.explainer-byline{font-family:var(--font-sans);align-items:center;gap:.875rem;margin-top:1.75rem;display:flex}.explainer-byline-portrait{object-fit:cover;filter:grayscale();border-radius:50%;flex-shrink:0;width:2.75rem;height:2.75rem}.explainer-byline-name{color:#57534e;font-size:.8125rem;line-height:1.5}.explainer-byline-name a{color:#1c1917;text-underline-offset:.2em;font-weight:500;text-decoration:underline #d9d3ca}.explainer-byline-bio{color:#57534e;margin-top:.2rem;font-size:.75rem;line-height:1.6}.explainer-author{border-top:2px solid #292524;border-bottom:1px solid #d9d3ca;grid-template-columns:4rem minmax(0,1fr);align-items:start;gap:1.25rem;margin-top:5rem;padding:2rem 0;display:grid}.explainer-author-portrait{object-fit:cover;filter:grayscale();width:4rem;height:5rem}.explainer-author-note h2{font-family:var(--font-sans);letter-spacing:.15em;text-align:left;text-transform:uppercase;color:#57534e;margin:0 0 .875rem;font-size:.6875rem;font-weight:500;line-height:1.5}.explainer-author-note p{max-width:38rem;font-family:var(--font-serif);color:#44403c;font-size:1rem;line-height:1.8}.explainer-author-invitation{margin-top:.875rem}.explainer-author a{color:#8b6e4e;text-underline-offset:.2em;text-decoration:underline}.explainer-author-links{font-family:var(--font-sans);flex-wrap:wrap;gap:.75rem 1.75rem;margin-top:1.5rem;font-size:.75rem;line-height:1.7;display:flex}.explainer-author-links a{align-items:baseline;gap:.5rem;display:inline-flex}.explainer-byline a:hover,.explainer-author a:hover{color:#92400e}.explainer-byline a:focus-visible,.explainer-author a:focus-visible{outline-offset:4px;outline:2px solid}@media (width>=640px){.explainer-author{grid-template-columns:6rem minmax(0,1fr);gap:2rem;padding:2.5rem 0}.explainer-author-portrait{width:6rem;height:7.5rem}}@media (prefers-color-scheme:dark){.explainer-byline-name,.explainer-byline-bio,.explainer-author-note h2{color:#a8a29e}.explainer-byline-name a{color:#f5f5f4;text-decoration-color:#57534e}.explainer-author{border-top-color:#d6d3d1;border-bottom-color:#44403c}.explainer-author-note p{color:#d6d3d1}.explainer-author a{color:#d4a574}.explainer-byline a:hover,.explainer-author a:hover{color:#e4b584}}@media (prefers-reduced-motion:reduce){html.scroll-smooth{scroll-behavior:auto}}@media print{[data-toc-mobile]{display:none!important}}.explainer-references ol{margin-bottom:2rem!important;margin-left:1.5rem!important;padding-left:.5rem!important;list-style-type:decimal!important;list-style-position:outside!important}.explainer-references li{margin-bottom:.75rem!important;padding-left:.5rem!important;display:list-item!important}.explainer-references a{word-break:break-word;overflow-wrap:anywhere}.explainer-references :not(pre)>code{color:inherit;background:#f5f5f4;border-radius:.2rem;padding:.15em .35em;font-family:ui-monospace,SFMono-Regular,Menlo,monospace;font-size:.9em}@media (prefers-color-scheme:dark){.explainer-references :not(pre)>code{background:#1c1917}}.explainer-content astro-island{max-width:100%;display:block}.explainer-content{font-family:var(--font-serif);color:#44403c;word-wrap:break-word;overflow-wrap:break-word;font-size:1.125rem;line-height:1.8}.explainer-content>h2,.explainer-content>h3,.explainer-content>h4{color:#1c1917;font-family:var(--font-serif);letter-spacing:-.02em;text-align:left;text-wrap:balance;scroll-margin-top:6rem;font-weight:600}.explainer-content>h2{letter-spacing:-.02em;align-items:center;gap:1rem;margin:4.75rem 0 1.25rem;font-size:1.5rem;display:flex}.explainer-content>h2:first-child{margin-top:0}.explainer-content>h2:after{content:"";background:#e7e5e4;flex:1 0 1.5rem;height:1px}.explainer-content>h3{letter-spacing:-.01em;margin:2.5rem 0 .75rem;font-size:1.5rem}.explainer-content>h4{margin:2rem 0 .75rem;font-size:1.25rem}.explainer-content>p{margin:0 0 1.15rem}.explainer-content>:not(h2):not(h3):not(h4):not(h5):not(h6):not(p):not(ul):not(ol):not(blockquote):not(pre):not(table):not(hr):not(section):not(script):not(.term){margin-top:2.5rem;margin-bottom:3rem}.explainer-content a{color:#8b6e4e;text-underline-offset:.15em}.explainer-content>ul,.explainer-content>ol,.explainer-content .footnotes ol{margin-bottom:1.5rem;margin-left:1.5rem;padding-left:.5rem}.explainer-content>ul{list-style-type:disc;list-style-position:outside}.explainer-content>ol,.explainer-content .footnotes ol{list-style-type:decimal;list-style-position:outside}.explainer-content li{margin-bottom:.75rem;padding-left:.5rem;display:list-item}.explainer-content>blockquote{color:#57534e;border-left:3px solid #8b6e4e;margin:2rem 0;padding-left:1.5rem;font-style:italic}.explainer-content :not(pre)>code{color:inherit;background:#f5f5f4;border-radius:.2rem;padding:.15em .35em;font-family:ui-monospace,SFMono-Regular,Menlo,monospace;font-size:.9em}.explainer-content>pre{background:#f5f5f4;border:1px solid #e7e5e4;border-radius:.5rem;margin:2rem 0;padding:1.5rem;overflow-x:auto}.explainer-content>pre code{background:0 0;padding:0}.explainer-content>table{border-collapse:collapse;font-variant-numeric:lining-nums tabular-nums;width:100%;margin:2.5rem 0;font-size:1rem}.explainer-content>table thead{border-top:2px solid #292524;border-bottom:1px solid #292524}.explainer-content>table tbody{border-bottom:2px solid #292524}.explainer-content>table th,.explainer-content>table td{text-align:left;padding:.75rem 1rem}.explainer-content>table th{font-family:var(--font-sans);letter-spacing:.02em;font-size:.95rem;font-weight:600}.explainer-content>table tbody tr:not(:last-child) td{border-bottom:1px solid #e7e5e4}.explainer-content>hr{border:0;border-top:1px solid #e7e5e4;margin:3rem 0}.explainer-content .katex-display{text-align:center;overflow:auto hidden;margin:2rem 0!important}.explainer-content .katex{font-size:1.1em;color:inherit!important}.explainer-content .katex-display>.katex{text-align:center}.explainer-content .katex,.explainer-content .katex *{color:inherit}.explainer-content .katex-html{color:inherit!important}.explainer-content .footnotes{border-top:0;margin-top:4.5rem;padding-top:0;scroll-margin-top:6rem;font-size:1rem;line-height:1.7}.explainer-content .footnotes>h2{clip:auto;clip-path:none;white-space:normal;color:#1c1917;width:auto;height:auto;font-family:var(--font-serif);letter-spacing:-.02em;text-align:left;border:0;border-bottom:1px solid #d9d3ca;margin:0 0 1rem;padding:0 0 .5rem;font-size:1.875rem;font-weight:600;position:static;overflow:visible}.explainer-content .footnotes p{margin:0 0 .5rem}.explainer-content .footnotes li{margin-bottom:.85rem}.explainer-content sup a{color:#8b6e4e;padding:0 .15em;font-weight:600;text-decoration:none}.explainer-content sup a:hover{color:#6b5536;text-decoration:underline}.explainer-content .footnotes .data-footnote-backref{margin-left:.25rem;font-size:.85em;text-decoration:none}@media (width>=768px){.explainer-content>h2{font-size:1.875rem}}@media (width<=639px){.explainer-content>h2{border-bottom:1px solid #e7e5e4;padding-bottom:.5rem;display:block}.explainer-content>h2:after{content:none}}@media (prefers-color-scheme:dark){.explainer-content{color:#d6d3d1}.explainer-content>h2,.explainer-content>h3,.explainer-content>h4,.explainer-content .footnotes>h2{color:#f5f5f4}.explainer-content>h2:after,.explainer-content>hr{background:#292524;border-color:#292524}.explainer-content>h2{border-bottom-color:#292524}.explainer-content>blockquote{color:#a8a29e}.explainer-content :not(pre)>code,.explainer-content>pre{background:#1c1917}.explainer-content>pre{border-color:#292524}.explainer-content>table thead,.explainer-content>table tbody{border-color:#78716c}.explainer-content>table tbody tr:not(:last-child) td{border-bottom-color:#292524}.explainer-content .footnotes>h2{border-bottom-color:#2d2d2d}.explainer-content sup a{color:#d4a574}.explainer-content sup a:hover{color:#e4b584}}.term[data-astro-cid-vn3nktsu]{display:inline}.term-trigger[data-astro-cid-vn3nktsu]{color:inherit;font:inherit;letter-spacing:inherit;line-height:inherit;text-align:inherit;vertical-align:baseline;cursor:help;text-underline-offset:.18em;background:0 0;border:0;margin:0;padding:0;text-decoration:underline 1px dotted #8b6e4e;display:inline}.term-trigger[data-astro-cid-vn3nktsu]:focus{outline:none}.term-trigger[data-astro-cid-vn3nktsu]:focus-visible{outline-offset:3px;outline:1px solid #8b6e4e}.term-panel[data-astro-cid-vn3nktsu]{z-index:30;box-sizing:border-box;color:#44403c;max-height:min(16rem,40vh);font-family:var(--font-serif);letter-spacing:0;text-align:left;text-wrap:pretty;background:#fffdf8;border:1px solid #e7e5e4;margin:0;padding:.65rem .8rem;font-size:.95rem;font-weight:400;line-height:1.45;text-decoration:none;display:block;position:fixed;overflow-y:auto;box-shadow:0 10px 28px #1c191714}.term-panel[data-astro-cid-vn3nktsu][hidden]{display:none}@media (prefers-color-scheme:dark){.term-trigger[data-astro-cid-vn3nktsu]{text-decoration-color:#c4a882}.term-trigger[data-astro-cid-vn3nktsu]:focus-visible{outline-color:#c4a882}.term-panel[data-astro-cid-vn3nktsu]{color:#d6d3d1;background:#1c1917;border-color:#44403c;box-shadow:0 10px 28px #0006}}@media print{.term-trigger[data-astro-cid-vn3nktsu]{cursor:auto;text-decoration:none}.term-panel[data-astro-cid-vn3nktsu]{display:none!important}}.word-analogy[data-astro-cid-k34medrw]{--analogy-accent:#a34b28;color:#292524;margin:1.5rem 0 2rem}svg[data-astro-cid-k34medrw]{width:100%;max-width:40rem;height:auto;margin:0 auto;display:block}.grid[data-astro-cid-k34medrw]{opacity:.07}.axes[data-astro-cid-k34medrw]{opacity:.45}.axis-labels[data-astro-cid-k34medrw]{font-family:var(--font-sans,sans-serif);opacity:.6;font-size:15px}.parallelogram[data-astro-cid-k34medrw]{fill:var(--analogy-accent);fill-opacity:.045;stroke:currentColor;stroke-opacity:.2;stroke-dasharray:4 6}.vectors[data-astro-cid-k34medrw]{opacity:.35}.offsets[data-astro-cid-k34medrw]{stroke:var(--analogy-accent)}.word[data-astro-cid-k34medrw]{font-family:var(--font-serif,serif);font-size:25px}.offset-labels[data-astro-cid-k34medrw]{font-family:var(--font-sans,sans-serif);font-size:17px}.equation[data-astro-cid-k34medrw]{text-align:center;font-family:var(--font-serif,serif);border-block:1px solid #a8a29e55;margin:0;padding:1rem 0;font-size:clamp(1.05rem,3.5vw,1.5rem)}.equation[data-astro-cid-k34medrw] span[data-astro-cid-k34medrw]{color:var(--analogy-accent);padding-inline:.15em}figcaption[data-astro-cid-k34medrw]{color:#57534e;margin-top:.85rem;font-size:.875rem;line-height:1.6}@media (prefers-color-scheme:dark){.word-analogy[data-astro-cid-k34medrw]{--analogy-accent:#e6a17c;color:#e7e5e4}figcaption[data-astro-cid-k34medrw]{color:#a8a29e}}.outline-figure[data-astro-cid-57ybwles]{--diagram-paper:#fafaf7;--diagram-ink:#292524;--diagram-muted:#66605a;--diagram-rule:#d9d3ca;--diagram-accent:#8b6e4e;color:var(--diagram-ink);margin:0}@media (prefers-color-scheme:dark){.outline-figure[data-astro-cid-57ybwles]{--diagram-paper:#0e0e0e;--diagram-ink:#e7e5e4;--diagram-muted:#aaa29a;--diagram-rule:#49423c;--diagram-accent:#c4a882}}.figure-header[data-astro-cid-57ybwles]{border-top:2px solid var(--diagram-ink);padding:1rem 0 1.25rem}.eyebrow[data-astro-cid-57ybwles],.figure-meta[data-astro-cid-57ybwles]{font-family:var(--font-sans)}.eyebrow[data-astro-cid-57ybwles]{color:var(--diagram-accent);letter-spacing:.15em;text-transform:uppercase;margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-57ybwles]{font-family:var(--font-serif);margin:0;font-size:clamp(1.25rem,3vw,1.65rem);line-height:1.4}.figure-meta[data-astro-cid-57ybwles]{color:var(--diagram-muted);margin:.5rem 0 0;font-size:.75rem}.outline-horizontal[data-astro-cid-57ybwles],.outline-vertical[data-astro-cid-57ybwles]{height:auto}.outline-vertical[data-astro-cid-57ybwles]{width:100%;max-width:22rem;margin-inline:auto;display:block}.outline-horizontal[data-astro-cid-57ybwles]{width:100%;display:none}@media (width>=64rem){.outline-vertical[data-astro-cid-57ybwles]{display:none}.outline-horizontal[data-astro-cid-57ybwles]{display:block}}@media print{.outline-vertical[data-astro-cid-57ybwles]{display:none!important}.outline-horizontal[data-astro-cid-57ybwles]{max-width:none;display:block!important}}.outline-figure[data-astro-cid-57ybwles] text[data-astro-cid-57ybwles]{fill:var(--diagram-ink)}.block-name[data-astro-cid-57ybwles],.io[data-astro-cid-57ybwles],.dimension[data-astro-cid-57ybwles],.junction[data-astro-cid-57ybwles]{font-family:var(--font-sans)}.block-name[data-astro-cid-57ybwles]{letter-spacing:.14em;text-transform:uppercase;font-size:12px}.io[data-astro-cid-57ybwles]{letter-spacing:.14em;text-transform:uppercase;fill:var(--diagram-muted);font-size:10px}.dimension[data-astro-cid-57ybwles]{fill:var(--diagram-muted);font-variant-numeric:tabular-nums;font-size:12px}.stream-name[data-astro-cid-57ybwles],.equation[data-astro-cid-57ybwles]{font-family:var(--font-serif);fill:var(--diagram-accent);font-size:16px}.junction[data-astro-cid-57ybwles]{fill:var(--diagram-accent);font-size:11px}.wire[data-astro-cid-57ybwles]{fill:none;stroke:var(--diagram-ink);stroke-width:1.2px;stroke-linejoin:round}.arrow-head[data-astro-cid-57ybwles]{fill:none;stroke:var(--diagram-ink);stroke-width:1.3px}.stream-line[data-astro-cid-57ybwles],.update[data-astro-cid-57ybwles],.plus[data-astro-cid-57ybwles]{fill:none;stroke:var(--diagram-accent);stroke-width:1.8px}.stream-arrow-head[data-astro-cid-57ybwles]{fill:none;stroke:var(--diagram-accent);stroke-width:1.3px}.stream-dot[data-astro-cid-57ybwles]{fill:var(--diagram-accent)}.tick[data-astro-cid-57ybwles]{fill:none;stroke:var(--diagram-muted);stroke-width:1px}.operation[data-astro-cid-57ybwles]{fill:var(--diagram-paper);stroke:var(--diagram-ink);stroke-width:1px}.add-node[data-astro-cid-57ybwles]{fill:var(--diagram-paper);stroke:var(--diagram-accent);stroke-width:1.8px}figcaption[data-astro-cid-57ybwles]{font-family:var(--font-serif);color:var(--diagram-muted);margin-top:1rem;font-size:.8rem;line-height:1.75}.transformer-figure[data-astro-cid-4p5w4esf]{--diagram-paper:#fafaf7;--diagram-ink:#292524;--diagram-muted:#66605a;--diagram-rule:#d9d3ca;--diagram-accent:#8b6e4e;color:var(--diagram-ink);margin:0}@media (prefers-color-scheme:dark){.transformer-figure[data-astro-cid-4p5w4esf]{--diagram-paper:#0e0e0e;--diagram-ink:#e7e5e4;--diagram-muted:#aaa29a;--diagram-rule:#49423c;--diagram-accent:#c4a882}}.figure-header[data-astro-cid-4p5w4esf]{border-top:2px solid var(--diagram-ink);padding:1rem 0 1.25rem}.eyebrow[data-astro-cid-4p5w4esf],.figure-meta[data-astro-cid-4p5w4esf],.scroll-hint[data-astro-cid-4p5w4esf],.notation-label[data-astro-cid-4p5w4esf]{font-family:var(--font-sans)}.eyebrow[data-astro-cid-4p5w4esf]{color:var(--diagram-accent);letter-spacing:.15em;text-transform:uppercase;margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-4p5w4esf]{font-family:var(--font-serif);margin:0;font-size:clamp(1.25rem,3vw,1.65rem);line-height:1.4}.figure-meta[data-astro-cid-4p5w4esf]{color:var(--diagram-muted);margin:.5rem 0 0;font-size:.75rem}.diagram-scroll[data-astro-cid-4p5w4esf]{overscroll-behavior-x:contain;overflow-x:auto}.diagram-scroll[data-astro-cid-4p5w4esf]:focus-visible{outline:2px solid var(--diagram-accent);outline-offset:4px}.block-diagram[data-astro-cid-4p5w4esf]{width:100%;min-width:640px;height:auto;display:block}.block-diagram[data-astro-cid-4p5w4esf] text[data-astro-cid-4p5w4esf]{fill:var(--diagram-ink)}.math[data-astro-cid-4p5w4esf]{font-family:var(--font-serif);font-size:19px}.note[data-astro-cid-4p5w4esf],.dimension[data-astro-cid-4p5w4esf],.small-label[data-astro-cid-4p5w4esf],.section-label[data-astro-cid-4p5w4esf],.stream-label[data-astro-cid-4p5w4esf]{font-family:var(--font-sans)}.note[data-astro-cid-4p5w4esf]{font-size:12px}.block-diagram[data-astro-cid-4p5w4esf] .dimension[data-astro-cid-4p5w4esf]{fill:var(--diagram-muted);font-variant-numeric:tabular-nums;font-size:12px}.small-label[data-astro-cid-4p5w4esf]{letter-spacing:1.2px;text-transform:uppercase;font-size:11px}.block-diagram[data-astro-cid-4p5w4esf] .section-label[data-astro-cid-4p5w4esf]{letter-spacing:1.5px;fill:var(--diagram-muted);font-size:10px}.block-diagram[data-astro-cid-4p5w4esf] .stream-label[data-astro-cid-4p5w4esf]{letter-spacing:1.3px;fill:var(--diagram-accent);font-size:11px}.wire[data-astro-cid-4p5w4esf]{fill:none;stroke:var(--diagram-ink);stroke-width:1.2px;stroke-linejoin:round}.arrow-head[data-astro-cid-4p5w4esf]{fill:none;stroke:var(--diagram-ink);stroke-width:1.3px}.stream-line[data-astro-cid-4p5w4esf],.update[data-astro-cid-4p5w4esf],.plus[data-astro-cid-4p5w4esf]{fill:none;stroke:var(--diagram-accent);stroke-width:1.8px}.stream-arrow-head[data-astro-cid-4p5w4esf]{fill:none;stroke:var(--diagram-accent);stroke-width:1.3px}.stream-dot[data-astro-cid-4p5w4esf],.block-diagram[data-astro-cid-4p5w4esf] .stream-text[data-astro-cid-4p5w4esf]{fill:var(--diagram-accent)}.operation[data-astro-cid-4p5w4esf]{fill:var(--diagram-paper);stroke:var(--diagram-ink);stroke-width:1px}.head-layer[data-astro-cid-4p5w4esf]{fill:var(--diagram-paper);stroke:var(--diagram-muted);stroke-width:1px}.group[data-astro-cid-4p5w4esf]{fill:none;stroke:var(--diagram-rule);stroke-width:1px}.paper[data-astro-cid-4p5w4esf]{fill:var(--diagram-paper)}.unboxed[data-astro-cid-4p5w4esf]{stroke:none}.add-node[data-astro-cid-4p5w4esf]{fill:var(--diagram-paper);stroke:var(--diagram-accent);stroke-width:1.8px}.notation[data-astro-cid-4p5w4esf]{border-top:1px solid var(--diagram-rule);border-bottom:1px solid var(--diagram-rule);grid-template-columns:repeat(3,minmax(0,1fr));gap:1.5rem;padding:1.25rem 0;display:grid}.notation[data-astro-cid-4p5w4esf] p[data-astro-cid-4p5w4esf]{margin:0}.notation[data-astro-cid-4p5w4esf] .head-explanation[data-astro-cid-4p5w4esf]{margin-top:.75rem}.weight-dimensions[data-astro-cid-4p5w4esf] dl[data-astro-cid-4p5w4esf]{font-family:var(--font-serif);margin:.75rem 0 0;font-size:.8rem;line-height:1.8}.weight-dimensions[data-astro-cid-4p5w4esf] dl[data-astro-cid-4p5w4esf]>div[data-astro-cid-4p5w4esf]{flex-wrap:wrap;justify-content:space-between;gap:0 .75rem;padding:.2rem 0;display:flex}.weight-dimensions[data-astro-cid-4p5w4esf] dt[data-astro-cid-4p5w4esf],.weight-dimensions[data-astro-cid-4p5w4esf] dd[data-astro-cid-4p5w4esf]{white-space:nowrap;margin:0}.weight-dimensions[data-astro-cid-4p5w4esf] dd[data-astro-cid-4p5w4esf]{color:var(--diagram-muted);font-variant-numeric:tabular-nums}.notation-label[data-astro-cid-4p5w4esf]{text-transform:uppercase;letter-spacing:.12em;color:var(--diagram-accent);margin-bottom:.55rem;font-size:.6rem;display:block}.norm-equation[data-astro-cid-4p5w4esf]{font-family:var(--font-serif);margin-bottom:.4rem;font-size:.85rem;line-height:1.8;display:block}.notation-detail[data-astro-cid-4p5w4esf],figcaption[data-astro-cid-4p5w4esf]{font-family:var(--font-serif);color:var(--diagram-muted);font-size:.8rem;line-height:1.75}figcaption[data-astro-cid-4p5w4esf]{margin-top:1rem}.scroll-hint[data-astro-cid-4p5w4esf]{color:var(--diagram-muted);margin:0 0 .75rem;font-size:.7rem;display:none}@media (width<=900px){.notation[data-astro-cid-4p5w4esf]{grid-template-columns:1fr;gap:1.5rem}.weight-dimensions[data-astro-cid-4p5w4esf] dl[data-astro-cid-4p5w4esf]{max-width:20rem}}@media (width<=700px){.scroll-hint[data-astro-cid-4p5w4esf]{display:block}}@media print{.block-diagram[data-astro-cid-4p5w4esf]{min-width:0}.scroll-hint[data-astro-cid-4p5w4esf]{display:none}.diagram-scroll[data-astro-cid-4p5w4esf]{overflow:visible}}.sampling-figure[data-astro-cid-aiyophsd]{--paper:#fafaf7;--ink:#292524;--muted:#66605a;--rule:#d9d3ca;--accent:#8b6e4e;color:var(--ink);display:block}@media (prefers-color-scheme:dark){.sampling-figure[data-astro-cid-aiyophsd]{--paper:#0e0e0e;--ink:#e7e5e4;--muted:#aaa29a;--rule:#49423c;--accent:#c4a882}}figure[data-astro-cid-aiyophsd]{margin:0}.figure-header[data-astro-cid-aiyophsd]{border-top:2px solid var(--ink);padding:1rem 0}.eyebrow[data-astro-cid-aiyophsd]{color:var(--accent);font:.6rem var(--font-sans);letter-spacing:.12em;text-transform:uppercase;margin:0 0 .5rem}.figure-title[data-astro-cid-aiyophsd]{font:clamp(1.25rem, 3vw, 1.65rem)/1.4 var(--font-serif);margin:0}.figure-meta[data-astro-cid-aiyophsd]{font:.75rem/1.6 var(--font-sans);color:var(--muted);margin:.5rem 0 0}.input-flow[data-astro-cid-aiyophsd]{border:1px solid var(--rule);font:.75rem/1.5 var(--font-serif);flex-wrap:wrap;justify-content:center;align-items:center;gap:.75rem;padding:.9rem;display:flex}.input-flow[data-astro-cid-aiyophsd] strong[data-astro-cid-aiyophsd]{border:1px solid var(--ink);padding:.4rem .65rem;font-weight:500}.controls[data-astro-cid-aiyophsd]{font:.75rem/1.5 var(--font-sans);grid-template-columns:repeat(3,1fr);gap:1.5rem;padding:1.2rem 0;display:grid}label[data-astro-cid-aiyophsd]{grid-template-columns:1fr auto;gap:.35rem;display:grid}label[data-astro-cid-aiyophsd] input[data-astro-cid-aiyophsd],label[data-astro-cid-aiyophsd]>span[data-astro-cid-aiyophsd]{grid-column:1/-1}input[data-astro-cid-aiyophsd]{width:100%;accent-color:var(--accent);cursor:pointer;margin:.3rem 0}output[data-astro-cid-aiyophsd]{font-variant-numeric:tabular-nums;color:var(--accent)}label[data-astro-cid-aiyophsd]>span[data-astro-cid-aiyophsd]{color:var(--muted);font-size:.65rem}.pipeline[data-astro-cid-aiyophsd]{border-block:1px solid var(--rule);grid-template-columns:1.2fr 1fr .85fr 1fr;gap:1rem;padding:1rem 0;display:grid}section[data-astro-cid-aiyophsd]{min-width:0}.stage[data-astro-cid-aiyophsd]{flex-direction:column;gap:.35rem;min-height:5.5rem;display:flex}.stage[data-astro-cid-aiyophsd] .eyebrow[data-astro-cid-aiyophsd]{margin:0}.stage[data-astro-cid-aiyophsd] strong[data-astro-cid-aiyophsd]{font:.8rem/1.3 var(--font-serif)}small[data-astro-cid-aiyophsd],.stage-note[data-astro-cid-aiyophsd]{font:.6rem/1.5 var(--font-sans);color:var(--muted)}.column-head[data-astro-cid-aiyophsd]{height:1.6rem;font:.55rem var(--font-sans);text-transform:uppercase;color:var(--muted);justify-content:space-between;display:flex}.logit-row[data-astro-cid-aiyophsd],.prob-row[data-astro-cid-aiyophsd]{height:1.65rem;font:.65rem var(--font-sans);font-variant-numeric:tabular-nums;justify-content:space-between;align-items:center;gap:.4rem;display:flex}.token[data-astro-cid-aiyophsd]{font-family:var(--font-serif);white-space:nowrap}.token[data-astro-cid-aiyophsd] small[data-astro-cid-aiyophsd]{margin-left:.15rem;font-size:.5rem}.prob-row[data-astro-cid-aiyophsd]>[data-astro-cid-aiyophsd][data-prob]{text-align:right;flex-shrink:0;width:3.2rem}.track[data-astro-cid-aiyophsd]{background:var(--rule);flex:1;height:.45rem;display:block}.bar[data-astro-cid-aiyophsd]{background:var(--ink);height:100%;display:block}.picked[data-astro-cid-aiyophsd]{color:var(--accent);font-weight:600}.picked[data-astro-cid-aiyophsd] .bar[data-astro-cid-aiyophsd]{background:var(--accent)}.discarded[data-astro-cid-aiyophsd]{opacity:.3}.mobile-token[data-astro-cid-aiyophsd]{display:none}.filter-box[data-astro-cid-aiyophsd]{border:1px solid var(--rule);text-align:center;margin-bottom:.6rem;padding:.6rem .4rem}.filter-box[data-astro-cid-aiyophsd]>span[data-astro-cid-aiyophsd],.filter-box[data-astro-cid-aiyophsd] strong[data-astro-cid-aiyophsd]{font:.85rem var(--font-serif);display:block}.filter-box[data-astro-cid-aiyophsd] p[data-astro-cid-aiyophsd]{font:.65rem/1.6 var(--font-sans);margin:.4rem 0}.stage-note[data-astro-cid-aiyophsd]{margin:.7rem 0 0}.draw-panel[data-astro-cid-aiyophsd]{padding:1.2rem 0}.draw-heading[data-astro-cid-aiyophsd]{flex-wrap:wrap;align-items:center;gap:.5rem 1rem;margin-bottom:1rem;display:flex}button[data-astro-cid-aiyophsd]{cursor:pointer;border:1px solid var(--ink);background:var(--ink);color:var(--paper);font:.75rem var(--font-sans);padding:.65rem 1rem}button[data-astro-cid-aiyophsd]:focus-visible,input[data-astro-cid-aiyophsd]:focus-visible{outline:2px solid var(--accent);outline-offset:4px}.draw-heading[data-astro-cid-aiyophsd] p[data-astro-cid-aiyophsd]{font:.8rem/1.5 var(--font-serif);margin:0}.unit-strip[data-astro-cid-aiyophsd]{border:1px solid var(--ink);height:1.7rem;display:flex;position:relative}[data-astro-cid-aiyophsd][data-segment]{background:var(--ink);opacity:.65;box-shadow:inset -1px 0 var(--paper)}[data-astro-cid-aiyophsd][data-segment]:nth-child(2n){opacity:.35}[data-astro-cid-aiyophsd][data-segment].picked{background:var(--accent);opacity:1}.draw-marker[data-astro-cid-aiyophsd]{background:var(--accent);pointer-events:none;width:2px;position:absolute;top:-.3rem;bottom:-.3rem;transform:translate(-1px)}.interval-labels[data-astro-cid-aiyophsd]{font:.6rem/1.5 var(--font-sans);color:var(--muted);justify-content:space-between;gap:.4rem;margin-top:.5rem;display:flex}.completion[data-astro-cid-aiyophsd]{font:1rem/1.8 var(--font-serif);margin:1rem 0 .5rem}mark[data-astro-cid-aiyophsd]{color:var(--accent);white-space:pre-wrap;background:0 0;font-weight:600}.history[data-astro-cid-aiyophsd]{font:.7rem/1.7 var(--font-sans);color:var(--muted);margin:.5rem 0}.reset[data-astro-cid-aiyophsd]{color:var(--muted);background:0 0;border:0;padding:.2rem 0;font-size:.65rem;text-decoration:underline}figcaption[data-astro-cid-aiyophsd]{border-top:1px solid var(--rule);font:.8rem/1.7 var(--font-serif);color:var(--muted);padding-top:1rem}figcaption[data-astro-cid-aiyophsd] a[data-astro-cid-aiyophsd]{text-decoration:underline}@media (width<=700px){.pipeline[data-astro-cid-aiyophsd]{grid-template-columns:1fr 1fr;gap:1.3rem}.filters[data-astro-cid-aiyophsd]{grid-column:1/-1;grid-template-columns:1fr 1fr;gap:.7rem;display:grid}.filters[data-astro-cid-aiyophsd] .stage[data-astro-cid-aiyophsd],.filters[data-astro-cid-aiyophsd] .stage-note[data-astro-cid-aiyophsd]{grid-column:1/-1;min-height:auto}.filters[data-astro-cid-aiyophsd] .filter-box[data-astro-cid-aiyophsd]{margin:0}.pipeline[data-astro-cid-aiyophsd]>section[data-astro-cid-aiyophsd]:last-child{grid-column:1/-1}section[data-astro-cid-aiyophsd]:last-child .mobile-token[data-astro-cid-aiyophsd]{min-width:5rem;display:block}.stage[data-astro-cid-aiyophsd]{min-height:5rem}.controls[data-astro-cid-aiyophsd]{gap:.8rem}.logit-row[data-astro-cid-aiyophsd],.prob-row[data-astro-cid-aiyophsd]{font-size:.7rem}.token[data-astro-cid-aiyophsd] small[data-astro-cid-aiyophsd]{display:none}.interval-labels[data-astro-cid-aiyophsd]{font-size:.55rem}}@media (width<=400px){.controls[data-astro-cid-aiyophsd]{grid-template-columns:1fr}}softmax-demo[data-astro-cid-qw3k62zn]{display:block}.temperature-control[data-astro-cid-qw3k62zn]{border-top:1px solid var(--diagram-rule);font-family:var(--font-sans);gap:.6rem;padding:1rem 0;font-size:.8rem;display:grid}.temperature-label[data-astro-cid-qw3k62zn]{justify-content:space-between;display:flex}.temperature-label[data-astro-cid-qw3k62zn] output[data-astro-cid-qw3k62zn]{font-variant-numeric:tabular-nums;font-weight:600}.temperature-control[data-astro-cid-qw3k62zn] input[data-astro-cid-qw3k62zn]{width:100%;accent-color:var(--diagram-accent);margin:0}.temperature-control[data-astro-cid-qw3k62zn] input[data-astro-cid-qw3k62zn]:focus-visible{outline:2px solid var(--diagram-accent);outline-offset:4px}.temperature-range[data-astro-cid-qw3k62zn]{color:var(--diagram-muted);justify-content:space-between;gap:1rem;font-size:.7rem;display:flex}.temperature-note[data-astro-cid-qw3k62zn]{font-family:var(--font-sans);color:var(--diagram-muted);margin:0 0 1rem;font-size:.75rem}.softmax-figure[data-astro-cid-qw3k62zn]{--diagram-paper:#fafaf7;--diagram-ink:#292524;--diagram-muted:#66605a;--diagram-rule:#d9d3ca;--diagram-accent:#8b6e4e;--seg-0:#292524;--seg-1:#8b6e4e;--seg-2:#c4a882;--seg-3:#d2c3b2;color:var(--diagram-ink);margin:0}@media (prefers-color-scheme:dark){.softmax-figure[data-astro-cid-qw3k62zn]{--diagram-paper:#0e0e0e;--diagram-ink:#e7e5e4;--diagram-muted:#aaa29a;--diagram-rule:#49423c;--diagram-accent:#c4a882;--seg-0:#f5f5f4;--seg-1:#e0c4a0;--seg-2:#a68462;--seg-3:#6e5c4c}}.figure-header[data-astro-cid-qw3k62zn]{border-top:2px solid var(--diagram-ink);padding:1rem 0 1.25rem}.eyebrow[data-astro-cid-qw3k62zn],.figure-meta[data-astro-cid-qw3k62zn]{font-family:var(--font-sans)}.eyebrow[data-astro-cid-qw3k62zn]{color:var(--diagram-accent);letter-spacing:.15em;text-transform:uppercase;margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-qw3k62zn]{font-family:var(--font-serif);margin:0;font-size:clamp(1.25rem,3vw,1.65rem);line-height:1.4}.figure-meta[data-astro-cid-qw3k62zn]{color:var(--diagram-muted);margin:.5rem 0 0;font-size:.75rem}.wide-diagram[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn]{width:100%;height:auto;display:block}.stack-diagram[data-astro-cid-qw3k62zn]{max-width:26rem;display:none}.wide-diagram[data-astro-cid-qw3k62zn] text[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] text[data-astro-cid-qw3k62zn]{fill:var(--diagram-ink)}.header[data-astro-cid-qw3k62zn],.sub[data-astro-cid-qw3k62zn],.footnote[data-astro-cid-qw3k62zn],.num[data-astro-cid-qw3k62zn]{font-family:var(--font-sans);font-variant-numeric:tabular-nums}.wide-diagram[data-astro-cid-qw3k62zn] .header[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] .header[data-astro-cid-qw3k62zn],.wide-diagram[data-astro-cid-qw3k62zn] .sub[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] .sub[data-astro-cid-qw3k62zn]{letter-spacing:1.4px;text-transform:uppercase;fill:var(--diagram-muted);font-size:11px}.wide-diagram[data-astro-cid-qw3k62zn] .sub[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] .sub[data-astro-cid-qw3k62zn]{letter-spacing:.08em}.wide-diagram[data-astro-cid-qw3k62zn] .footnote[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] .footnote[data-astro-cid-qw3k62zn]{fill:var(--diagram-muted);font-size:12px}.piece[data-astro-cid-qw3k62zn],.expr[data-astro-cid-qw3k62zn],.op[data-astro-cid-qw3k62zn],.conclusion[data-astro-cid-qw3k62zn]{font-family:var(--font-serif)}.piece[data-astro-cid-qw3k62zn]{font-size:15px}.label[data-astro-cid-qw3k62zn]{font-size:13px}.expr[data-astro-cid-qw3k62zn]{font-size:15px}.num[data-astro-cid-qw3k62zn]{font-size:14px}.wide-diagram[data-astro-cid-qw3k62zn] .op[data-astro-cid-qw3k62zn],.stack-diagram[data-astro-cid-qw3k62zn] .op[data-astro-cid-qw3k62zn]{fill:var(--diagram-muted);font-size:15px;font-style:italic}.sup[data-astro-cid-qw3k62zn]{font-size:10px;font-style:italic}.conclusion[data-astro-cid-qw3k62zn]{font-size:14px;font-style:italic}.mass[data-astro-cid-qw3k62zn]{fill:var(--diagram-ink)}.mass[data-astro-cid-qw3k62zn].negative{fill:var(--diagram-accent)}.share-0[data-astro-cid-qw3k62zn]{fill:var(--seg-0)}.share-1[data-astro-cid-qw3k62zn]{fill:var(--seg-1)}.share-2[data-astro-cid-qw3k62zn]{fill:var(--seg-2)}.share-3[data-astro-cid-qw3k62zn]{fill:var(--seg-3)}.origin[data-astro-cid-qw3k62zn]{fill:var(--diagram-ink)}.axis[data-astro-cid-qw3k62zn],.wire[data-astro-cid-qw3k62zn]{fill:none;stroke:var(--diagram-ink);stroke-width:1.25px;stroke-linecap:round;stroke-linejoin:round}.axis[data-astro-cid-qw3k62zn]{stroke:var(--diagram-rule);stroke-width:1px}.plate[data-astro-cid-qw3k62zn]{fill:var(--diagram-paper);stroke:var(--diagram-ink);stroke-width:1px}figcaption[data-astro-cid-qw3k62zn]{width:100%;font-family:var(--font-serif);color:var(--diagram-muted);margin-top:1rem;font-size:.875rem;line-height:1.7}figcaption[data-astro-cid-qw3k62zn] em[data-astro-cid-qw3k62zn]{font-style:italic}@media (width<=640px){.wide-diagram[data-astro-cid-qw3k62zn]{display:none}.stack-diagram[data-astro-cid-qw3k62zn]{display:block}}.unembedding-figure[data-astro-cid-67yl7ync]{--diagram-paper:#fafaf7;--diagram-ink:#292524;--diagram-muted:#66605a;--diagram-rule:#d9d3ca;--diagram-accent:#8b6e4e;color:var(--diagram-ink);margin:0}@media (prefers-color-scheme:dark){.unembedding-figure[data-astro-cid-67yl7ync]{--diagram-paper:#0e0e0e;--diagram-ink:#e7e5e4;--diagram-muted:#aaa29a;--diagram-rule:#49423c;--diagram-accent:#c4a882}}.figure-header[data-astro-cid-67yl7ync]{border-top:2px solid var(--diagram-ink);padding:1rem 0 1.25rem}.eyebrow[data-astro-cid-67yl7ync],.figure-meta[data-astro-cid-67yl7ync],.notation-label[data-astro-cid-67yl7ync],.kicker[data-astro-cid-67yl7ync],.dimension[data-astro-cid-67yl7ync],.note[data-astro-cid-67yl7ync],.label[data-astro-cid-67yl7ync],.vmark[data-astro-cid-67yl7ync]{font-family:var(--font-sans)}.eyebrow[data-astro-cid-67yl7ync]{color:var(--diagram-accent);letter-spacing:.15em;text-transform:uppercase;margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-67yl7ync]{font-family:var(--font-serif);margin:0;font-size:clamp(1.25rem,3vw,1.65rem);line-height:1.4}.figure-meta[data-astro-cid-67yl7ync]{color:var(--diagram-muted);margin:.5rem 0 0;font-size:.75rem}.wide-diagram[data-astro-cid-67yl7ync],.stack-diagram[data-astro-cid-67yl7ync]{width:100%;height:auto;display:block}.stack-diagram[data-astro-cid-67yl7ync]{max-width:26rem;display:none}.wide-diagram[data-astro-cid-67yl7ync] text[data-astro-cid-67yl7ync],.stack-diagram[data-astro-cid-67yl7ync] text[data-astro-cid-67yl7ync]{fill:var(--diagram-ink)}.math[data-astro-cid-67yl7ync],.token[data-astro-cid-67yl7ync],.norm-equation[data-astro-cid-67yl7ync],figcaption[data-astro-cid-67yl7ync],.notation-detail[data-astro-cid-67yl7ync]{font-family:var(--font-serif)}.math[data-astro-cid-67yl7ync],.name[data-astro-cid-67yl7ync]{font-size:18px}.dim-num[data-astro-cid-67yl7ync]{font-size:20px}.token[data-astro-cid-67yl7ync]{font-size:13px}.kicker[data-astro-cid-67yl7ync]{letter-spacing:1.4px;text-transform:uppercase;fill:var(--diagram-muted);font-size:10px}.dimension[data-astro-cid-67yl7ync]{fill:var(--diagram-muted);font-variant-numeric:tabular-nums;font-size:12px}.note[data-astro-cid-67yl7ync]{fill:var(--diagram-muted);font-size:12px}.label[data-astro-cid-67yl7ync]{font-size:12px}.vmark[data-astro-cid-67yl7ync]{font-variant-numeric:tabular-nums;font-size:12px}.ellipsis[data-astro-cid-67yl7ync]{font-family:var(--font-serif);fill:var(--diagram-muted);font-size:16px}.hot[data-astro-cid-67yl7ync]{fill:var(--diagram-accent)}.frame[data-astro-cid-67yl7ync],.strip[data-astro-cid-67yl7ync]{fill:var(--diagram-paper);stroke:var(--diagram-ink);stroke-width:1px}.edge[data-astro-cid-67yl7ync]{fill:none;stroke:var(--diagram-ink);stroke-width:1px}.grid[data-astro-cid-67yl7ync]{fill:none;stroke:var(--diagram-rule);stroke-width:1px}.tick[data-astro-cid-67yl7ync]{fill:none;stroke:var(--diagram-accent);stroke-width:1.2px}.wire[data-astro-cid-67yl7ync]{fill:none;stroke:var(--diagram-ink);stroke-width:1.2px;stroke-linejoin:round;stroke-linecap:round}.arrow-head[data-astro-cid-67yl7ync]{fill:none;stroke:var(--diagram-ink);stroke-width:1.3px}.row-hot[data-astro-cid-67yl7ync]{fill:var(--diagram-accent);fill-opacity:.32;stroke:var(--diagram-accent);stroke-width:1.4px}.column[data-astro-cid-67yl7ync]{fill:var(--diagram-accent);fill-opacity:.5;stroke:var(--diagram-accent);stroke-width:1.5px}.cell[data-astro-cid-67yl7ync]{fill:var(--diagram-accent);stroke:none}.readout[data-astro-cid-67yl7ync]{fill:var(--diagram-paper);stroke:var(--diagram-accent);stroke-width:1.6px}.notation[data-astro-cid-67yl7ync]{border-top:1px solid var(--diagram-rule);border-bottom:1px solid var(--diagram-rule);grid-template-columns:minmax(0,1.15fr) minmax(0,.9fr) minmax(0,.95fr);gap:1.5rem;padding:1.25rem 0;display:grid}.notation[data-astro-cid-67yl7ync] p[data-astro-cid-67yl7ync]{margin:0}.notation-label[data-astro-cid-67yl7ync]{text-transform:uppercase;letter-spacing:.12em;color:var(--diagram-accent);margin-bottom:.55rem;font-size:.6rem;display:block}.norm-equation[data-astro-cid-67yl7ync]{margin-bottom:.4rem;font-size:.85rem;line-height:1.8;display:block}.notation-detail[data-astro-cid-67yl7ync],figcaption[data-astro-cid-67yl7ync]{color:var(--diagram-muted);font-size:.8rem;line-height:1.75}figcaption[data-astro-cid-67yl7ync]{margin-top:1rem}.notation[data-astro-cid-67yl7ync] dl[data-astro-cid-67yl7ync]{font-family:var(--font-serif);margin:.75rem 0 0;font-size:.8rem;line-height:1.8}.notation[data-astro-cid-67yl7ync] dl[data-astro-cid-67yl7ync]>div[data-astro-cid-67yl7ync]{flex-wrap:wrap;justify-content:space-between;gap:0 .75rem;padding:.2rem 0;display:flex}.notation[data-astro-cid-67yl7ync] dt[data-astro-cid-67yl7ync],.notation[data-astro-cid-67yl7ync] dd[data-astro-cid-67yl7ync]{white-space:nowrap;margin:0}.notation[data-astro-cid-67yl7ync] dd[data-astro-cid-67yl7ync]{color:var(--diagram-muted);font-variant-numeric:tabular-nums}.notation[data-astro-cid-67yl7ync] em[data-astro-cid-67yl7ync]{font-style:italic}@media (width<=900px){.notation[data-astro-cid-67yl7ync]{grid-template-columns:1fr;gap:1.5rem}.notation[data-astro-cid-67yl7ync] dl[data-astro-cid-67yl7ync]{max-width:20rem}}@media (width<=760px){.wide-diagram[data-astro-cid-67yl7ync]{display:none}.stack-diagram[data-astro-cid-67yl7ync]{display:block}}@media print{.wide-diagram[data-astro-cid-67yl7ync]{display:block}.stack-diagram[data-astro-cid-67yl7ync]{display:none}}.rope-figure[data-astro-cid-ds6ksxjg]{--ink:#292524;--muted:#57534e;--rule:#d6d3d1;--paper:#fafaf7;--accent:#98632e;color:var(--ink);font-family:var(--font-sans);margin:2rem 0}@media (prefers-color-scheme:dark){.rope-figure[data-astro-cid-ds6ksxjg]{--ink:#e7e5e4;--muted:#a8a29e;--rule:#57534e;--paper:#1c1917;--accent:#d6ad77}}header[data-astro-cid-ds6ksxjg]{border-top:1px solid var(--rule);padding-top:1rem}.eyebrow[data-astro-cid-ds6ksxjg]{letter-spacing:.12em;text-transform:uppercase;color:var(--accent);margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-ds6ksxjg]{font-family:var(--font-serif);margin:0 0 1.25rem;font-size:1.3rem}.stages[data-astro-cid-ds6ksxjg]{border:1px solid var(--rule);background:var(--paper);grid-template-columns:repeat(3,minmax(0,1fr));display:grid}.stage[data-astro-cid-ds6ksxjg]+.stage[data-astro-cid-ds6ksxjg]{border-left:1px solid var(--rule)}.stage-label[data-astro-cid-ds6ksxjg]{border-bottom:1px solid var(--rule);letter-spacing:.06em;text-transform:uppercase;margin:0;padding:.85rem 1rem;font-size:.7rem}svg[data-astro-cid-ds6ksxjg]{width:100%;height:auto;fill:var(--ink);display:block}.math[data-astro-cid-ds6ksxjg]{font-family:var(--font-serif);font-size:20px}.dimension[data-astro-cid-ds6ksxjg]{font-size:17px}.note[data-astro-cid-ds6ksxjg],.row-label[data-astro-cid-ds6ksxjg]{fill:var(--muted);font-size:12px}.coordinate[data-astro-cid-ds6ksxjg]{fill:var(--muted);font-size:11px}.highlight[data-astro-cid-ds6ksxjg],.after-label[data-astro-cid-ds6ksxjg]{fill:var(--accent)}.matrix[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--ink)}.selected[data-astro-cid-ds6ksxjg]{fill:var(--accent);fill-opacity:.13;stroke:var(--accent)}.grid[data-astro-cid-ds6ksxjg],.axis[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--rule)}.orbit[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--rule);stroke-dasharray:3 5}.before-vector[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--muted);stroke-width:2px;stroke-dasharray:5 3}.after-vector[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--accent);stroke-width:2px}.turn[data-astro-cid-ds6ksxjg]{fill:none;stroke:var(--accent);stroke-width:1.5px}.arrow-head[data-astro-cid-ds6ksxjg]{fill:none;stroke:context-stroke;stroke-width:1.5px}.origin[data-astro-cid-ds6ksxjg]{fill:var(--ink)}.before-label[data-astro-cid-ds6ksxjg],.after-label[data-astro-cid-ds6ksxjg]{font-size:13px}figcaption[data-astro-cid-ds6ksxjg]{color:var(--muted);margin-top:.85rem;font-size:.8rem;line-height:1.75}@media (width<=800px){.stages[data-astro-cid-ds6ksxjg]{grid-template-columns:1fr}.stage[data-astro-cid-ds6ksxjg]+.stage[data-astro-cid-ds6ksxjg]{border-left:0;border-top:1px solid var(--rule)}svg[data-astro-cid-ds6ksxjg]{max-width:360px;margin-inline:auto}}rope-angle-map[data-astro-cid-mxkglkw3]{display:block}figure[data-astro-cid-mxkglkw3]{--ink:#292524;--muted:#57534e;--rule:#d6d3d1;--paper:#fafaf7;--accent:#98632e;color:var(--ink);font-family:var(--font-sans);margin:2rem 0}@media (prefers-color-scheme:dark){figure[data-astro-cid-mxkglkw3]{--ink:#e7e5e4;--muted:#a8a29e;--rule:#57534e;--paper:#1c1917;--accent:#d6ad77}}header[data-astro-cid-mxkglkw3]{border-top:1px solid var(--rule);padding-top:1rem}.eyebrow[data-astro-cid-mxkglkw3]{color:var(--accent);letter-spacing:.12em;text-transform:uppercase;margin:0 0 .5rem;font-size:.65rem}.figure-title[data-astro-cid-mxkglkw3]{font-family:var(--font-serif);margin:0 0 1.25rem;font-size:1.3rem}.controls[data-astro-cid-mxkglkw3]{border:1px solid var(--rule);background:var(--paper);padding:1rem}label[data-astro-cid-mxkglkw3]{justify-content:space-between;gap:1rem;font-size:.9rem;display:flex}output[data-astro-cid-mxkglkw3]{font-variant-numeric:tabular-nums;font-weight:600}input[data-astro-cid-mxkglkw3]{width:100%;accent-color:var(--accent);margin:.75rem 0 .25rem;display:block}.range-labels[data-astro-cid-mxkglkw3],.control-footer[data-astro-cid-mxkglkw3]{color:var(--muted);justify-content:space-between;gap:.75rem;font-size:.7rem;display:flex}.control-footer[data-astro-cid-mxkglkw3]{flex-wrap:wrap;align-items:center;margin-top:.75rem}button[data-astro-cid-mxkglkw3]{border:1px solid var(--rule);color:var(--ink);background:var(--paper);cursor:pointer;font:inherit;padding:.35rem .6rem}[data-astro-cid-mxkglkw3]:is(button,input,canvas):focus-visible{outline:2px solid var(--accent);outline-offset:4px}.chart[data-astro-cid-mxkglkw3]{color:var(--muted);grid-template-rows:auto 1.5rem 1.5rem;grid-template-columns:1.1rem 2rem minmax(0,1fr);margin-top:1.5rem;font-size:.7rem;display:grid}.y-title[data-astro-cid-mxkglkw3]{writing-mode:vertical-rl;text-align:center;transform:rotate(180deg)}.y-ticks[data-astro-cid-mxkglkw3]{position:relative}.y-ticks[data-astro-cid-mxkglkw3] span[data-astro-cid-mxkglkw3]{position:absolute;right:.4rem;transform:translateY(-50%)}canvas[data-astro-cid-mxkglkw3]{width:100%;height:auto;image-rendering:pixelated;display:block}.x-ticks[data-astro-cid-mxkglkw3]{grid-column:3;position:relative}.x-ticks[data-astro-cid-mxkglkw3] span[data-astro-cid-mxkglkw3]{position:absolute;top:.25rem;transform:translate(-50%)}.x-title[data-astro-cid-mxkglkw3]{text-align:center;grid-column:3}.legend[data-astro-cid-mxkglkw3]{color:var(--muted);margin:1rem 0 0 3.1rem;font-size:.7rem}.colorbar[data-astro-cid-mxkglkw3]{background:linear-gradient(90deg,#4242d7,#d742d7,#d74242,#d7d742,#42d742,#42d7d7,#4242d7);height:.8rem;margin-top:.4rem}.legend-ticks[data-astro-cid-mxkglkw3]{justify-content:space-between;margin-top:.2rem;display:flex}.readout[data-astro-cid-mxkglkw3]{font-variant-numeric:tabular-nums;min-height:2.8em;margin:1rem 0 .5rem;font-size:.75rem}figcaption[data-astro-cid-mxkglkw3]{color:var(--muted);font-size:.8rem;line-height:1.75}.attention-figure[data-astro-cid-t4jsvl3q]{--ink:#292524;--muted:#57534e;--rule:#d6d3d1;--paper:#fafaf7;--query:#98632e;--key:#596b90;--value:#4d7767;color:var(--ink);font-family:var(--font-sans);margin:2.5rem 0}@media (prefers-color-scheme:dark){.attention-figure[data-astro-cid-t4jsvl3q]{--ink:#e7e5e4;--muted:#a8a29e;--rule:#57534e;--paper:#1c1917;--query:#d6ad77;--key:#9eafd1;--value:#93b8a8}}header[data-astro-cid-t4jsvl3q]{border-top:1px solid var(--rule);padding-top:1rem}.eyebrow[data-astro-cid-t4jsvl3q]{color:var(--query);letter-spacing:.12em;text-transform:uppercase;margin:0 0 .6rem;font-size:.65rem}.figure-title[data-astro-cid-t4jsvl3q]{font-family:var(--font-serif);margin:0 0 .7rem;font-size:1.5rem}.intro[data-astro-cid-t4jsvl3q],.stage-caption[data-astro-cid-t4jsvl3q]{font-size:.85rem;line-height:1.8}.intro[data-astro-cid-t4jsvl3q]{color:var(--muted);margin:0 0 1.5rem}.stage[data-astro-cid-t4jsvl3q]{border:1px solid var(--rule);background:var(--paper);margin-top:1.25rem}.stage-label[data-astro-cid-t4jsvl3q]{border-bottom:1px solid var(--rule);letter-spacing:.06em;text-transform:uppercase;margin:0;padding:.85rem 1rem;font-size:.7rem}.diagram-scroll[data-astro-cid-t4jsvl3q]{overflow-x:auto}.diagram-scroll[data-astro-cid-t4jsvl3q]:focus-visible{outline:2px solid var(--query);outline-offset:3px}svg[data-astro-cid-t4jsvl3q]{width:100%;min-width:760px;height:auto;fill:var(--ink);display:block}.math[data-astro-cid-t4jsvl3q]{font-family:var(--font-serif);font-size:19px}.shape[data-astro-cid-t4jsvl3q]{font-size:15px}.note[data-astro-cid-t4jsvl3q]{fill:var(--muted);font-size:12px}.operator[data-astro-cid-t4jsvl3q]{font-size:30px;font-family:var(--font-serif)}.query[data-astro-cid-t4jsvl3q]{fill:var(--query)}.key[data-astro-cid-t4jsvl3q]{fill:var(--key)}.value[data-astro-cid-t4jsvl3q]{fill:var(--value)}.wire[data-astro-cid-t4jsvl3q]{fill:none;stroke:var(--muted);stroke-width:1.3px}.operation[data-astro-cid-t4jsvl3q]{fill:var(--paper);stroke:var(--rule)}.stage-caption[data-astro-cid-t4jsvl3q]{border-top:1px solid var(--rule);color:var(--muted);margin:0;padding:.85rem 1rem}.stage-caption[data-astro-cid-t4jsvl3q] strong[data-astro-cid-t4jsvl3q]{color:var(--ink);font-weight:500}.return-path[data-astro-cid-t4jsvl3q]{border-block:1px solid var(--rule);margin-top:1.5rem;padding:1rem 0}.return-path[data-astro-cid-t4jsvl3q]>p[data-astro-cid-t4jsvl3q]:last-child{margin:0;font-size:.9rem;line-height:2}.return-path[data-astro-cid-t4jsvl3q] span[data-astro-cid-t4jsvl3q]{white-space:nowrap;color:var(--query)}figcaption[data-astro-cid-t4jsvl3q]{color:var(--muted);margin-top:.85rem;font-size:.8rem;line-height:1.75}.scroll-hint[data-astro-cid-t4jsvl3q]{color:var(--muted);font-size:.75rem;display:none}@media (width<=850px){.scroll-hint[data-astro-cid-t4jsvl3q]{display:block}}.swiglu-figure[data-astro-cid-yoyrhivz]{--ink:#292524;--muted:#57534e;--rule:#d6d3d1;--paper:#fafaf7;--query:#98632e;--key:#596b90;--value:#4d7767;color:var(--ink);font-family:var(--font-sans);margin:2.5rem 0}@media (prefers-color-scheme:dark){.swiglu-figure[data-astro-cid-yoyrhivz]{--ink:#e7e5e4;--muted:#a8a29e;--rule:#57534e;--paper:#1c1917;--query:#d6ad77;--key:#9eafd1;--value:#93b8a8}}header[data-astro-cid-yoyrhivz]{border-top:1px solid var(--rule);padding-top:1rem}.eyebrow[data-astro-cid-yoyrhivz]{color:var(--query);letter-spacing:.12em;text-transform:uppercase;margin:0 0 .6rem;font-size:.65rem}.figure-title[data-astro-cid-yoyrhivz]{font-family:var(--font-serif);margin:0 0 .7rem;font-size:1.5rem}.intro[data-astro-cid-yoyrhivz],.stage-caption[data-astro-cid-yoyrhivz],.note-copy[data-astro-cid-yoyrhivz]{color:var(--muted);font-size:.85rem;line-height:1.8}.intro[data-astro-cid-yoyrhivz]{margin:0 0 1.5rem}.familiar-path[data-astro-cid-yoyrhivz]{border-left:2px solid var(--query);padding:.25rem 1rem}.familiar-path[data-astro-cid-yoyrhivz]>p[data-astro-cid-yoyrhivz]:nth-child(2),.return-path[data-astro-cid-yoyrhivz]>p[data-astro-cid-yoyrhivz]:nth-child(2){margin:0;font-size:.9rem;line-height:2}.note-copy[data-astro-cid-yoyrhivz]{margin:.5rem 0 0}.stage[data-astro-cid-yoyrhivz]{border:1px solid var(--rule);background:var(--paper);margin-top:1.25rem}.stage-label[data-astro-cid-yoyrhivz]{border-bottom:1px solid var(--rule);letter-spacing:.06em;text-transform:uppercase;margin:0;padding:.85rem 1rem;font-size:.7rem}.diagram-scroll[data-astro-cid-yoyrhivz]{overflow-x:auto}.diagram-scroll[data-astro-cid-yoyrhivz]:focus-visible{outline:2px solid var(--query);outline-offset:3px}svg[data-astro-cid-yoyrhivz]{width:100%;min-width:760px;height:auto;fill:var(--ink);display:block}.math[data-astro-cid-yoyrhivz]{font-family:var(--font-serif);font-size:19px}.shape[data-astro-cid-yoyrhivz]{font-size:15px}.note[data-astro-cid-yoyrhivz]{fill:var(--muted);font-size:12px}.branch-step[data-astro-cid-yoyrhivz]{font-size:16px}.operator[data-astro-cid-yoyrhivz]{font-size:30px;font-family:var(--font-serif)}.wire[data-astro-cid-yoyrhivz]{fill:none;stroke:var(--muted);stroke-width:1.3px}.operation[data-astro-cid-yoyrhivz]{fill:var(--paper);stroke:var(--rule)}.stage-caption[data-astro-cid-yoyrhivz]{border-top:1px solid var(--rule);margin:0;padding:.85rem 1rem}.stage-caption[data-astro-cid-yoyrhivz] strong[data-astro-cid-yoyrhivz]{color:var(--ink);font-weight:500}.return-path[data-astro-cid-yoyrhivz]{border-block:1px solid var(--rule);margin-top:1.5rem;padding:1rem 0}.return-path[data-astro-cid-yoyrhivz] span[data-astro-cid-yoyrhivz]{white-space:nowrap;color:var(--query)}figcaption[data-astro-cid-yoyrhivz]{color:var(--muted);margin-top:.85rem;font-size:.8rem;line-height:1.75}.scroll-hint[data-astro-cid-yoyrhivz]{color:var(--muted);font-size:.75rem;display:none}@media (width<=850px){.scroll-hint[data-astro-cid-yoyrhivz]{display:block}}
