.sticky-quick-nav[data-astro-cid-jztdymv3]{z-index:50;-webkit-backdrop-filter:blur(12px);border-bottom:1px solid var(--card-border,rgb(var(--gray-light)));background:#ffffffe6;margin:-1rem -1rem 2rem;padding:.6rem 0;position:sticky;top:0;box-shadow:0 4px 15px #0000000a}html[data-theme=dark] .sticky-quick-nav[data-astro-cid-jztdymv3]{background:#0b0f19e6;border-color:#1f2937;box-shadow:0 4px 15px #00000059}.quick-nav-track[data-astro-cid-jztdymv3]{scrollbar-width:none;align-items:center;gap:.5rem;max-width:1000px;margin:0 auto;padding:0 1rem;display:flex;overflow-x:auto}.quick-nav-track[data-astro-cid-jztdymv3]::-webkit-scrollbar{display:none}.quick-nav-title[data-astro-cid-jztdymv3]{text-transform:uppercase;letter-spacing:.05em;color:rgb(var(--gray));white-space:nowrap;font-size:.78rem;font-weight:700}.quick-nav-chip[data-astro-cid-jztdymv3]{background:rgba(var(--gray-light), .6);color:rgb(var(--gray-dark));white-space:nowrap;border:1px solid #0000;border-radius:9999px;padding:.3rem .75rem;font-size:.82rem;font-weight:600;text-decoration:none;transition:all .2s}html[data-theme=dark] .quick-nav-chip[data-astro-cid-jztdymv3]{color:#cbd5e1;background:#1e293b}.quick-nav-chip[data-astro-cid-jztdymv3]:hover{color:#fff;background:#0284c7;border-color:#0284c7;transform:translateY(-1px)}@media print{.sticky-quick-nav[data-astro-cid-jztdymv3]{display:none!important}}.interactive-card[data-astro-cid-l55cx5up]{background:var(--card-bg,#fff);border:1px solid var(--card-border,rgb(var(--gray-light)));border-radius:14px;margin-bottom:3.5rem;padding:2rem;box-shadow:0 10px 30px #0000000d}html[data-theme=dark] .interactive-card[data-astro-cid-l55cx5up]{background:#111827;border-color:#1f2937;box-shadow:0 10px 30px #00000059}.pinn-interactive-card[data-astro-cid-l55cx5up]{border-top:4px solid #0284c7}.card-header[data-astro-cid-l55cx5up]{flex-wrap:wrap;justify-content:space-between;align-items:flex-start;gap:1rem;margin-bottom:.75rem;display:flex}.card-tag[data-astro-cid-l55cx5up]{text-transform:uppercase;letter-spacing:.06em;color:#0284c7;font-size:.75rem;font-weight:700}html[data-theme=dark] .card-tag[data-astro-cid-l55cx5up]{color:#38bdf8}.card-header[data-astro-cid-l55cx5up] h2[data-astro-cid-l55cx5up]{margin:.25rem 0 0;font-size:1.5rem}.pinn-status[data-astro-cid-l55cx5up]{color:#059669;background:#10b9811a;border:1px solid #10b98140;border-radius:9999px;align-items:center;gap:.4rem;padding:.35rem .85rem;font-size:.85rem;font-weight:600;display:flex}html[data-theme=dark] .pinn-status[data-astro-cid-l55cx5up]{color:#34d399}.pulse-dot[data-astro-cid-l55cx5up]{background:#10b981;border-radius:50%;width:8px;height:8px;animation:1.8s infinite pulseDot;box-shadow:0 0 #10b981b3}@keyframes pulseDot{0%{transform:scale(.95);box-shadow:0 0 #10b981b3}70%{transform:scale(1);box-shadow:0 0 0 6px #10b98100}to{transform:scale(.95);box-shadow:0 0 #10b98100}}.card-desc[data-astro-cid-l55cx5up]{color:rgb(var(--gray));margin-bottom:1.75rem;font-size:.95rem;line-height:1.6}.simulator-box[data-astro-cid-l55cx5up]{grid-template-columns:1.4fr 1fr;align-items:start;gap:2rem;display:grid}@media (width<=860px){.simulator-box[data-astro-cid-l55cx5up]{grid-template-columns:1fr}}.canvas-container[data-astro-cid-l55cx5up]{background:#090d16;border:1px solid #1e293b;border-radius:12px;flex-direction:column;align-items:center;padding:1.25rem 1rem 1rem;display:flex;box-shadow:inset 0 2px 10px #00000080}#burgersCanvas[data-astro-cid-l55cx5up]{width:100%;height:auto;max-height:320px}.canvas-legend[data-astro-cid-l55cx5up]{color:#94a3b8;flex-wrap:wrap;gap:1.25rem;margin-top:.85rem;font-size:.78rem;display:flex}.legend-item[data-astro-cid-l55cx5up]{align-items:center;gap:.4rem;display:flex}.legend-color[data-astro-cid-l55cx5up]{border-radius:2px;width:16px;height:3px}.color-pinn[data-astro-cid-l55cx5up]{background:#38bdf8;box-shadow:0 0 8px #38bdf899}.color-exact[data-astro-cid-l55cx5up]{background:#94a3b8}.controls-panel[data-astro-cid-l55cx5up]{flex-direction:column;gap:1.25rem;display:flex}.control-group[data-astro-cid-l55cx5up]{flex-direction:column;gap:.4rem;display:flex}.control-label[data-astro-cid-l55cx5up]{justify-content:space-between;font-size:.9rem;font-weight:600;display:flex}.control-label[data-astro-cid-l55cx5up] strong[data-astro-cid-l55cx5up]{color:#0284c7;font-family:var(--font-mono,monospace)}html[data-theme=dark] .control-label[data-astro-cid-l55cx5up] strong[data-astro-cid-l55cx5up]{color:#38bdf8}.range-slider[data-astro-cid-l55cx5up]{accent-color:#0284c7;cursor:pointer;width:100%}.range-bounds[data-astro-cid-l55cx5up]{color:rgb(var(--gray));justify-content:space-between;font-size:.75rem;display:flex}.action-buttons[data-astro-cid-l55cx5up]{gap:.75rem;display:flex}.btn-primary[data-astro-cid-l55cx5up]{color:#fff;cursor:pointer;background:#0284c7;border:none;border-radius:8px;align-items:center;gap:.4rem;padding:.55rem 1.15rem;font-size:.88rem;font-weight:600;transition:background-color .2s;display:inline-flex}.btn-primary[data-astro-cid-l55cx5up]:hover{background:#0369a1}.btn-primary[data-astro-cid-l55cx5up].playing{background:#d97706}.btn-secondary[data-astro-cid-l55cx5up]{background:rgba(var(--gray-light), .5);color:rgb(var(--black));border:1px solid var(--card-border,rgb(var(--gray-light)));cursor:pointer;border-radius:8px;padding:.55rem 1rem;font-size:.88rem;font-weight:600;transition:all .2s}html[data-theme=dark] .btn-secondary[data-astro-cid-l55cx5up]{color:#f1f5f9;background:#1e293b;border-color:#334155}.metrics-grid[data-astro-cid-l55cx5up]{grid-template-columns:1fr 1fr;gap:1rem;margin-top:.5rem;display:grid}.metric-box[data-astro-cid-l55cx5up]{background:var(--bg-alt,#00000005);border:1px solid var(--card-border,rgb(var(--gray-light)));text-align:center;border-radius:8px;padding:.85rem}html[data-theme=dark] .metric-box[data-astro-cid-l55cx5up]{background:#0f172a;border-color:#1e293b}.m-label[data-astro-cid-l55cx5up]{color:rgb(var(--gray));margin-bottom:.35rem;font-size:.75rem;display:block}.m-val[data-astro-cid-l55cx5up]{font-size:1.15rem;font-weight:700;font-family:var(--font-mono,monospace);color:#0284c7}html[data-theme=dark] .m-val[data-astro-cid-l55cx5up]{color:#38bdf8}.definition-section[data-astro-cid-rxn5g72y]{margin-bottom:4rem}.section-heading[data-astro-cid-rxn5g72y]{text-align:center;margin-bottom:2.5rem}.badge-sub[data-astro-cid-rxn5g72y]{text-transform:uppercase;letter-spacing:.08em;color:#0284c7;background:#38bdf81f;border:1px solid #38bdf84d;border-radius:9999px;margin-bottom:.6rem;padding:.2rem .75rem;font-size:.78rem;font-weight:700;display:inline-block}html[data-theme=dark] .badge-sub[data-astro-cid-rxn5g72y]{color:#38bdf8}.section-heading[data-astro-cid-rxn5g72y] h2[data-astro-cid-rxn5g72y]{margin:0 0 .5rem;font-size:2rem}.section-lead[data-astro-cid-rxn5g72y]{color:rgb(var(--gray));max-width:800px;margin:0 auto;font-size:1.05rem;line-height:1.6}.definition-grid[data-astro-cid-rxn5g72y]{grid-template-columns:1fr 1fr;gap:1.5rem;display:grid}@media (width<=768px){.definition-grid[data-astro-cid-rxn5g72y]{grid-template-columns:1fr}}.def-card[data-astro-cid-rxn5g72y]{background:var(--card-bg,#fff);border:1px solid var(--card-border,rgb(var(--gray-light)));border-radius:12px;flex-direction:column;padding:1.75rem;display:flex}html[data-theme=dark] .def-card[data-astro-cid-rxn5g72y]{background:#111827;border-color:#1f2937}.def-card[data-astro-cid-rxn5g72y].full-card{grid-column:1/-1}.def-badge[data-astro-cid-rxn5g72y]{text-transform:uppercase;letter-spacing:.06em;color:#0284c7;margin-bottom:.5rem;font-size:.72rem;font-weight:700}html[data-theme=dark] .def-badge[data-astro-cid-rxn5g72y]{color:#38bdf8}.def-card[data-astro-cid-rxn5g72y] h3[data-astro-cid-rxn5g72y]{margin:0 0 .75rem;font-size:1.25rem}.def-card[data-astro-cid-rxn5g72y] p[data-astro-cid-rxn5g72y]{color:rgb(var(--gray-dark));margin:0;font-size:.9rem;line-height:1.6}.formula-card[data-astro-cid-rxn5g72y]{background:var(--code-bg,rgba(var(--gray-light), .5));border:1px solid var(--card-border,rgb(var(--gray-light)));text-align:center;border-radius:8px;margin:.85rem 0 1.25rem;padding:1rem;overflow-x:auto}html[data-theme=dark] .formula-card[data-astro-cid-rxn5g72y]{background:#0f172a;border-color:#1e293b}.theorem-section[data-astro-cid-org4axmu]{margin-bottom:4rem}.section-heading[data-astro-cid-org4axmu]{text-align:center;margin-bottom:2.5rem}.badge-sub[data-astro-cid-org4axmu]{text-transform:uppercase;letter-spacing:.08em;color:#0284c7;background:#38bdf81f;border:1px solid #38bdf84d;border-radius:9999px;margin-bottom:.6rem;padding:.2rem .75rem;font-size:.78rem;font-weight:700;display:inline-block}html[data-theme=dark] .badge-sub[data-astro-cid-org4axmu]{color:#38bdf8}.section-heading[data-astro-cid-org4axmu] h2[data-astro-cid-org4axmu]{margin:0 0 .5rem;font-size:2rem}.section-lead[data-astro-cid-org4axmu]{color:rgb(var(--gray));max-width:800px;margin:0 auto;font-size:1.05rem;line-height:1.6}.theorem-grid[data-astro-cid-org4axmu]{grid-template-columns:1fr 1fr;gap:1.5rem;margin-bottom:1.5rem;display:grid}@media (width<=768px){.theorem-grid[data-astro-cid-org4axmu]{grid-template-columns:1fr}}.theorem-card[data-astro-cid-org4axmu]{background:var(--card-bg,#fff);border:1px solid var(--card-border,rgb(var(--gray-light)));border-radius:12px;flex-direction:column;padding:1.75rem;display:flex}html[data-theme=dark] .theorem-card[data-astro-cid-org4axmu]{background:#111827;border-color:#1f2937}.thm-tag[data-astro-cid-org4axmu]{text-transform:uppercase;letter-spacing:.06em;color:#0284c7;margin-bottom:.5rem;font-size:.72rem;font-weight:700}html[data-theme=dark] .thm-tag[data-astro-cid-org4axmu]{color:#38bdf8}.theorem-card[data-astro-cid-org4axmu] h3[data-astro-cid-org4axmu]{margin:0 0 .75rem;font-size:1.2rem}.theorem-card[data-astro-cid-org4axmu] p[data-astro-cid-org4axmu]{color:rgb(var(--gray-dark));margin:0;font-size:.9rem;line-height:1.6}.formula-card[data-astro-cid-org4axmu]{background:var(--code-bg,rgba(var(--gray-light), .5));border:1px solid var(--card-border,rgb(var(--gray-light)));text-align:center;border-radius:8px;margin:.85rem 0 1.25rem;padding:1rem;overflow-x:auto}html[data-theme=dark] .formula-card[data-astro-cid-org4axmu]{background:#0f172a;border-color:#1e293b}.theorem-takeaway[data-astro-cid-org4axmu]{background:#38bdf80f;border:1px solid #38bdf840;border-radius:12px;padding:1.5rem}html[data-theme=dark] .theorem-takeaway[data-astro-cid-org4axmu]{background:#38bdf81a;border-color:#38bdf84d}.takeaway-title[data-astro-cid-org4axmu]{color:#0284c7;margin-bottom:.5rem;font-size:.95rem;font-weight:700}html[data-theme=dark] .takeaway-title[data-astro-cid-org4axmu]{color:#38bdf8}.theorem-takeaway[data-astro-cid-org4axmu] p[data-astro-cid-org4axmu]{color:rgb(var(--gray-dark));margin:0;font-size:.92rem;line-height:1.6}.aws-feature-section[data-astro-cid-oyiukhez]{margin-bottom:4rem}.aws-card[data-astro-cid-oyiukhez]{background:linear-gradient(145deg,#0284c70d,#0ea5e905);border:1.5px solid #38bdf859;border-radius:16px;padding:2.25rem;box-shadow:0 12px 36px #0284c714}html[data-theme=dark] .aws-card[data-astro-cid-oyiukhez]{background:linear-gradient(145deg,#0f172af2,#082f4933);border-color:#38bdf840;box-shadow:0 12px 36px #0006}.aws-header[data-astro-cid-oyiukhez]{margin-bottom:2rem}.aws-badge-group[data-astro-cid-oyiukhez]{flex-wrap:wrap;gap:.5rem;margin-bottom:.75rem;display:flex}.aws-event-badge[data-astro-cid-oyiukhez]{text-transform:uppercase;letter-spacing:.05em;color:#111827;background:#f90;border-radius:9999px;padding:.25rem .75rem;font-size:.75rem;font-weight:800}.aws-track-badge[data-astro-cid-oyiukhez]{text-transform:uppercase;letter-spacing:.05em;color:#0284c7;background:#0284c726;border:1px solid #0284c74d;border-radius:9999px;padding:.25rem .75rem;font-size:.75rem;font-weight:700}html[data-theme=dark] .aws-track-badge[data-astro-cid-oyiukhez]{color:#38bdf8}.aws-header[data-astro-cid-oyiukhez] h2[data-astro-cid-oyiukhez]{color:rgb(var(--black));margin:.5rem 0 .75rem;font-size:1.85rem}.aws-lead[data-astro-cid-oyiukhez]{color:rgb(var(--gray-dark));margin:0;font-size:1.05rem;line-height:1.6}.aws-pillars-grid[data-astro-cid-oyiukhez]{grid-template-columns:repeat(auto-fit,minmax(220px,1fr));gap:1.25rem;margin-bottom:2rem;display:grid}.aws-pillar[data-astro-cid-oyiukhez]{background:var(--card-bg,#fff);border:1px solid var(--card-border,rgb(var(--gray-light)));border-radius:10px;flex-direction:column;padding:1.25rem;display:flex}html[data-theme=dark] .aws-pillar[data-astro-cid-oyiukhez]{background:#0f172a;border-color:#1e293b}.pillar-icon[data-astro-cid-oyiukhez]{margin-bottom:.5rem;font-size:1.5rem}.aws-pillar[data-astro-cid-oyiukhez] h4[data-astro-cid-oyiukhez]{color:rgb(var(--black));margin:0 0 .5rem;font-size:1rem}.aws-pillar[data-astro-cid-oyiukhez] p[data-astro-cid-oyiukhez]{color:rgb(var(--gray));flex-grow:1;margin:0;font-size:.84rem;line-height:1.5}.aws-footer-cta[data-astro-cid-oyiukhez]{border-top:1px solid #38bdf840;flex-wrap:wrap;justify-content:space-between;align-items:center;gap:1rem;padding-top:1.25rem;display:flex}.aws-tech-stack[data-astro-cid-oyiukhez]{color:rgb(var(--gray));flex-wrap:wrap;align-items:center;gap:.4rem;font-size:.8rem;display:flex}.aws-tech-stack[data-astro-cid-oyiukhez] code[data-astro-cid-oyiukhez]{border-radius:4px;padding:.15rem .45rem;font-size:.75rem}.btn-aws-project[data-astro-cid-oyiukhez]{color:#fff;background:#0284c7;border-radius:8px;padding:.6rem 1.25rem;font-size:.9rem;font-weight:600;text-decoration:none;transition:background-color .2s}.btn-aws-project[data-astro-cid-oyiukhez]:hover{background:#0369a1}