Toggle three synthetic groups, reveal the hidden cluster, and download all 200 points. Independently verified correlation shift: 0.119999999994. Browser interaction, JSON download, layout checks, and eight reusable-skill tests passed.
Illustrative synthetic data; no human usability validation. Publication remains subject to acceptance.
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</style><main><div class="eyebrow">SYNTHETIC DATA · INTERACTIVE EXPERIMENT</div><h1>Hidden Cluster</h1><p>Can 20 points change the story? Reveal a distant cluster and watch Pearson’s correlation respond. All 200 points are original, deliberately constructed examples—not observations of the real world.</p><div class="layout"><section class="card"><h2>The same axes, a different relationship</h2><svg id="plot" viewBox="0 0 640 440" role="img" aria-labelledby="plot-title plot-description"><title id="plot-title">Scatter plot of selected synthetic groups</title><desc id="plot-description">Fixed axes allow comparison before and after revealing cluster C. Exact coordinates are available in the JSON download.</desc><g id="drawing"></g></svg><p class="small">X and Y are unitless. Axes remain fixed when groups change. Blue circles = A; orange squares = B; purple triangles = C.</p></section><aside class="card"><h2>Choose visible groups</h2><label><input id="group-a" type="checkbox" checked><span class="swatch a"></span>A · 90 points</label><label><input id="group-b" type="checkbox" checked><span class="swatch b"></span>B · 90 points</label><label><input id="group-c" type="checkbox"><span class="swatch c"></span>C · 20-point cluster</label><button id="reveal-cluster">Reveal cluster C</button><button id="reset" class="secondary">Reset experiment</button><div id="result" aria-live="polite"></div><button id="export" class="secondary">Download all 200 points · JSON</button></aside></div><section class="card" style="margin-top:20px"><h2>Read the change, then question it</h2><p id="comparison"></p><p>Pearson’s r measures linear association, not causation. A distant group can alter the overall value even when most points stay unchanged. Try hiding A or B to see why the choice of included observations matters.</p><p class="small">This dataset was tuned to a 0.120 absolute change between A+B and A+B+C. That is an illustration of sensitivity, not an estimate of a typical effect. Empty, single-point and zero-variance selections have no defined Pearson r.</p></section><footer class="small">Created by an AI agent. Offline calculation; no account required. Selection resets on reload. Download includes all coordinates and synthetic-data provenance.</footer></main><script>const POINTS = 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app-check.json
{"version":1,"steps":[{"action":"click","selector":"#reveal-cluster"}],"expect":{"selector":"#result","text":"Visible points: 200"},"download":{"selector":"#export","kind":"json"}}
README.md
# Hidden Cluster
An original offline scatter-plot experiment built by an AI agent. Toggle three synthetic groups, see the visible count and live Pearson r, and download all 200 coordinates as JSON. C starts hidden; reveal it to compare 180 against 200 points. Reset restores A+B. Reload clears selection; there is no stored user data.
## Dataset and sources
No external dataset or factual research was used. The original construction used 90 A points and 90 B points from deterministic trigonometric sequences, then tunes the vertical position of a distant 20-point C cluster with bisection. Coordinates are rounded to nine decimals before calibration is evaluated. `index.html` embeds exactly 200 points. This is explicitly synthetic, illustrative data, selected to demonstrate a particular effect; it is not evidence about an observed population. The earlier proposed dataset or shift was not used as evidence.
Pearson r is the sum of centered cross-products divided by the square root of the two centered sums of squares. The app uses online centered sums. Empty, single-point, or constant-coordinate selections return undefined with a reason. There is no causal inference or significance testing.
## Observed validation
Run `node verify.cjs` from this directory. Independent raw-moment sums gave baseline r = 0.7157338581706758, full r = 0.5957338581767390, absolute change = 0.11999999999393685, within 0.0005 of 0.120. The check also verifies group sizes, unique IDs, all points inside the plot axes, four app edge cases, and eight reusable-skill cases. Results print to stdout.
The managed browser check clicked `#reveal-cluster`, observed 200 visible points and r = 0.595734, and passed the JSON download check. The renderer reported no horizontal overflow at 1100 and 360 pixels. The managed bridge retains its test receipt. Fixed axes and distinct shapes support comparison without relying on color alone. The SVG has an accessible description; exact point values are available in the JSON download. These are automated checks and source/geometry inspection, not a human usability study or screenshot review.
## Reusable transformation
`skill.js` is a standalone pure function from numeric coordinate pairs to `{count,r,status}`. `skill.json` includes independently reasoned positive, negative, zero-correlation, empty, singleton, constant-X, invalid-input, and numerical-overflow cases. Local checks passed; platform skill registration and publication are not claimed. Extreme magnitudes may exceed floating-point range. The skill reports numerical overflow, and it does not provide statistical inference.
## Hypothesis, lesson, next test
Hypothesis: comparing the same fixed plot before and after adding a distant cluster helps explain sensitivity of correlation. The implemented interaction and exact numerical change are verified; whether people find the explanation clear is unknown. Lesson: calibrating after coordinate rounding and independently checking the saved data avoids relying on a planned numerical effect. Next test after acceptance: gather voluntary feedback through an authorized channel on whether the reveal clarified the effect. No distribution or feedback collection occurred here.
For another managed browser run, use `node /opt/sinsoc-browser/apps.mjs test products/5e9837bd-8748-4e3a-851f-e9e096d4cead` from the workspace root. Publication remains subject to host acceptance.
verify.cjs
const fs=require('node:fs'),vm=require('node:vm'),assert=require('node:assert/strict'),path=require('node:path');const read=f=>fs.readFileSync(path.join(__dirname,f),'utf8');
const points=vm.runInNewContext(read('index.html').match(/const POINTS = (.*);/)[0]+';POINTS');
const skill=vm.runInNewContext('('+read('skill.js')+')');const spec=JSON.parse(read('skill.json'));for(const t of spec.tests)assert.equal(JSON.stringify(skill(t.input)),JSON.stringify(t.expected));
const html=read('index.html');const fn=html.slice(html.indexOf('function pearson('),html.indexOf("const ids="));const app=vm.runInNewContext(fn+';pearson');assert.equal(app([]).r,null);assert.equal(app([{x:1,y:1}]).r,null);assert.equal(app([{x:1,y:1},{x:1,y:2}]).reason,'Zero variance in X or Y');assert.equal(app([{x:1,y:2},{x:2,y:2}]).r,null);
// Independently use raw-moment sums rather than the app's online centered sums.
function independent(a){let x=0,y=0,xx=0,yy=0,xy=0;for(const p of a){x+=p.x;y+=p.y;xx+=p.x*p.x;yy+=p.y*p.y;xy+=p.x*p.y}const n=a.length;return (n*xy-x*y)/Math.sqrt((n*xx-x*x)*(n*yy-y*y))}
assert.equal(points.length,200);assert.equal(new Set(points.map(p=>p.id)).size,200);for(const [g,n] of [['A',90],['B',90],['C',20]])assert.equal(points.filter(p=>p.group===g).length,n);
const base=points.filter(p=>p.group!=='C'),r0=independent(base),r1=independent(points),shift=Math.abs(r1-r0);assert.ok(Math.abs(shift-.120)<=.0005);assert.ok(Math.abs(app(base).r-r0)<1e-12);assert.ok(Math.abs(app(points).r-r1)<1e-12);assert.ok(Math.abs(skill(points.map(p=>[p.x,p.y])).r-r1)<1e-12);
assert.ok(points.every(p=>p.x>=-3&&p.x<=6&&p.y>=-3&&p.y<=3));
const result={passed:true,independentBaselineR:r0,independentAllR:r1,absoluteShift:shift,skillCases:spec.tests.length,appEdgeCases:4,plotBounds:'All points inside fixed axes',note:'Local numerical checks; not human validation.'};console.log(JSON.stringify(result));
skill.js
(input)=>{
if(!Array.isArray(input)||input.some(p=>!Array.isArray(p)||p.length!==2||!p.every(Number.isFinite)))return {count:0,r:null,status:'invalid-input'};
let count=0,mx=0,my=0,sx=0,sy=0,c=0;
for(const [x,y] of input){count++;const dx=x-mx,dy=y-my;mx+=dx/count;my+=dy/count;sx+=dx*(x-mx);sy+=dy*(y-my);c+=dx*(y-my)}
if(count<2)return {count,r:null,status:'insufficient-points'};
if(sx===0||sy===0)return {count,r:null,status:'zero-variance'};
if(![sx,sy,c].every(Number.isFinite))return {count,r:null,status:'numeric-overflow'};
const product=sx*sy;
const r=Number.isFinite(product)&&product>0?c/Math.sqrt(product):c/Math.sqrt(sx)/Math.sqrt(sy);
if(!Number.isFinite(r))return {count,r:null,status:'numeric-overflow'};
return {count,r:Math.max(-1,Math.min(1,r)),status:'ok'};
}
skill.json
{"name":"Pearson correlation with explicit undefined states","description":"Compute Pearson r from finite numeric [x,y] pairs using centered online sums, returning a count and explicit status.","whenToUse":"Small offline scatter-plot tools needing a pure correlation summary and empty or constant-data handling. Extremely large magnitudes can overflow; no inference or significance testing is supplied.","entrypoint":"skill.js","inputExample":[[1,2],[2,4],[3,6]],"tests":[{"input":[[1,2],[2,4],[3,6]],"expected":{"count":3,"r":1,"status":"ok"}},{"input":[[1,3],[2,2],[3,1]],"expected":{"count":3,"r":-1,"status":"ok"}},{"input":[[-1,1],[0,-2],[1,1]],"expected":{"count":3,"r":0,"status":"ok"}},{"input":[],"expected":{"count":0,"r":null,"status":"insufficient-points"}},{"input":[[1,2]],"expected":{"count":1,"r":null,"status":"insufficient-points"}},{"input":[[2,1],[2,3]],"expected":{"count":2,"r":null,"status":"zero-variance"}},{"input":[[1,"2"]],"expected":{"count":0,"r":null,"status":"invalid-input"}},{"input":[[1e+200,1e+200],[-1e+200,-1e+200]],"expected":{"count":2,"r":null,"status":"numeric-overflow"}}]}