diff --git a/overlay/index.html b/overlay/index.html
index aeef7a5..49822c6 100644
--- a/overlay/index.html
+++ b/overlay/index.html
@@ -40,6 +40,7 @@ input[type=range]{width:100%;accent-color:var(--fit)}
     <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>
+    <button id="l-outer" aria-pressed="true" style="--sw:var(--muted)">outer</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>
@@ -65,10 +66,15 @@ function seg(a,b,n=500){const o=[];for(let i=0;i<=n;i++){const t=i/n;o.push([a[0
 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 V0=P(150,160.66014976539617), M1=P(150,174.24660560764943);
+// outer yantra: lotus rings, petals, bhupura (square with four gates), in yantra units (rim = 1)
+const circ=(r,n=360)=>Array.from({length:n+1},(_,i)=>{const a=i/n*Math.PI*2;return[r*Math.cos(a),r*Math.sin(a)]});
+function petals(r0,r1,k){const o=[];for(let i=0;i<k;i++){const a0=i/k*Math.PI*2,a1=(i+1)/k*Math.PI*2,am=(a0+a1)/2,pts=[];for(let j=0;j<=40;j++){const t=j/40;const a=a0+(am-a0)*t;const r=r0+(r1-r0)*Math.sin(t*Math.PI/2);pts.push([r*Math.cos(a),r*Math.sin(a)])}for(let j=0;j<=40;j++){const t=j/40;const a=am+(a1-am)*t;const r=r1-(r1-r0)*(1-Math.cos(t*Math.PI/2));pts.push([r*Math.cos(a),r*Math.sin(a)])}o.push(pts)}return o}
+function bhupura(){const q=[[1.6,-1.6],[1.6,-0.6],[1.73,-0.6],[1.73,-1.2],[1.97,-1.2],[1.97,1.2],[1.73,1.2],[1.73,0.6],[1.6,0.6],[1.6,1.6]];const corners=[];for(let k=0;k<4;k++){const c=Math.cos(k*Math.PI/2),s=Math.sin(k*Math.PI/2);q.forEach(([x,y])=>corners.push([x*c-y*s,x*s+y*c]))}corners.push(corners[0]);const o=[];for(let i=0;i<corners.length-1;i++)o.push(...seg(corners[i],corners[i+1],120).slice(i?1:0));return o}
+const OUTER=[circ(1.2),circ(1.4),circ(1.5),...petals(1,1.2,8),...petals(1.2,1.4,16),bhupura()];
 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];
+let L={orig:true,unit:false,fit:true,outer: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(){
@@ -77,18 +83,19 @@ function draw(){
   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));
+  const O=L.outer?OUTER:[];
+  if(L.unit){ring(1,col.ring);sides.forEach(sd=>path(sd.pts.map(p=>inv(p,1)),col.ring,.7,1.1));O.forEach(o=>path(o.map(p=>inv(p,1)),col.ring,.4,1))}
+  if(L.fit){ring(rho,col.fit);sides.forEach(sd=>path(sd.pts.map(p=>inv(p,rho*rho)),col.fit,.85,1.2));O.forEach(o=>path(o.map(p=>inv(p,rho*rho)),col.fit,.45,1))}
+  if(L.orig){sides.forEach(sd=>path(sd.pts,sd.up?col.up:col.down,1,1.3));O.forEach(o=>path(o,col.fg,.45,1));path(circ(1),col.fg,.6,1)}
   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.');
+   (Math.abs(rho-RHO_FIT)<1e-3?`Fit: ρ = ${RHO_FIT.toFixed(4)}. Two big lobes and one inner lobe meet at the image of a triple point (the T4 apex on the T6 base); this ρ lands it on 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()});
+['orig','unit','fit','outer'].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);