warn)}.toast--error{border-left-color:var(--bad)}.toast--leaving{animation:toast-out .24s ease-out forwards}@keyframes toast-in{0%{opacity:0;transform:translateY(.4rem)}to{opacity:1;transform:translateY(0)}}@keyframes toast-out{to{opacity:0;transform:translateY(.4rem)}}.notice-stack{position:fixed;inset-block-start:calc(var(--header-height, 2.85rem) + .6rem);inset-inline-start:50%;transform:translate(-50%);display:flex;flex-direction:column;gap:.5rem;z-index:150;max-width:min(48rem,calc(100vw - 2rem));pointer-events:none}.notice{background:color-mix(in srgb,var(--ok) 15%,var(--bg-elev));color:var(--ink);padding-block:.65rem;padding-inline:1.05rem;border:1px solid color-mix(in srgb,var(--ok) 55%,var(--bg-elev));border-inline-start:4px solid var(--ok);border-radius:6px;font-family:var(--sans);font-size:.92rem;line-height:1.4;box-shadow:var(--shadow);text-align:center;white-space:pre-wrap;animation:notice-in .22s cubic-bezier(.2,.9,.3,1.2)}.notice--leaving{animation:notice-out .2s ease-out forwards}@keyframes notice-in{0%{opacity:0;transform:translateY(-.5rem)}to{opacity:1;transform:translateY(0)}}@keyframes notice-out{to{opacity:0;transform:translateY(-.35rem)}}@media(prefers-reduced-motion:reduce){.notice,.notice--leaving{animation:none}}.fatal-card{position:fixed;top:50%;left:50%;transform:translate(-50%,-50%);background:var(--bg-elev);border:1px solid var(--rule);border-left:4px solid var(--bad);padding:1.1rem 1.4rem;border-radius:6px;box-shadow:var(--shadow-lg);font-family:var(--sans);color:var(--ink);max-width:min(34rem,calc(100vw - 2rem));z-index:200;animation:toast-in .22s ease-out}.fatal-card__title{font-weight:600;font-size:1rem;color:var(--bad);margin-bottom:.4rem}.fatal-card__detail{font-size:.88rem;color:var(--ink-soft);margin-bottom:.7rem;white-space:pre-wrap}.fatal-card__countdown{font-family:var(--mono, monospace);font-size:.82rem;color:var(--ink-soft)}.pane-header{display:flex;align-items:center;justify-content:space-between;gap:.75rem;height:2.4rem;padding:0 .85rem;background:var(--bg-sunken);border-bottom:1px solid var(--rule-soft);font-size:.85rem;color:var(--ink-soft);flex:0 0 auto}.pane-stats{display:flex;align-items:center;flex-wrap:wrap;row-gap:0;column-gap:.75rem;min-height:1.8rem;padding:.25rem .85rem;background:var(--bg-sunken);border-bottom:1px solid var(--rule);font-family:var(--mono);font-variant-numeric:tabular-nums;font-size:.74rem;color:var(--ink-muted);flex:0 0 auto;min-width:0}.pane-stats .caption{text-transform:uppercase;letter-spacing:.08em;font-family:var(--sans);font-size:.66rem;color:color-mix(in oklab,var(--ink-soft) 75%,var(--accent));flex:0 0 auto}.pane-stats #status{color:var(--ink-soft);flex:0 0 auto}.pane-stats #char-count{color:var(--ink-soft);margin-left:auto;flex:0 0 auto}.pane-stats .timings{margin-left:auto;display:flex;flex-wrap:nowrap;gap:.9rem;flex:1 1 auto;justify-content:flex-end;min-width:0}.pane-stats .timings:empty{display:none}.timings-row{display:flex;flex-wrap:nowrap;gap:.9rem;justify-content:flex-end;white-space:nowrap;flex:0 0 auto}.timings-row:empty{display:none}@container pane-stats (max-width: 52rem){.pane-stats .timings{flex-basis:100%}}@container pane-stats (max-width: 42rem){.pane-stats .timings{flex-direction:column;align-items:flex-start;gap:.1rem}.pane-stats .timings .timings-row:last-child{align-self:flex-end}}.pane-stats{container:pane-stats / inline-size}.timings .stage{display:inline-flex;gap:.25rem}.timings .stage .label{color:var(--ink-muted)}.timings .stage .value{color:var(--ink-soft)}.timings .stage--total .value{color:var(--accent);font-weight:600}.timings .stage--total.tier-ok .value{color:var(--ok)}.timings .stage--total.tier-warn .value{color:var(--warn)}.timings .stage--total.tier-bad .value{color:var(--bad)}.timings .stage.slowest .value{font-weight:600;color:var(--signal);text-shadow:0 0 6px color-mix(in oklab,var(--signal) 55%,transparent)}.pane-header select{font:inherit;color:var(--ink);background:var(--bg-elev);border:1px solid var(--rule);border-radius:3px;padding:.15rem .4rem}#status,#counter{font-family:var(--mono);font-variant-numeric:tabular-nums;font-size:.82rem}#status{cursor:pointer}.muted{color:var(--ink-muted)}.codemirror-host{flex:1;min-height:0;overflow:hidden}.codemirror-host .cm-editor{height:100%}:root[data-theme=light] .codemirror-host .cm-editor,:root[data-theme=light] .codemirror-host .cm-editor .cm-scroller{background-color:var(--bg-elev)}:root[data-theme=light] .codemirror-host .cm-editor .cm-gutters{background-color:var(--bg-sunken);border-right:1px solid var(--rule-soft)}:root[data-theme=light] .codemirror-host .cm-editor .cm-activeLine,:root[data-theme=light] .codemirror-host .cm-editor .cm-activeLineGutter{background-color:color-mix(in oklab,var(--bg-sunken) 50%,var(--bg-elev))}.preview{flex:1;min-height:0;background:var(--bg-elev);position:relative}.preview:before{content:"";position:absolute;top:0;right:0;bottom:0;left:0;z-index:2;pointer-events:none;opacity:0;transition:opacity .18s ease;background:repeating-linear-gradient(-45deg,transparent 0,transparent 14px,color-mix(in srgb,var(--ink) 7%,transparent) 14px,color-mix(in srgb,var(--ink) 7%,transparent) 28px)}.preview--loading:before{opacity:1}body.converting,body.converting *{cursor:progress!important}@media(prefers-reduced-motion:reduce){.preview:before{transition:none}}.log{flex:1;min-height:0;max-height:calc(100vh - var(--header-h));overflow:auto;margin:0;padding:.8rem 1rem;background:var(--bg-sunken);color:var(--ink-soft);font-family:var(--mono);font-size:.82rem;white-space:pre-wrap}@media(max-width:760px){.ar5iv-editor-shell{grid-template-columns:0 0 minmax(0,1fr) 4px minmax(0,1fr);grid-template-rows:minmax(0,50vh) 4px 1fr;grid-template-areas:"src src src res prv" "src src src res prv" "src src src res prv"}.pane-files,.resizer[data-edge=files-source]{display:none}.pane-source{border-right:none;border-bottom:1px solid var(--rule);overflow:hidden}}.validate-form{display:flex;flex-direction:column;gap:.75rem}.validate-controls{display:flex;align-items:center;gap:.75rem;flex-wrap:wrap}.validate-controls label{color:var(--ink-soft);font-size:.9rem}.validate-controls select{flex:1 1 16rem;padding:.45rem .6rem;font:inherit;color:var(--ink);background:var(--bg-elev);border:1px solid var(--rule);border-radius:6px}.validate-controls button{padding:.45rem 1.4rem;font:inherit;font-weight:600;color:var(--bg-elev);background:var(--accent);border:none;border-radius:6px;cursor:pointer}.validate-controls button:disabled{opacity:.6;cursor:progress}#validate-source{width:100%;font-family:var(--mono);font-size:.85rem;line-height:1.45;color:var(--ink);background:var(--bg-elev);border:1px solid var(--rule);border-radius:8px;padding:.75rem;resize:vertical}.validate-file{font-size:.9rem}.validate-report{max-width:64rem;width:100%;margin:0 auto;padding:0 1.5rem 3rem}.validate-report h2{font-family:var(--serif)}.validate-verdict--ok{color:var(--ok, #2e7d32)}.validate-verdict--fail{color:var(--error, #c62828)}.validate-messages{list-style:none;margin:0;padding:0;display:flex;flex-direction:column;gap:.6rem}.validate-msg{border:1px solid var(--rule);border-left-width:4px;border-radius:6px;padding:.55rem .8rem;display:grid;grid-template-columns:auto auto 1fr;gap:.25rem .75rem;align-items:baseline}.validate-msg--error{border-left-color:var(--error, #c62828)}.validate-msg--warning{border-left-color:var(--warn, #e09100)}.validate-msg--info{border-left-color:var(--accent)}.validate-msg__badge{font-family:var(--mono);font-size:.72rem;text-transform:uppercase;letter-spacing:.06em;color:var(--ink-soft)}.validate-msg__loc{font-family:var(--mono);font-size:.8rem;color:var(--ink-soft)}.validate-msg__text{grid-column:3}.validate-msg__extract{grid-column:1 / -1;font-family:var(--mono);font-size:.78rem;background:var(--bg-sunken);border-radius:4px;padding:.3rem .5rem;overflow-x:auto;white-space:pre}.validate-msg__context{grid-column:1 / -1;position:relative;font-family:var(--mono);font-size:.78rem;line-height:1.45;background:var(--bg-sunken);border-radius:4px;padding:.3rem 0;overflow-x:auto}.validate-ctx__row{display:flex;white-space:pre}.validate-ctx__ln{flex:none;min-width:4em;padding:0 .6em 0 .4em;text-align:right;color:var(--ink-soft);border-right:1px solid var(--rule);margin-right:.5em;-webkit-user-select:none;user-select:none;position:sticky;left:0;background:var(--bg-sunken)}.validate-msg__context mark{background:var(--accent);color:var(--bg-sunken);border-radius:2px;padding:0 1px}body.validate-busy,body.validate-busy *{cursor:progress!important}.validate-page .upload-intro{position:relative}.validate-credit{font-family:var(--serif);font-style:italic;font-size:.85rem;line-height:1.55;color:var(--ink-soft);border-left:2px solid var(--rule);padding-left:.8rem;margin:0 0 1.4rem;max-width:36rem}@media(min-width:96em){.validate-credit{position:absolute;left:100%;top:3.2rem;margin:0 0 0 1.5rem;width:14rem}}.validate-fileinfo{border:1px solid var(--rule);border-radius:6px;padding:.4rem .7rem;background:var(--bg-elev)}.validate-fileinfo summary{cursor:pointer;font-family:var(--mono);font-size:.85rem;display:flex;align-items:center;gap:.6rem}.validate-fileinfo summary button{margin-left:auto;border:none;background:none;color:var(--ink-soft);font-size:1rem;cursor:pointer;line-height:1}.validate-fileinfo summary button:hover{color:var(--error, #c62828)}.validate-filemeta{display:grid;grid-template-columns:auto 1fr;gap:.2rem 1rem;margin:.5rem 0 .2rem;font-size:.85rem}.validate-filemeta dt{color:var(--ink-soft)}.validate-filemeta dd{margin:0;font-family:var(--mono)}@font-face{font-display:block;font-family:KaTeX_AMS;font-style:normal;font-weight:400;src:url(/KaTeX_AMS-Regular.woff2) format("woff2"),url(/KaTeX_AMS-Regular.woff) format("woff"),url(/KaTeX_AMS-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Caligraphic;font-style:normal;font-weight:700;src:url(/KaTeX_Caligraphic-Bold.woff2) format("woff2"),url(/KaTeX_Caligraphic-Bold.woff) format("woff"),url(/KaTeX_Caligraphic-Bold.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Caligraphic;font-style:normal;font-weight:400;src:url(/KaTeX_Caligraphic-Regular.woff2) format("woff2"),url(/KaTeX_Caligraphic-Regular.woff) format("woff"),url(/KaTeX_Caligraphic-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Fraktur;font-style:normal;font-weight:700;src:url(/KaTeX_Fraktur-Bold.woff2) format("woff2"),url(/KaTeX_Fraktur-Bold.woff) format("woff"),url(/KaTeX_Fraktur-Bold.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Fraktur;font-style:normal;font-weight:400;src:url(/KaTeX_Fraktur-Regular.woff2) format("woff2"),url(/KaTeX_Fraktur-Regular.woff) format("woff"),url(/KaTeX_Fraktur-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:normal;font-weight:700;src:url(/KaTeX_Main-Bold.woff2) format("woff2"),url(/KaTeX_Main-Bold.woff) format("woff"),url(/KaTeX_Main-Bold.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:italic;font-weight:700;src:url(/KaTeX_Main-BoldItalic.woff2) format("woff2"),url(/KaTeX_Main-BoldItalic.woff) format("woff"),url(/KaTeX_Main-BoldItalic.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:italic;font-weight:400;src:url(/KaTeX_Main-Italic.woff2) format("woff2"),url(/KaTeX_Main-Italic.woff) format("woff"),url(/KaTeX_Main-Italic.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Main;font-style:normal;font-weight:400;src:url(/KaTeX_Main-Regular.woff2) format("woff2"),url(/KaTeX_Main-Regular.woff) format("woff"),url(/KaTeX_Main-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Math;font-style:italic;font-weight:700;src:url(/KaTeX_Math-BoldItalic.woff2) format("woff2"),url(/KaTeX_Math-BoldItalic.woff) format("woff"),url(/KaTeX_Math-BoldItalic.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Math;font-style:italic;font-weight:400;src:url(/KaTeX_Math-Italic.woff2) format("woff2"),url(/KaTeX_Math-Italic.woff) format("woff"),url(/KaTeX_Math-Italic.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:normal;font-weight:700;src:url(/KaTeX_SansSerif-Bold.woff2) format("woff2"),url(/KaTeX_SansSerif-Bold.woff) format("woff"),url(/KaTeX_SansSerif-Bold.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:italic;font-weight:400;src:url(/KaTeX_SansSerif-Italic.woff2) format("woff2"),url(/KaTeX_SansSerif-Italic.woff) format("woff"),url(/KaTeX_SansSerif-Italic.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_SansSerif;font-style:normal;font-weight:400;src:url(/KaTeX_SansSerif-Regular.woff2) format("woff2"),url(/KaTeX_SansSerif-Regular.woff) format("woff"),url(/KaTeX_SansSerif-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Script;font-style:normal;font-weight:400;src:url(/KaTeX_Script-Regular.woff2) format("woff2"),url(/KaTeX_Script-Regular.woff) format("woff"),url(/KaTeX_Script-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size1;font-style:normal;font-weight:400;src:url(/KaTeX_Size1-Regular.woff2) format("woff2"),url(/KaTeX_Size1-Regular.woff) format("woff"),url(/KaTeX_Size1-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size2;font-style:normal;font-weight:400;src:url(/KaTeX_Size2-Regular.woff2) format("woff2"),url(/KaTeX_Size2-Regular.woff) format("woff"),url(/KaTeX_Size2-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size3;font-style:normal;font-weight:400;src:url(data:font/woff2;base64,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) format("woff2"),url(/KaTeX_Size3-Regular.woff) format("woff"),url(/KaTeX_Size3-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Size4;font-style:normal;font-weight:400;src:url(/KaTeX_Size4-Regular.woff2) format("woff2"),url(/KaTeX_Size4-Regular.woff) format("woff"),url(/KaTeX_Size4-Regular.ttf) format("truetype")}@font-face{font-display:block;font-family:KaTeX_Typewriter;font-style:normal;font-weight:400;src:url(/KaTeX_Typewriter-Regular.woff2) format("woff2"),url(/KaTeX_Typewriter-Regular.woff) format("woff"),url(/KaTeX_Typewriter-Regular.ttf) format("truetype")}.katex{font: 1.21em KaTeX_Main,Times New Roman,serif;line-height:1.2;position:relative;text-indent:0;text-rendering:auto}.katex *{-ms-high-contrast-adjust:none!important;border-color:currentColor}.katex .katex-version:after{content:"0.16.45"}.katex .katex-mathml{clip:rect(1px,1px,1px,1px);border:0;height:1px;overflow:hidden;padding:0;position:absolute;width:1px}.katex .katex-html>.newline{display:block}.katex .base{position:relative;white-space:nowrap;width:-webkit-min-content;width:-moz-min-content;width:min-content}.katex .base,.katex .strut{display:inline-block}.katex .textbf{font-weight:700}.katex .textit{font-style:italic}.katex .textrm{font-family:KaTeX_Main}.katex .textsf{font-family:KaTeX_SansSerif}.katex .texttt{font-family:KaTeX_Typewriter}.katex .mathnormal{font-family:KaTeX_Math;font-style:italic}.katex .mathit{font-family:KaTeX_Main;font-style:italic}.katex .mathrm{font-style:normal}.katex .mathbf{font-family:KaTeX_Main;font-weight:700}.katex .boldsymbol{font-family:KaTeX_Math;font-style:italic;font-weight:700}.katex .amsrm,.katex .mathbb,.katex .textbb{font-family:KaTeX_AMS}.katex .mathcal{font-family:KaTeX_Caligraphic}.katex .mathfrak,.katex .textfrak{font-family:KaTeX_Fraktur}.katex .mathboldfrak,.katex .textboldfrak{font-family:KaTeX_Fraktur;font-weight:700}.katex .mathtt{font-family:KaTeX_Typewriter}.katex .mathscr,.katex .textscr{font-family:KaTeX_Script}.katex .mathsf,.katex .textsf{font-family:KaTeX_SansSerif}.katex .mathboldsf,.katex .textboldsf{font-family:KaTeX_SansSerif;font-weight:700}.katex .mathitsf,.katex .mathsfit,.katex .textitsf{font-family:KaTeX_SansSerif;font-style:italic}.katex .mainrm{font-family:KaTeX_Main;font-style:normal}.katex .vlist-t{border-collapse:collapse;display:inline-table;table-layout:fixed}.katex .vlist-r{display:table-row}.katex .vlist{display:table-cell;position:relative;vertical-align:bottom}.katex .vlist>span{display:block;height:0;position:relative}.katex .vlist>span>span{display:inline-block}.katex .vlist>span>.pstrut{overflow:hidden;width:0}.katex .vlist-t2{margin-right:-2px}.katex .vlist-s{display:table-cell;font-size:1px;min-width:2px;vertical-align:bottom;width:2px}.katex .vbox{align-items:baseline;display:inline-flex;flex-direction:column}.katex .hbox{width:100%}.katex .hbox,.katex .thinbox{display:inline-flex;flex-direction:row}.katex .thinbox{max-width:0;width:0}.katex .msupsub{text-align:left}.katex .mfrac>span>span{text-align:center}.katex .mfrac .frac-line{border-bottom-style:solid;display:inline-block;width:100%}.katex .hdashline,.katex .hline,.katex .mfrac .frac-line,.katex .overline .overline-line,.katex .rule,.katex .underline .underline-line{min-height:1px}.katex .mspace{display:inline-block}.katex .smash{display:inline;line-height:0}.katex .clap,.katex .llap,.katex .rlap{position:relative;width:0}.katex .clap>.inner,.katex .llap>.inner,.katex .rlap>.inner{position:absolute}.katex .clap>.fix,.katex .llap>.fix,.katex .rlap>.fix{display:inline-block}.katex .llap>.inner{right:0}.katex .clap>.inner,.katex .rlap>.inner{left:0}.katex .clap>.inner>span{margin-left:-50%;margin-right:50%}.katex .rule{border:0 solid;display:inline-block;position:relative}.katex .hline,.katex .overline .overline-line,.katex .underline .underline-line{border-bottom-style:solid;display:inline-block;width:100%}.katex .hdashline{border-bottom-style:dashed;display:inline-block;width:100%}.katex .sqrt>.root{margin-left:.2777777778em;margin-right:-.5555555556em}.katex .fontsize-ensurer.reset-size1.size1,.katex .sizing.reset-size1.size1{font-size:1em}.katex .fontsize-ensurer.reset-size1.size2,.katex .sizing.reset-size1.size2{font-size:1.2em}.katex .fontsize-ensurer.reset-size1.size3,.katex .sizing.reset-size1.size3{font-size:1.4em}.katex .fontsize-ensurer.reset-size1.size4,.katex .sizing.reset-size1.size4{font-size:1.6em}.katex .fontsize-ensurer.reset-size1.size5,.katex .sizing.reset-size1.size5{font-size:1.8em}.katex .fontsize-ensurer.reset-size1.size6,.katex .sizing.reset-size1.size6{font-size:2em}.katex .fontsize-ensurer.reset-size1.size7,.katex .sizing.reset-size1.size7{font-size:2.4em}.katex .fontsize-ensurer.reset-size1.size8,.katex .sizing.reset-size1.size8{font-size:2.88em}.katex .fontsize-ensurer.reset-size1.size9,.katex .sizing.reset-size1.size9{font-size:3.456em}.katex .fontsize-ensurer.reset-size1.size10,.katex .sizing.reset-size1.size10{font-size:4.148em}.katex .fontsize-ensurer.reset-size1.size11,.katex .sizing.reset-size1.size11{font-size:4.976em}.katex .fontsize-ensurer.reset-size2.size1,.katex .sizing.reset-size2.size1{font-size:.8333333333em}.katex .fontsize-ensurer.reset-size2.size2,.katex .sizing.reset-size2.size2{font-size:1em}.katex .fontsize-ensurer.reset-size2.size3,.katex .sizing.reset-size2.size3{font-size:1.1666666667em}.katex .fontsize-ensurer.reset-size2.size4,.katex .sizing.reset-size2.size4{font-size:1.3333333333em}.katex .fontsize-ensurer.reset-size2.size5,.katex .sizing.reset-size2.size5{font-size:1.5em}.katex .fontsize-ensurer.reset-size2.size6,.katex .sizing.reset-size2.size6{font-size:1.6666666667em}.katex .fontsize-ensurer.reset-size2.size7,.katex .sizing.reset-size2.size7{font-size:2em}.katex .fontsize-ensurer.reset-size2.size8,.katex .sizing.reset-size2.size8{font-size:2.4em}.katex .fontsize-ensurer.reset-size2.size9,.katex .sizing.reset-size2.size9{font-size:2.88em}.katex .fontsize-ensurer.reset-size2.size10,.katex .sizing.reset-size2.size10{font-size:3.4566666667em}.katex .fontsize-ensurer.reset-size2.size11,.katex .sizing.reset-size2.size11{font-size:4.1466666667em}.katex .fontsize-ensurer.reset-size3.size1,.katex .sizing.reset-size3.size1{font-size:.7142857143em}.katex .fontsize-ensurer.reset-size3.size2,.katex .sizing.reset-size3.size2{font-size:.8571428571em}.katex .fontsize-ensurer.reset-size3.size3,.katex .sizing.reset-size3.size3{font-size:1em}.katex .fontsize-ensurer.reset-size3.size4,.katex .sizing.reset-size3.size4{font-size:1.1428571429em}.katex .fontsize-ensurer.reset-size3.size5,.katex .sizing.reset-size3.size5{font-size:1.2857142857em}.katex .fontsize-ensurer.reset-size3.size6,.katex .sizing.reset-size3.size6{font-size:1.4285714286em}.katex .fontsize-ensurer.reset-size3.size7,.katex .sizing.reset-size3.size7{font-size:1.7142857143em}.katex .fontsize-ensurer.reset-size3.size8,.katex .sizing.reset-size3.size8{font-size:2.0571428571em}.katex .fontsize-ensurer.reset-size3.size9,.katex .sizing.reset-size3.size9{font-size:2.4685714286em}.katex .fontsize-ensurer.reset-size3.size10,.katex .sizing.reset-size3.size10{font-size:2.9628571429em}.katex .fontsize-ensurer.reset-size3.size11,.katex .sizing.reset-size3.size11{font-size:3.5542857143em}.katex .fontsize-ensurer.reset-size4.size1,.katex .sizing.reset-size4.size1{font-size:.625em}.katex .fontsize-ensurer.reset-size4.size2,.katex .sizing.reset-size4.size2{font-size:.75em}.katex .fontsize-ensurer.reset-size4.size3,.katex .sizing.reset-size4.size3{font-size:.875em}.katex .fontsize-ensurer.reset-size4.size4,.katex .sizing.reset-size4.size4{font-size:1em}.katex .fontsize-ensurer.reset-size4.size5,.katex .sizing.reset-size4.size5{font-size:1.125em}.katex .fontsize-ensurer.reset-size4.size6,.katex .sizing.reset-size4.size6{font-size:1.25em}.katex .fontsize-ensurer.reset-size4.size7,.katex .sizing.reset-size4.size7{font-size:1.5em}.katex .fontsize-ensurer.reset-size4.size8,.katex .sizing.reset-size4.size8{font-size:1.8em}.katex .fontsize-ensurer.reset-size4.size9,.katex .sizing.reset-size4.size9{font-size:2.16em}.katex .fontsize-ensurer.reset-size4.size10,.katex .sizing.reset-size4.size10{font-size:2.5925em}.katex .fontsize-ensurer.reset-size4.size11,.katex .sizing.reset-size4.size11{font-size:3.11em}.katex .fontsize-ensurer.reset-size5.size1,.katex .sizing.reset-size5.size1{font-size:.5555555556em}.katex .fontsize-ensurer.reset-size5.size2,.katex .sizing.reset-size5.size2{font-size:.6666666667em}.katex .fontsize-ensurer.reset-size5.size3,.katex .sizing.reset-size5.size3{font-size:.7777777778em}.katex .fontsize-ensurer.reset-size5.size4,.katex .sizing.reset-size5.size4{font-size:.8888888889em}.katex .fontsize-ensurer.reset-size5.size5,.katex .sizing.reset-size5.size5{font-size:1em}.katex .fontsize-ensurer.reset-size5.size6,.katex .sizing.reset-size5.size6{font-size:1.1111111111em}.katex .fontsize-ensurer.reset-size5.size7,.katex .sizing.reset-size5.size7{font-size:1.3333333333em}.katex .fontsize-ensurer.reset-size5.size8,.katex .sizing.reset-size5.size8{font-size:1.6em}.katex .fontsize-ensurer.reset-size5.size9,.katex .sizing.reset-size5.size9{font-size:1.92em}.katex .fontsize-ensurer.reset-size5.size10,.katex .sizing.reset-size5.size10{font-size:2.3044444444em}.katex .fontsize-ensurer.reset-size5.size11,.katex .sizing.reset-size5.size11{font-size:2.7644444444em}.katex .fontsize-ensurer.reset-size6.size1,.katex .sizing.reset-size6.size1{font-size:.5em}.katex .fontsize-ensurer.reset-size6.size2,.katex .sizing.reset-size6.size2{font-size:.6em}.katex .fontsize-ensurer.reset-size6.size3,.katex .sizing.reset-size6.size3{font-size:.7em}.katex .fontsize-ensurer.reset-size6.size4,.katex .sizing.reset-size6.size4{font-size:.8em}.katex .fontsize-ensurer.reset-size6.size5,.katex .sizing.reset-size6.size5{font-size:.9em}.katex .fontsize-ensurer.reset-size6.size6,.katex .sizing.reset-size6.size6{font-size:1em}.katex .fontsize-ensurer.reset-size6.size7,.katex .sizing.reset-size6.size7{font-size:1.2em}.katex .fontsize-ensurer.reset-size6.size8,.katex .sizing.reset-size6.size8{font-size:1.44em}.katex .fontsize-ensurer.reset-size6.size9,.katex .sizing.reset-size6.size9{font-size:1.728em}.katex .fontsize-ensurer.reset-size6.size10,.katex .sizing.reset-size6.size10{font-size:2.074em}.katex .fontsize-ensurer.reset-size6.size11,.katex .sizing.reset-size6.size11{font-size:2.488em}.katex .fontsize-ensurer.reset-size7.size1,.katex .sizing.reset-size7.size1{font-size:.4166666667em}.katex .fontsize-ensurer.reset-size7.size2,.katex .sizing.reset-size7.size2{font-size:.5em}.katex .fontsize-ensurer.reset-size7.size3,.katex .sizing.reset-size7.size3{font-size:.5833333333em}.katex .fontsize-ensurer.reset-size7.size4,.katex .sizing.reset-size7.size4{font-size:.6666666667em}.katex .fontsize-ensurer.reset-size7.size5,.katex .sizing.reset-size7.size5{font-size:.75em}.katex .fontsize-ensurer.reset-size7.size6,.katex .sizing.reset-size7.size6{font-size:.8333333333em}.katex .fontsize-ensurer.reset-size7.size7,.katex .sizing.reset-size7.size7{font-size:1em}.katex .fontsize-ensurer.reset-size7.size8,.katex .sizing.reset-size7.size8{font-size:1.2em}.katex .fontsize-ensurer.reset-size7.size9,.katex .sizing.reset-size7.size9{font-size:1.44em}.katex .fontsize-ensurer.reset-size7.size10,.katex .sizing.reset-size7.size10{font-size:1.7283333333em}.katex .fontsize-ensurer.reset-size7.size11,.katex .sizing.reset-size7.size11{font-size:2.0733333333em}.katex .fontsize-ensurer.reset-size8.size1,.katex .sizing.reset-size8.size1{font-size:.3472222222em}.katex .fontsize-ensurer.reset-size8.size2,.katex .sizing.reset-size8.size2{font-size:.4166666667em}.katex .fontsize-ensurer.reset-size8.size3,.katex .sizing.reset-size8.size3{font-size:.4861111111em}.katex .fontsize-ensurer.reset-size8.size4,.katex .sizing.reset-size8.size4{font-size:.5555555556em}.katex .fontsize-ensurer.reset-size8.size5,.katex .sizing.reset-size8.size5{font-size:.625em}.katex .fontsize-ensurer.reset-size8.size6,.katex .sizing.reset-size8.size6{font-size:.6944444444em}.katex .fontsize-ensurer.reset-size8.size7,.katex .sizing.reset-size8.size7{font-size:.8333333333em}.katex .fontsize-ensurer.reset-size8.size8,.katex .sizing.reset-size8.size8{font-size:1em}.katex .fontsize-ensurer.reset-size8.size9,.katex .sizing.reset-size8.size9{font-size:1.2em}.katex .fontsize-ensurer.reset-size8.size10,.katex .sizing.reset-size8.size10{font-size:1.4402777778em}.katex .fontsize-ensurer.reset-size8.size11,.katex .sizing.reset-size8.size11{font-size:1.7277777778em}.katex .fontsize-ensurer.reset-size9.size1,.katex .sizing.reset-size9.size1{font-size:.2893518519em}.katex .fontsize-ensurer.reset-size9.size2,.katex .sizing.reset-size9.size2{font-size:.3472222222em}.katex .fontsize-ensurer.reset-size9.size3,.katex .sizing.reset-size9.size3{font-size:.4050925926em}.katex .fontsize-ensurer.reset-size9.size4,.katex .sizing.reset-size9.size4{font-size:.462962963em}.katex .fontsize-ensurer.reset-size9.size5,.katex .sizing.reset-size9.size5{font-size:.5208333333em}.katex .fontsize-ensurer.reset-size9.size6,.katex .sizing.reset-size9.size6{font-size:.5787037037em}.katex .fontsize-ensurer.reset-size9.size7,.katex .sizing.reset-size9.size7{font-size:.6944444444em}.katex .fontsize-ensurer.reset-size9.size8,.katex .sizing.reset-size9.size8{font-size:.8333333333em}.katex .fontsize-ensurer.reset-size9.size9,.katex .sizing.reset-size9.size9{font-size:1em}.katex .fontsize-ensurer.reset-size9.size10,.katex .sizing.reset-size9.size10{font-size:1.2002314815em}.katex .fontsize-ensurer.reset-size9.size11,.katex .sizing.reset-size9.size11{font-size:1.4398148148em}.katex .fontsize-ensurer.reset-size10.size1,.katex .sizing.reset-size10.size1{font-size:.2410800386em}.katex .fontsize-ensurer.reset-size10.size2,.katex .sizing.reset-size10.size2{font-size:.2892960463em}.katex .fontsize-ensurer.reset-size10.size3,.katex .sizing.reset-size10.size3{font-size:.337512054em}.katex .fontsize-ensurer.reset-size10.size4,.katex .sizing.reset-size10.size4{font-size:.3857280617em}.katex .fontsize-ensurer.reset-size10.size5,.katex .sizing.reset-size10.size5{font-size:.4339440694em}.katex .fontsize-ensurer.reset-size10.size6,.katex .sizing.reset-size10.size6{font-size:.4821600771em}.katex .fontsize-ensurer.reset-size10.size7,.katex .sizing.reset-size10.size7{font-size:.5785920926em}.katex .fontsize-ensurer.reset-size10.size8,.katex .sizing.reset-size10.size8{font-size:.6943105111em}.katex .fontsize-ensurer.reset-size10.size9,.katex .sizing.reset-size10.size9{font-size:.8331726133em}.katex .fontsize-ensurer.reset-size10.size10,.katex .sizing.reset-size10.size10{font-size:1em}.katex .fontsize-ensurer.reset-size10.size11,.katex .sizing.reset-size10.size11{font-size:1.1996142719em}.katex .fontsize-ensurer.reset-size11.size1,.katex .sizing.reset-size11.size1{font-size:.2009646302em}.katex .fontsize-ensurer.reset-size11.size2,.katex .sizing.reset-size11.size2{font-size:.2411575563em}.katex .fontsize-ensurer.reset-size11.size3,.katex .sizing.reset-size11.size3{font-size:.2813504823em}.katex .fontsize-ensurer.reset-size11.size4,.katex .sizing.reset-size11.size4{font-size:.3215434084em}.katex .fontsize-ensurer.reset-size11.size5,.katex .sizing.reset-size11.size5{font-size:.3617363344em}.katex .fontsize-ensurer.reset-size11.size6,.katex .sizing.reset-size11.size6{font-size:.4019292605em}.katex .fontsize-ensurer.reset-size11.size7,.katex .sizing.reset-size11.size7{font-size:.4823151125em}.katex .fontsize-ensurer.reset-size11.size8,.katex .sizing.reset-size11.size8{font-size:.578778135em}.katex .fontsize-ensurer.reset-size11.size9,.katex .sizing.reset-size11.size9{font-size:.6945337621em}.katex .fontsize-ensurer.reset-size11.size10,.katex .sizing.reset-size11.size10{font-size:.8336012862em}.katex .fontsize-ensurer.reset-size11.size11,.katex .sizing.reset-size11.size11{font-size:1em}.katex .delimsizing.size1{font-family:KaTeX_Size1}.katex .delimsizing.size2{font-family:KaTeX_Size2}.katex .delimsizing.size3{font-family:KaTeX_Size3}.katex .delimsizing.size4{font-family:KaTeX_Size4}.katex .delimsizing.mult .delim-size1>span{font-family:KaTeX_Size1}.katex .delimsizing.mult .delim-size4>span{font-family:KaTeX_Size4}.katex .nulldelimiter{display:inline-block;width:.12em}.katex .delimcenter,.katex .op-symbol{position:relative}.katex .op-symbol.small-op{font-family:KaTeX_Size1}.katex .op-symbol.large-op{font-family:KaTeX_Size2}.katex .accent>.vlist-t,.katex .op-limits>.vlist-t{text-align:center}.katex .accent .accent-body{position:relative}.katex .accent .accent-body:not(.accent-full){width:0}.katex .overlay{display:block}.katex .mtable .vertical-separator{display:inline-block;min-width:1px}.katex .mtable .arraycolsep{display:inline-block}.katex .mtable .col-align-c>.vlist-t{text-align:center}.katex .mtable .col-align-l>.vlist-t{text-align:left}.katex .mtable .col-align-r>.vlist-t{text-align:right}.katex .svg-align{text-align:left}.katex svg{fill:currentColor;stroke:currentColor;display:block;height:inherit;position:absolute;width:100%}.katex svg path{stroke:none}.katex svg{fill-rule:nonzero;fill-opacity:1;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1}.katex img{border-style:none;max-height:none;max-width:none;min-height:0;min-width:0}.katex .stretchy{display:block;overflow:hidden;position:relative;width:100%}.katex .stretchy:after,.katex .stretchy:before{content:""}.katex .hide-tail{overflow:hidden;position:relative;width:100%}.katex .halfarrow-left{left:0;overflow:hidden;position:absolute;width:50.2%}.katex .halfarrow-right{overflow:hidden;position:absolute;right:0;width:50.2%}.katex .brace-left{left:0;overflow:hidden;position:absolute;width:25.1%}.katex .brace-center{left:25%;overflow:hidden;position:absolute;width:50%}.katex .brace-right{overflow:hidden;position:absolute;right:0;width:25.1%}.katex .x-arrow-pad{padding:0 .5em}.katex .cd-arrow-pad{padding:0 .55556em 0 .27778em}.katex .mover,.katex .munder,.katex .x-arrow{text-align:center}.katex .boxpad{padding:0 .3em}.katex .fbox,.katex .fcolorbox{border:.04em solid;box-sizing:border-box}.katex .cancel-pad{padding:0 .2em}.katex .cancel-lap{margin-left:-.2em;margin-right:-.2em}.katex .sout{border-bottom-style:solid;border-bottom-width:.08em}.katex .angl{border-right:.049em solid;border-top:.049em solid;box-sizing:border-box;margin-right:.03889em}.katex .anglpad{padding:0 .03889em}.katex .eqn-num:before{content:"(" counter(katexEqnNo) ")";counter-increment:katexEqnNo}.katex .mml-eqn-num:before{content:"(" counter(mmlEqnNo) ")";counter-increment:mmlEqnNo}.katex .mtr-glue{width:50%}.katex .cd-vert-arrow{display:inline-block;position:relative}.katex .cd-label-left{display:inline-block;position:absolute;right:calc(50% + .3em);text-align:left}.katex .cd-label-right{display:inline-block;left:calc(50% + .3em);position:absolute;text-align:right}.katex-display{display:block;margin:1em 0;text-align:center}.katex-display>.katex{display:block;text-align:center;white-space:nowrap}.katex-display>.katex>.katex-html{display:block;position:relative}.katex-display>.katex>.katex-html>.tag{position:absolute;right:0}.katex-display.leqno>.katex>.katex-html>.tag{left:0;right:auto}.katex-display.fleqn>.katex{padding-left:2em;text-align:left}body{counter-reset:katexEqnNo mmlEqnNo}