Model memory cost for your session pattern

The model is one function, matter_cost(pattern, design), that walks every turn of every session and charges each token at the price it would really get: a cache write, a cache read, plain input or output. The decision that matters most is modelling the cache across sessions. If the gap between sessions is shorter than the cache lifetime, a full-history session starts by reading the old prefix and writing only the new history; if it's longer, it rewrites everything. That single condition creates the crossover. The model is checked first against the lesson's worked example, so every extension starts from numbers you've already verified by hand.