.hgp-section,.hgp-lemma-note,.hgp-result-note{--hgp-ink:#102d3d;--hgp-muted:#536775;--hgp-teal:#007e72;--hgp-aqua:#58d9bb;--hgp-line:#cbd8df;--hgp-pale:#f1f6f8;box-sizing:border-box}
.hgp-section{color:var(--hgp-ink);font:17px/1.65 ui-sans-serif,system-ui,-apple-system,BlinkMacSystemFont,"Segoe UI",sans-serif;padding:64px 0;scroll-margin-top:90px}
.hgp-section *{box-sizing:border-box}.hgp-section h2,.hgp-section h3,.hgp-section h4,.hgp-section p{margin-top:0}.hgp-section p{margin-bottom:1.1em}.hgp-section p:last-child{margin-bottom:0}
.hgp-section h2{font:500 clamp(1.9rem,3.1vw,2.65rem)/1.22 Georgia,"Times New Roman",serif;letter-spacing:-.02em;margin-bottom:20px}.hgp-section h2 math{font-size:1em}.hgp-section h3{font-size:1.25rem;line-height:1.35;font-weight:650;margin-bottom:20px}.hgp-section h4{font-size:1.4rem;font-weight:650;line-height:1.3;margin-bottom:16px}
.hgp-wrap{width:min(1160px,calc(100% - 64px));margin:0 auto}.hgp-light{background:#fff}.hgp-geometry{background:#f1f6f8;border-top:1px solid #cbd8df}.hgp-kicker,.hgp-label,.hgp-step-label{font-size:12px;font-weight:700;letter-spacing:.085em;text-transform:uppercase;line-height:1.6}.hgp-kicker{color:var(--hgp-teal);margin-bottom:20px!important}.hgp-label{color:var(--hgp-muted)}.hgp-lead{font-size:19px;line-height:1.65;max-width:930px;margin-bottom:32px!important}
.hgp-section a,.hgp-lemma-note a{color:var(--hgp-teal);text-underline-offset:4px}.hgp-section button,.hgp-section select{font:inherit}.hgp-section button,.hgp-section select,.hgp-section summary{touch-action:manipulation}.hgp-section button:focus-visible,.hgp-section select:focus-visible,.hgp-section a:focus-visible,.hgp-section summary:focus-visible,.hgp-section [tabindex]:focus-visible{outline:3px solid #b56818;outline-offset:4px}
.hgp-section math{font-family:"Cambria Math","STIX Two Math","STIXGeneral","DejaVu Math TeX Gyre",math;font-size:1.06em;line-height:1.4}.hgp-section math[display=block]{margin:0;text-align:left}.hgp-section .hgp-equation{overflow-x:auto;overflow-y:hidden;padding:8px 0 13px;max-width:100%;font-size:20px;line-height:1.7;scrollbar-width:thin;margin:9px 0 12px}.hgp-section .hgp-equation math{width:max-content;min-width:0;max-width:none;display:block}
.hgp-formula-grid{display:grid;grid-template-columns:1fr 1fr;gap:24px;align-items:stretch}.hgp-card{min-width:0;border:1px solid var(--hgp-line);padding:27px 28px;background:#fff;border-radius:6px}.hgp-accent-card{background:#eff8f5;border-top:3px solid var(--hgp-teal);padding-top:25px}.hgp-rule{border-top:1px solid var(--hgp-line);padding:14px 0 2px}.hgp-rule>b{font-size:14px;font-weight:650}.hgp-rule .hgp-equation{font-size:19px;margin-top:4px}.hgp-small{font-size:14px;line-height:1.6;color:var(--hgp-muted)}.hgp-source{font-size:13px;line-height:1.7;color:var(--hgp-muted);margin-top:22px}
.hgp-notice{padding:20px 24px;border-left:3px solid var(--hgp-teal);background:#e7f4ef;margin:26px 0;line-height:1.65}.hgp-notice strong{font-weight:700}
.hgp-demo{border:1px solid var(--hgp-line);border-radius:6px;margin-top:32px;overflow:hidden;background:#fff}.hgp-demo-heading{padding:23px 26px;display:flex;justify-content:space-between;align-items:center;gap:22px}.hgp-demo-heading .hgp-label{margin:0 0 4px}.hgp-demo-heading h3{margin:0}.hgp-controls{display:flex;gap:16px;flex-wrap:wrap}.hgp-controls label{font-size:12px;font-weight:650;display:grid;gap:5px;color:var(--hgp-muted)}.hgp-controls select{font-size:15px;font-weight:500;min-height:43px;min-width:155px;padding:8px 33px 8px 10px;border:1px solid var(--hgp-line);border-radius:4px;color:var(--hgp-ink);background:white}
.hgp-step-buttons{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:1px;border-top:1px solid var(--hgp-line);border-bottom:1px solid var(--hgp-line);background:var(--hgp-line)}.hgp-step-buttons button{padding:17px 16px 15px;border:0;background:var(--hgp-pale);color:var(--hgp-ink);text-align:left;font-size:15px;cursor:pointer;line-height:1.5}.hgp-step-buttons button>b{display:inline-block;margin-right:10px;color:var(--hgp-teal);font-family:Georgia,serif;font-size:21px}.hgp-step-buttons button>span{display:block;font-size:12px;color:var(--hgp-muted);margin-top:5px}.hgp-step-buttons button[aria-pressed=true]{background:var(--hgp-ink);color:white;box-shadow:inset 0 -3px 0 var(--hgp-aqua)}.hgp-step-buttons button[aria-pressed=true]>b{color:var(--hgp-aqua)}.hgp-step-buttons button[aria-pressed=true]>span{color:#cee0e7}
.hgp-graph-grid{display:grid;grid-template-columns:minmax(0,1.4fr) minmax(250px,1fr);gap:24px;padding:26px}.hgp-svg-box{min-width:0}.hgp-svg-box svg{width:100%;height:auto;display:block}.hgp-svg-box .hgp-edge{stroke:#b7c6ce;stroke-width:1.3;stroke-dasharray:5 5;opacity:.5}.hgp-svg-box .hgp-edge.kept{stroke:#007e72;stroke-width:2.8;stroke-dasharray:none;opacity:.9}.hgp-svg-box .hgp-edge.focused{stroke:#a65b05;stroke-width:4;opacity:1}.hgp-svg-box .hgp-node circle{fill:white;stroke:#bbc8d0;stroke-width:1.7}.hgp-svg-box .hgp-node text{font-family:Georgia,serif;fill:#80939e}.hgp-svg-box .hgp-node.kept{cursor:pointer}.hgp-svg-box .hgp-node.kept circle{fill:#102d3d;stroke:white;stroke-width:2}.hgp-svg-box .hgp-node.kept text{fill:#102d3d;font-weight:bold}.hgp-svg-box .hgp-node.selected circle{fill:#d8862e;stroke:#102d3d;stroke-width:2.4}.hgp-svg-box .hgp-node .hgp-degree{font:12px ui-sans-serif,system-ui,sans-serif;fill:#536775}.hgp-svg-box .hgp-node text.label-bg{stroke:#fff;stroke-width:6px;stroke-linejoin:round;paint-order:stroke;fill:#102d3d}.hgp-graph-reading{padding:18px 0 5px}.hgp-readout{border-top:1px solid var(--hgp-line);border-bottom:1px solid var(--hgp-line);padding:17px 0;margin:19px 0}.hgp-readout>p{margin:3px 0 10px;font-weight:600}.hgp-incident-row{padding:6px 0;display:grid;grid-template-columns:1fr 1fr;gap:10px;border-bottom:1px solid #e4eaee;font-size:14px}.hgp-incident-row:last-child{border:0}.hgp-incident-row span:first-child{font-family:Georgia,serif;font-size:16px}.hgp-incident-row span:last-child{font-family:Georgia,serif;color:var(--hgp-muted)}
.hgp-details{border-top:1px solid var(--hgp-line);border-bottom:0;margin-top:20px;scroll-margin-top:95px}.hgp-details:last-child{border-bottom:1px solid var(--hgp-line)}.hgp-details>summary{display:block;font-size:17px;font-weight:600;line-height:1.6;cursor:pointer;list-style:none;position:relative;padding:18px 36px 18px 0}.hgp-details>summary::-webkit-details-marker{display:none}.hgp-details>summary:after{content:'+';position:absolute;right:4px;top:14px;color:var(--hgp-teal);font-size:24px;font-weight:400}.hgp-details[open]>summary:after{content:'−'}.hgp-details>div{padding:9px 0 25px;max-width:1000px}.hgp-details>div>p{max-width:970px}
.hgp-roles{display:grid;grid-template-columns:1fr 1fr;gap:24px;align-items:stretch}.hgp-role{padding:29px 28px;border:1px solid var(--hgp-line);border-radius:6px;background:#fff;min-width:0}.hgp-typea{background:var(--hgp-ink);color:white;border-color:var(--hgp-ink)}.hgp-typea .hgp-label,.hgp-typea a{color:var(--hgp-aqua)}.hgp-typea .hgp-source{color:#c4d5df}.hgp-typea .hgp-key-equation{border-left:3px solid var(--hgp-aqua);padding-left:18px;margin:24px 0}.hgp-key-equation .hgp-equation{font-size:25px}.hgp-implication{border-top:1px solid var(--hgp-line);padding:17px 0 0;margin-top:17px}.hgp-implication>b{display:block;font-size:18px;font-family:Georgia,serif;color:var(--hgp-teal);margin-bottom:6px}.hgp-implication p{font-size:16px}.hgp-step-label{color:var(--hgp-teal);margin-top:25px!important}.hgp-proof article{border-top:1px solid var(--hgp-line);margin-top:26px}.hgp-proof .hgp-equation{font-size:21px}.hgp-sandwich{border-left:3px solid var(--hgp-teal);background:#fff;padding:15px 23px;margin:24px 0}.hgp-sandwich .hgp-equation{margin:0;padding:5px 0 12px}.hgp-sandwich .hgp-equation:not(:first-child){padding-left:22px}
.hgp-lemma-note{border-left:3px solid #58d9bb;background:#163a49;color:#e2f0f5;padding:17px 22px;font-size:16px;line-height:1.7;margin:24px 0 30px;max-width:980px}.hgp-lemma-note a{color:#9cebd9;display:inline;text-underline-offset:4px}.hgp-result-note{font-size:15px;line-height:1.7;color:inherit;margin:24px 0}.hgp-result-note a{color:inherit;text-decoration:underline;text-underline-offset:4px}
@media(max-width:1000px){.hgp-formula-grid,.hgp-roles{grid-template-columns:1fr}.hgp-formula-grid .hgp-card{padding:24px}.hgp-graph-grid{grid-template-columns:1fr 280px}.hgp-demo-heading{align-items:flex-start;flex-direction:column}.hgp-role .hgp-key-equation{max-width:650px}.hgp-roles .hgp-role{padding:27px}.hgp-graph-grid{gap:10px;padding:20px}}
@media(max-width:700px){.hgp-wrap{width:calc(100% - 36px)}.hgp-section{padding:40px 0;font-size:16px}.hgp-lead{font-size:17px}.hgp-section h2{font-size:1.95rem}.hgp-graph-grid{grid-template-columns:1fr;padding:14px}.hgp-graph-reading{padding:12px}.hgp-svg-box{max-width:540px}.hgp-step-buttons{grid-template-columns:1fr}.hgp-step-buttons button{padding:11px 14px;font-size:15px}.hgp-step-buttons button>span{margin-top:0;display:inline;margin-left:9px;font-size:11px}.hgp-controls{gap:10px;width:100%}.hgp-controls label{flex:1 1 130px;min-width:0}.hgp-controls select{min-width:0;width:100%}.hgp-demo-heading{padding:18px}.hgp-role,.hgp-roles .hgp-role,.hgp-formula-grid .hgp-card{padding:20px}.hgp-section .hgp-equation,.hgp-proof .hgp-equation{font-size:18px}.hgp-section .hgp-rule .hgp-equation{font-size:18px}.hgp-section .hgp-key-equation .hgp-equation{font-size:21px}.hgp-sandwich{padding:10px 12px}.hgp-sandwich .hgp-equation:not(:first-child){padding-left:12px}.hgp-notice{padding:16px}.hgp-details>summary{font-size:16px}.hgp-lemma-note{font-size:15px;padding:15px}.hgp-incident-row{font-size:13px}}
@media(prefers-reduced-motion:reduce){.hgp-section{scroll-behavior:auto}}
@media print{.hgp-section{break-before:page}.hgp-controls,.hgp-step-buttons{display:none}.hgp-section,.hgp-typea{background:#fff;color:#111}.hgp-section a,.hgp-typea .hgp-label{color:#111}.hgp-details>div{display:block!important}.hgp-section .hgp-equation{overflow:visible;font-size:17px}.hgp-roles,.hgp-formula-grid{display:block}.hgp-card,.hgp-role{break-inside:avoid;margin-bottom:20px}}

/* R10: one-line mathematical statements, matched heading sizes, and edge conditions. */
.hgp-section .hgp-single-line math{white-space:nowrap;width:max-content;max-width:none}
.hgp-condition-list{margin:10px 0 12px;padding-left:1.4em;font-size:18px;line-height:1.8}
.hgp-condition-list li{padding-left:.25em;margin:6px 0}
.hgp-condition-list math{display:inline math;white-space:nowrap}
@media(min-width:1001px){.hgp-formula-grid{grid-template-columns:minmax(0,1.1fr) minmax(0,1fr)}}
@media(max-width:700px){.hgp-condition-list{font-size:16px}}