TLC flash tolerates ~3,000 program/erase cycles per block. Each write spends one. The stock never refills.
One number — the rent on a single erase cycle, η — routes every memory: RAM, flash, cloud, or forget. The rule holds however value and write-rate correlate.
When valuable memories are also the most rewritten, those are the ones to keep off local flash — they'd burn the chip out first. Value stops being monotone.
At datasheet prices the endurance budget never binds: η = 0. The learned controller doesn't beat simple price-based routing. The economics do the work.
Denser NAND, heavier writes, robots that revisit scenes for years — the budget tightens and η turns on. And it re-prices cleanly: when NAND prices spike in the 2025–26 supercycle, the equilibrium rent re-clears ~39% lower while the keep/evict boundary stays fixed.
Any embodied-memory system answers three questions in sequence. Prior work solved the first. This paper supplies the other two — and the price that closes the loop.
Placement is ordinary capital budgeting. Each tier return is a per-item income statement; only one line carries the wear, and that single line is what bends the optimum.
The whole non-monotone branch hinges on one empirical antecedent: is χ > 0 on real robots? Measured at a pre-specified gate before any controller was trained, the answer is not a law — it is a property of the deployment.
One synthetic population of memories, three linked views. Move the controls and watch the shadow price η re-clear, memories route across the tiers, and the persist curve bend. Everything below is solved live. The η shown is an illustrative toy quantity (sim units), not the paper's calibrated η — which is 0 today.