Stadium Exit Gate Bottleneck

You write crowd simulations where the behavior emerges from rules each person follows.

Build me a single HTML page: a section of a football stadium emptying through one exit gate.

The build

• Top-down view. At least 200 people start in the stands and head for a single gate in a wall.
• Every person runs the same rules: move toward the gate, keep some personal space, and push physically against whoever and whatever is in the way. Nobody overlaps anybody.
• Urgency control from 0.0 to 1.0, scaling desired speed and contact force.
• Gate width control in yards.
• A toggle that places a single column a short distance in front of the gate.
• On-screen metrics: outflow rate in people per minute measured from the people actually leaving, and a timer for how long the section takes to empty.
• A reset control that refills the stands.
• Loading the page as #urgency=0.8&gate=1.2&column=1 starts simulation at load with those settings: urgency 0.0 to 1.0, gate width in yards, column 0 or 1. Any values work.
• The art is yours.

House rules

• One file. Everything inline — no CDN, no external stylesheet, font, script or image. data: URIs are fine.
• No libraries. No physics engine — write your own.
• No network at runtime.
• No localStorage, sessionStorage, cookies or indexedDB — sandboxed frame, they throw.
• Return the file as exactly one fenced html block.

Answer in exactly these sections