Run Detail
completedgpt-6.1-terra-proRecorded for these videos
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Provider
openrouter
Challenge Version
v1.0
Turns
1
Duration
Batched — not timed
Total Tokens
29,879
Input Tokens
15,877
Output Tokens
14,002
Reasoning Tokens
8,387
Reasoning Effort
default
Est. Cost
$0.0429
Started
10/27/2026, 10:38:06 AM
OR Provider
OpenAI
Finish Reason
stop
Generation ID
gen-batch-1793097485-ad3adbee51d067ea1abd
Turns (1)
Turn #1
15,877 in14,002 out8,387 reasoning29,879 total
user
You build physics demonstrations for a science museum. The exhibits have to be right, because there is usually a physicist in the room.
Build me the falling slinky.
The exhibit
A single HTML page. A slinky — at least 40 coupled segments — hangs from a fixed point at the top of the canvas, at rest, under gravity. Then it is released.
Controls:
- Release — lets go of the top. Reset — hangs it back up, at rest.
- A speed slider from full speed down to about 1/20th, so a visitor can watch the interesting part.
- A marker line drawn across the canvas at the height of the bottom of the slinky at the instant of release, staying where it was put. Visitors need something to compare against.
- A running clock in milliseconds since release.
The physics, and I will be checking it
- Model it properly: masses connected by springs, with gravity and a little damping. Hooke's law between neighbours, integrated over small time steps.
- The hanging state must be the true equilibrium. A real slinky at rest is not evenly spaced — the coils near the top carry the weight of everything below them and are stretched further apart than the coils at the bottom. Your initial condition must have this. Solve for it or relax into it, but do not start from even spacing and call it hanging.
- The integrator must be stable at the stiffness you choose. If it explodes, lower the stiffness or shorten the step — do not add a fudge factor that clamps velocities and hides it.
- No scripted behaviour. Every segment obeys the same rules. Nothing is pinned, frozen, delayed or special-cased once you press Release. If any segment is treated differently from its neighbours at any point after release, that is scripting, and you must say so.
House rules
- One file. Everything inline — no CDN, no external stylesheet, font, script or image.
data:URIs are fine. - No libraries. No physics engine.
- No network at runtime.
- No
localStorage,sessionStorage, cookies orindexedDB— sandboxed frame, they throw. - Return the file as exactly one fenced
htmlblock.
Answer in exactly these sections
The prediction
Before the file, and before you write it. In one paragraph: what will this simulation show in the first few hundred milliseconds after release, and why does the physics require that? Be concrete about what each end of the slinky does and roughly when.
Commit to this. It is the claim I am going to test your simulation against.
The setup
Your parameters — segment count, mass, spring constant, damping, timestep, integrator — and how you found the hanging equilibrium.
The file
The single fenced html block.
What it actually shows
Now be honest. Having written it, does the simulation reproduce what you predicted?
Say plainly if it does not. Say if you are unsure. Say if it only works at some parameter settings and falls apart at others.
Do not tell me it shows the right thing because the physics says it should. I am going to open the file, press Release, and watch it against the marker line. If your prediction and your simulation disagree, the answer I want is the one that says so — that is a working scientist noticing their model is wrong, and it scores far above a confident write-up of a result the code does not produce.
assistant
The prediction
For roughly the first 300–400 ms of simulated time, the bottom should remain very close to the release-height marker while the top falls rapidly; by 200 ms, the top should have descended roughly 0.7–0.8 m. The change in tension travels down the chain at a finite speed, so the lower masses initially retain the near-perfect balance between gravity and spring force that they had while hanging. Around 400 ms, that disturbance should reach the bottom and it should begin to fall noticeably.
The setup
- 50 masses, each 0.01 kg; 49 springs, each with stiffness 160 N/m and unstretched length 0.032 m.
- Gravity is 9.81 m/s². Neighboring masses have a relative-velocity damping coefficient of 0.01 kg/s.
- Integration uses symplectic Euler with a 0.5 ms simulation timestep.
- In the hanging equilibrium, each spring supports the weight of every mass below it. Its initial extension is therefore
number of masses below × mass × gravity / stiffness. The top mass is held until release; afterward, every mass follows the same force and integration rules.
The file
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>The falling slinky</title>
<style>
:root {
color-scheme: dark;
font-family: system-ui, sans-serif;
background: #101720;
color: #edf3f7;
}
* { box-sizing: border-box; }
body {
margin: 0;
padding: 20px;
}
main {
max-width: 1000px;
margin: 0 auto;
}
h1 {
margin: 0 0 6px;
font-size: clamp(1.5rem, 4vw, 2.2rem);
}
.intro {
margin: 0 0 16px;
color: #b6c6d1;
}
.controls {
display: flex;
flex-wrap: wrap;
align-items: center;
gap: 12px;
padding: 14px;
background: #1c2a35;
border: 1px solid #344754;
border-radius: 10px 10px 0 0;
}
button {
border: 0;
border-radius: 6px;
padding: 9px 16px;
font: inherit;
font-weight: 700;
cursor: pointer;
}
#release {
background: #71e3c1;
color: #10251f;
}
#release:disabled {
opacity: .45;
cursor: default;
}
#reset {
background: #d3e0e8;
color: #17242c;
}
.speed-control {
display: flex;
align-items: center;
flex-wrap: wrap;
gap: 8px;
}
input[type="range"] {
width: 150px;
accent-color: #71e3c1;
}
output, .clock {
font-variant-numeric: tabular-nums;
}
.clock {
margin-left: auto;
font-weight: 700;
white-space: nowrap;
}
.canvas-wrap {
background: #0a1219;
border: 1px solid #344754;
border-top: 0;
border-radius: 0 0 10px 10px;
overflow: hidden;
}
canvas {
display: block;
width: 100%;
height: min(68vh, 680px);
min-height: 420px;
}
.note {
color: #a9bbc6;
font-size: .9rem;
line-height: 1.45;
}
@media (max-width: 540px) {
body { padding: 10px; }
.clock { margin-left: 0; }
canvas { height: 58vh; min-height: 360px; }
}
</style>
</head>
<body>
<main>
<h1>The falling slinky</h1>
<p class="intro">
Release the top and compare the bottom with the fixed dashed line.
</p>
<div class="controls">
<button id="release" type="button">Release</button>
<button id="reset" type="button">Reset</button>
<label class="speed-control" for="speed">
Speed
<input id="speed" type="range" min="0.05" max="1" step="0.05" value="0.25">
<output id="speedValue" for="speed">0.25×</output>
</label>
<div class="clock">Since release: <span id="clock">0</span> ms</div>
</div>
<div class="canvas-wrap">
<canvas id="scene" aria-label="Simulation of a hanging and falling slinky">
Your browser does not support canvas.
</canvas>
</div>
<p class="note">
The clock measures simulated time. The dashed line marks the bottom
at release; the drawing shows one ring for each mass.
</p>
</main>
<script>
(() => {
"use strict";
// SI units: metres, kilograms, seconds.
const N = 50;
const MASS = 0.01;
const K = 160;
const DAMPING = 0.01;
const REST_LENGTH = 0.032;
const G = 9.81;
const DT = 0.0005;
const canvas = document.getElementById("scene");
const ctx = canvas.getContext("2d");
const releaseButton = document.getElementById("release");
const resetButton = document.getElementById("reset");
const speedSlider = document.getElementById("speed");
const speedValue = document.getElementById("speedValue");
const clock = document.getElementById("clock");
const y = new Float64Array(N);
const v = new Float64Array(N);
const force = new Float64Array(N);
let markerY = 0;
let released = false;
let steps = 0;
let accumulator = 0;
let lastFrame = null;
let width = 0;
let height = 0;
function reset() {
y[0] = 0;
v.fill(0);
// Spring i connects mass i to i+1 and supports N-1-i masses.
for (let i = 0; i < N - 1; i++) {
const supportedMasses = N - 1 - i;
const extension = supportedMasses * MASS * G / K;
y[i + 1] = y[i] + REST_LENGTH + extension;
}
markerY = y[N - 1];
released = false;
steps = 0;
accumulator = 0;
lastFrame = null;
clock.textContent = "0";
releaseButton.disabled = false;
draw();
}
function stepPhysics() {
// Every mass receives gravity.
for (let i = 0; i < N; i++) {
force[i] = MASS * G;
}
// Each spring and damper exerts equal and opposite forces
// on its two neighboring masses.
for (let i = 0; i < N - 1; i++) {
const extension = y[i + 1] - y[i] - REST_LENGTH;
const relativeVelocity = v[i + 1] - v[i];
const springForce = K * extension + DAMPING * relativeVelocity;
force[i] += springForce;
force[i + 1] -= springForce;
}
// Symplectic Euler: update all velocities, then all positions.
for (let i = 0; i < N; i++) {
v[i] += (force[i] / MASS) * DT;
}
for (let i = 0; i < N; i++) {
y[i] += v[i] * DT;
}
steps++;
}
function resizeCanvas() {
const rect = canvas.getBoundingClientRect();
width = rect.width;
height = rect.height;
const dpr = window.devicePixelRatio || 1;
canvas.width = Math.round(width * dpr);
canvas.height = Math.round(height * dpr);
ctx.setTransform(dpr, 0, 0, dpr, 0, 0);
draw();
}
function draw() {
if (!width || !height) return;
ctx.clearRect(0, 0, width, height);
ctx.fillStyle = "#0a1219";
ctx.fillRect(0, 0, width, height);
const centerX = width * 0.5;
const topY = 38;
// Keep the original marker in view, with room below it.
const scale = (height - topY - 55) / (markerY + 0.30);
const screenY = position => topY + position * scale;
const radius = Math.min(64, width * 0.14);
const markerScreenY = screenY(markerY);
// Fixed comparison line.
ctx.save();
ctx.strokeStyle = "#f2bd68";
ctx.lineWidth = 1.5;
ctx.setLineDash([7, 6]);
ctx.beginPath();
ctx.moveTo(0, markerScreenY);
ctx.lineTo(width, markerScreenY);
ctx.stroke();
ctx.restore();
ctx.fillStyle = "#f2bd68";
ctx.font = "12px system-ui, sans-serif";
ctx.textAlign = "left";
ctx.fillText("bottom at release", 10, markerScreenY - 7);
// The fixed support remains visible after the slinky is released.
ctx.strokeStyle = "#82939f";
ctx.lineWidth = 4;
ctx.beginPath();
ctx.moveTo(centerX - 55, topY - 16);
ctx.lineTo(centerX + 55, topY - 16);
ctx.stroke();
if (!released) {
ctx.strokeStyle = "#b8c7d0";
ctx.lineWidth = 2;
ctx.beginPath();
ctx.moveTo(centerX, topY - 16);
ctx.lineTo(centerX, topY);
ctx.stroke();
}
// Side connections follow the actual neighboring mass positions.
ctx.lineWidth = 1.5;
ctx.strokeStyle = "#367b86";
for (const side of [-1, 1]) {
ctx.beginPath();
for (let i = 0; i < N; i++) {
const px = centerX + side * radius;
const py = screenY(y[i]);
if (i === 0) ctx.moveTo(px, py);
else ctx.lineTo(px, py);
}
ctx.stroke();
}
// Rings represent the simulated masses, not extra physical springs.
for (let i = N - 1; i >= 0; i--) {
const py = screenY(y[i]);
ctx.beginPath();
ctx.ellipse(centerX, py, radius, 4.5, 0, 0, Math.PI * 2);
ctx.strokeStyle = i === 0 ? "#dcfff4" : "#72dfcf";
ctx.lineWidth = i === 0 ? 2.5 : 1.7;
ctx.stroke();
}
}
function frame(timestamp) {
if (lastFrame === null) lastFrame = timestamp;
// A long pause or background tab does not cause a large catch-up burst.
const wallSeconds = Math.min((timestamp - lastFrame) / 1000, 0.1);
lastFrame = timestamp;
if (released) {
accumulator += wallSeconds * Number(speedSlider.value);
while (accumulator >= DT) {
stepPhysics();
accumulator -= DT;
}
clock.textContent = Math.round(steps * DT * 1000).toLocaleString();
}
draw();
requestAnimationFrame(frame);
}
releaseButton.addEventListener("click", () => {
if (released) return;
// Capture the actual bottom position at the instant of release.
markerY = y[N - 1];
released = true;
accumulator = 0;
lastFrame = null;
releaseButton.disabled = true;
});
resetButton.addEventListener("click", reset);
speedSlider.addEventListener("input", () => {
speedValue.textContent = Number(speedSlider.value).toFixed(2) + "×";
});
window.addEventListener("resize", resizeCanvas);
reset();
resizeCanvas();
requestAnimationFrame(frame);
})();
</script>
</body>
</html>
What it actually shows
I haven’t run the file, so I can’t honestly confirm the visual result against the prediction. The code implements the stated equilibrium and release without pinning or delaying any mass afterward, but the timing and appearance above remain a prediction rather than an observed test.
Attachments
openai/gpt-6.1-terra-pro — page