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+<!doctype html>
+<html lang="en">
+<head>
+<meta charset="utf-8">
+<meta name="viewport" content="width=device-width, initial-scale=1, viewport-fit=cover">
+<title>Yantra Overlays</title>
+<link rel="stylesheet" href="https://fonts.googleapis.com/css2?family=Cormorant+Garamond:ital,wght@0,500;1,500&family=JetBrains+Mono:wght@400;500&display=swap">
+<style>
+/* Layout: full-bleed canvas; title top-left, control tray at the bottom. Single dark look, matching the sphere page. */
+:root{--bg:#0b0a12;--panel:#15131f;--line:#2a2638;--fg:#e9e4f2;--muted:#9a93ad;--up:#f0b44c;--down:#e2559a;--bindu:#ff3b4e;--ring:#7d74a0;--fit:#6ec5d6;
+--display:"Cormorant Garamond",Georgia,serif;--mono:"JetBrains Mono",ui-monospace,monospace;color-scheme:dark}
+html,body{height:100%;margin:0}
+body{background:var(--bg);color:var(--fg);font-family:var(--mono);font-size:14px;overflow:hidden}
+canvas{position:fixed;inset:0;width:100%;height:100%;touch-action:none}
+header{position:fixed;top:0;left:0;right:0;padding-top:calc(12px + env(safe-area-inset-top,0px));padding-left:max(16px,env(safe-area-inset-left,0px));padding-right:max(16px,env(safe-area-inset-right,0px));pointer-events:none}
+.home{pointer-events:auto;display:inline-block;margin-bottom:4px;color:var(--muted);font-size:11px;text-decoration:none;letter-spacing:.05em}
+h1{font-family:var(--display);font-weight:500;font-size:26px;margin:0}
+h1 i{color:var(--down)}
+.sub{color:var(--muted);font-size:11px;margin-top:2px;letter-spacing:.04em}
+.tray{position:fixed;left:0;right:0;bottom:0;background:linear-gradient(transparent,var(--bg) 30%);padding-top:28px;padding-bottom:calc(14px + env(safe-area-inset-bottom,0px));padding-left:max(16px,env(safe-area-inset-left,0px));padding-right:max(16px,env(safe-area-inset-right,0px))}
+.inner{max-width:560px;margin:0 auto;display:flex;flex-direction:column;gap:12px}
+.row{display:flex;gap:8px;flex-wrap:wrap;align-items:center}
+.seg{display:flex;border:1px solid var(--line);border-radius:999px;overflow:hidden;flex-wrap:wrap;width:max-content;max-width:100%}
+.seg button,.btn{background:transparent;color:var(--muted);border:0;font:inherit;font-size:11px;padding:7px 12px;cursor:pointer;letter-spacing:.05em;opacity:.55}
+.seg button[aria-pressed="true"]{background:var(--panel);color:var(--fg);opacity:1}
+.seg button[aria-pressed="true"]::before{content:"";display:inline-block;width:6px;height:6px;border-radius:50%;background:var(--sw,var(--down));margin-right:7px;vertical-align:middle}
+.btn{border:1px solid var(--line);border-radius:999px;opacity:1;color:var(--fg)}
+button:focus-visible,input:focus-visible{outline:2px solid var(--down);outline-offset:2px}
+label.sl{display:grid;grid-template-columns:auto 1fr auto;align-items:center;gap:10px;font-size:11px;color:var(--muted)}
+input[type=range]{width:100%;accent-color:var(--fit)}
+.val{font-variant-numeric:tabular-nums;color:var(--fg);min-width:4.5em;text-align:right}
+.note{font-size:10.5px;color:var(--muted);line-height:1.5}
+</style>
+</head>
+<body>
+<canvas id="c"></canvas>
+<header><a class="home" href="/">← maths</a><h1>Śrī Yantra <i>overlays</i></h1><div class="sub">drag to pan · pinch or scroll to zoom</div></header>
+<div class="tray"><div class="inner">
+  <div class="seg" role="group" aria-label="Layers">
+    <button id="l-orig" aria-pressed="true" style="--sw:var(--fg)">yantra</button>
+    <button id="l-unit" aria-pressed="false" style="--sw:var(--ring)">inverse · rim</button>
+    <button id="l-fit" aria-pressed="true" style="--sw:var(--fit)">inverse · ρ</button>
+  </div>
+  <div class="row">
+    <label class="sl" for="rho" style="flex:1;min-width:220px">ρ <input id="rho" type="range" min="-1" max="0.6" step="0.001" value="-0.31"> <span class="val" id="rv"></span></label>
+    <button class="btn" id="snap">fit trefoil</button>
+  </div>
+  <div class="note" id="note"></div>
+</div></div>
+<script>
+const T=[
+[53.65669559977147,123.20508075688774,250,246.34330440022853,0],
+[52.984011026495736,174.24660560764943,50,247.01598897350425,1],
+[98.71823312733801,220.03828947357886,123.20508075688774,201.281766872662,1],
+[78.26467997914015,197.92315674002487,78.10499177949904,221.73532002085986,1],
+[90.4856922951427,78.10499177949904,160.66014976539617,209.51430770485734,0],
+[80.98384838952128,103.12199145016105,220.03828947357886,219.0161516104787,0],
+[114.9488500600036,160.66014976539617,103.12199145016105,185.0511499399964,1],
+[116.35142605010424,134.30757626706648,197.92315674002487,183.64857394989576,0],
+[124.61190803072795,144.79777263138968,174.24660560764943,175.38809196927207,0]];
+const P=(X,Y)=>[(X-150)/100,-(Y-150)/100];
+const css=n=>getComputedStyle(document.documentElement).getPropertyValue(n).trim();
+const col={up:css('--up'),down:css('--down'),bindu:css('--bindu'),ring:css('--ring'),fit:css('--fit'),fg:css('--fg')};
+function seg(a,b,n=500){const o=[];for(let i=0;i<=n;i++){const t=i/n;o.push([a[0]+(b[0]-a[0])*t,a[1]+(b[1]-a[1])*t])}return o}
+const sides=[];T.forEach(([lx,by,ay,rx,ty])=>{const A=P(lx,by),B=P(150,ay),C=P(rx,by);[[A,B],[B,C],[C,A]].forEach(([a,b])=>sides.push({up:!!ty,pts:seg(a,b)}))});
+// Fit: send the outer downward triangle's vertices (where two outer lobes meet) onto the
+// side midpoints of the outer upward triangle, which lie on the same three rays: rho^2 = |V||M|.
+const V0=P(150,250), M1=P(150,174.24660560764943);
+const RHO_FIT=Math.sqrt(Math.hypot(...V0)*Math.hypot(...M1));
+const inv=(p,r2)=>{const r=p[0]*p[0]+p[1]*p[1];return r<1e-12?null:[r2*p[0]/r,r2*p[1]/r]};
+let L={orig:true,unit:false,fit:true},rho=RHO_FIT,zoom=1,pan=[0,0];
+const cv=document.getElementById('c'),ctx=cv.getContext('2d');
+function size(){const d=Math.min(devicePixelRatio,2);cv.width=innerWidth*d;cv.height=innerHeight*d;ctx.setTransform(d,0,0,d,0,0);draw()}
+function draw(){
+  const w=innerWidth,h=innerHeight,cx=w/2+pan[0],cy=h*0.44+pan[1],s=Math.min(w,h)*0.34*zoom;
+  ctx.fillStyle=css('--bg');ctx.fillRect(0,0,w,h);
+  const X=p=>cx+p[0]*s,Y=p=>cy-p[1]*s;
+  const ring=(r,c)=>{ctx.strokeStyle=c;ctx.globalAlpha=.8;ctx.lineWidth=1;ctx.setLineDash([4,4]);ctx.beginPath();ctx.arc(cx,cy,r*s,0,Math.PI*2);ctx.stroke();ctx.setLineDash([]);ctx.globalAlpha=1};
+  const path=(pts,c,a,lw)=>{ctx.strokeStyle=c;ctx.globalAlpha=a;ctx.lineWidth=lw;ctx.beginPath();let pen=false;for(const p of pts){if(!p||Math.abs(p[0])>200||Math.abs(p[1])>200){pen=false;continue}pen?ctx.lineTo(X(p),Y(p)):ctx.moveTo(X(p),Y(p));pen=true}ctx.stroke();ctx.globalAlpha=1};
+  if(L.unit){ring(1,col.ring);sides.forEach(sd=>path(sd.pts.map(p=>inv(p,1)),col.ring,.7,1.1))}
+  if(L.fit){ring(rho,col.fit);sides.forEach(sd=>path(sd.pts.map(p=>inv(p,rho*rho)),col.fit,.85,1.2))}
+  if(L.orig)sides.forEach(sd=>path(sd.pts,sd.up?col.up:col.down,1,1.3));
+  if(L.fit&&Math.abs(rho-RHO_FIT)<1e-3){ctx.fillStyle=col.fit;const A=Math.atan2(M1[1],M1[0]),m=Math.hypot(...M1);for(let k=0;k<3;k++){const a=A+k*2*Math.PI/3;ctx.beginPath();ctx.arc(X([m*Math.cos(a),0]),Y([0,m*Math.sin(a)]),3.5,0,7);ctx.fill()}}
+  ctx.fillStyle=col.bindu;ctx.beginPath();ctx.arc(cx,cy,2.4,0,Math.PI*2);ctx.fill();
+  document.getElementById('rv').textContent=rho.toFixed(4);
+  document.getElementById('note').textContent=
+   'Yantra in gold and pink; its inversion in the rim (ρ = 1) in violet; its inversion in a circle of radius ρ in teal. '+
+   (Math.abs(rho-RHO_FIT)<1e-3?`Fit: ρ = ${RHO_FIT.toFixed(4)} sends the points where two outer lobes meet onto the side midpoints of the outer upward triangle (teal dots).`:'Fit trefoil snaps ρ so the lobe meeting points land on the outer triangle’s side midpoints.');
+}
+const $=id=>document.getElementById(id);
+['orig','unit','fit'].forEach(k=>$('l-'+k).onclick=e=>{L[k]=!L[k];e.currentTarget.setAttribute('aria-pressed',L[k]);draw()});
+$('rho').oninput=e=>{rho=Math.pow(10,+e.target.value);draw()};
+$('snap').onclick=()=>{rho=RHO_FIT;$('rho').value=Math.log10(rho);if(!L.fit){L.fit=true;$('l-fit').setAttribute('aria-pressed','true')}draw()};
+$('rho').value=Math.log10(RHO_FIT);
+const ptrs=new Map();let pinch=null;
+cv.addEventListener('pointerdown',e=>{cv.setPointerCapture(e.pointerId);ptrs.set(e.pointerId,[e.clientX,e.clientY])});
+cv.addEventListener('pointermove',e=>{if(!ptrs.has(e.pointerId))return;const prev=ptrs.get(e.pointerId);ptrs.set(e.pointerId,[e.clientX,e.clientY]);
+  if(ptrs.size===1){pan[0]+=e.clientX-prev[0];pan[1]+=e.clientY-prev[1];draw()}
+  else if(ptrs.size===2){const [a,b]=[...ptrs.values()];const d=Math.hypot(a[0]-b[0],a[1]-b[1]);if(pinch){zoom=Math.min(40,Math.max(.05,zoom*d/pinch));draw()}pinch=d}});
+const up=e=>{ptrs.delete(e.pointerId);if(ptrs.size<2)pinch=null};
+cv.addEventListener('pointerup',up);cv.addEventListener('pointercancel',up);
+cv.addEventListener('wheel',e=>{e.preventDefault();zoom=Math.min(40,Math.max(.05,zoom*Math.exp(-e.deltaY*0.0015)));draw()},{passive:false});
+addEventListener('resize',size);size();
+</script>
+</body>
+</html>