Price an overnight archive classifier on the batch API

Nobody waits for an archive. Run it overnight at half price, and get the half right.

Your task

Declare the classifier's pipeline, then write the function that prices it per month.

• declare PIPELINE: one entry per step, with an eval and a fallback on every model step
• write monthly_cost(pipeline, prices, items_per_day, days) and get the arithmetic right
• prices are dollars per million tokens; the cache discount applies to INPUT tokens only
• a step marked "batch": True bills at half the rate, input and output, after the cache discount
• runs_per_item is fan-out: a step that runs on 92 percent of documents is 0.92

design.md and cost_math.md are read by the critique, not by the suite.