Particle system in pure Lua, no shaders

$ Build me a custom particle system module for LÖVE 11.x in pure Lua.

// shape
- A module returned via "return Particles" exposing:
  - Particles.new_emitter(opts) → emitter instance
  - emitter:emit(n) — spawn n particles
  - emitter:update(dt)
  - emitter:draw()

// emitter options
- position: { x, y }
- lifetime: { min, max } seconds
- speed: { min, max } pixels/sec
- direction: { angle, spread } radians (angle = base direction, spread = +- random offset)
- gravity: { x, y } pixels/sec^2
- size: { start, end } pixels (linearly interpolated over particle lifetime)
- colors: { start, end } each = {r,g,b,a} (linearly interpolated)

// behavior
- update(dt) advances every particle: position by velocity * dt, velocity by gravity * dt, age by dt. Removes particles whose age > lifetime.
- draw() iterates particles. For each: compute t = age / lifetime, lerp size and color, draw a love.graphics.rectangle("fill", ...) at the current position with the lerped size.

// constraints
- Pure Lua, no external libs.
- No globals. Each emitter is independent.
- Use love.graphics.setColor / love.graphics.rectangle. No SpriteBatches, no shaders.
- Cap particles at 500 per emitter. Drop new emits if at cap.

// return format
- One file particles.lua in a code block.
- Include a 12-line example showing a "coin pickup" sparkle effect from love.update.
- No prose before or after.