Memory as a Wasting Asset: Pricing Flash Endurance for Embodied Agents, and the Limits of Doing So

Figure 4 : Wear phase diagram (illustrative; model-derived). Headline subject: the \eta>\bar{\eta} persist-probability curve (rise-then-fall in value v ), whose theory interior down-crossing v^{\star}_{\mathrm{DC}} lies beyond the normalized value support at the measured point estimate ( section ˜ 3.8 ); the faint \eta=0 monotone step ( Proposition ˜ 1 ) is the contrast reference. The annotated marker is the price-statics break-even v^{\star}_{\mathrm{BE}}=0.91 (the persist/evict crossover inside support [0.056,1.034] ); it and the “do-NOT-persist-locally” band boundary are read from the real

Figure 11 : When wear-aware placement beats endurance-blind routing. The advantage in net realized (modeled) value is flat at zero until write-intensity dispersion \mathrm{CV}(w) is substantial (synthetic control, \chi>0 fixed, \mathrm{CV}(w) swept; cloud priced at the model’s V^{\mathrm{slow}} in the binding commodity-QLC regime). LIBERO’s measured \mathrm{CV}(w)=0.13\% sits at the floor, where the wear-augmented index collapses to value-ranking. Value is the proxy \hat{v} , not realized task success.

Figure 13 : Controller robustness and the metric-gaming finding. Left: per-seed H3 outcome (controller/oracle primary-metric ratio); the non-gaming seed is AURA-identical (ratio 0.996 ), the rejecting seeds exceed the oracle (ratios 1.13 , 2.11 , the impossibility signature of gaming). Right: the H3 verdict is invariant across all four stitch families (spread 0.010 ; adversarial \equiv random), confirming the difference is a fixed policy property, not a wear-economics effect.

Figure 14 : Price comparative-statics fan over the unified Low/Base/High band (real re-solved outputs): the equilibrium rent \eta_{\mathrm{sim}} declines monotonically across the band (left) while the population NVM share \sigma_{N} stays budget-pinned at \approx 0.29 – 0.30 (right), with the break-even v^{\star}_{\mathrm{BE}}=0.91 annotated.

Figure 1 : The core idea in one picture. On-board NAND endurance is a non-renewable stock: each persisted write spends one of a few thousand program/erase cycles and is gone, whereas RAM capacity refills every period. Every retained memory therefore faces a priced choice—keep in RAM, persist to flash (spending an erase cycle), offload to cloud, or forget—governed by a single endurance rent \eta . No fielded embodied-memory system prices this; we build that price.

Figure 8 : Recurrence-driven vs. churn-driven write-intensity: the mechanism behind the sign. Left: w is tight on LIBERO-Long ( \mathrm{std}\,0.0013 , dominated by re-observation of recurrent scenes) and wide on DROID ( \mathrm{std}\,0.024 , range 1.0006 – 1.63 , driven by teleoperation churn). Right: episode-length dispersion, a recurrence proxy ( 268\pm 57 steps LIBERO vs. 303\pm 230 DROID; 909 unique instructions over the 1{,}300 -scene full DROID pool. The \chi estimate is reported on the pre-specified 1{,}200 -new-only analyzed subset: 1{,}300 is the full pool, 1{,}200 the analyzed subset

Figure 12 : The recurrence–dispersion tension. A wear-aware win needs both \chi>0 and high write-dispersion \mathrm{CV}(w) , but they are anti-correlated across all three write-generating mechanisms: recurrence (manipulation) gives \chi>0 at low dispersion; churn (teleoperation) and navigation give high dispersion but \chi<0 . Four in-house workloads (round/plus/square/diamond) and nine external robot workloads (stars) from an \approx 20 -workload Open-X / LeRobot survey trace an anti-correlated band; the win quadrant ( \chi>0 , \mathrm{CV}(w)>20\% , threshold from fig. ˜ 11 ) is empty. The lo

Figure 3 : Every headline claim, by epistemic tier. What is proven (the wear-augmented index and the conditional non-monotone optimum, as theorems); measured on a value proxy (the regime-dependent sign of \chi , replicated but small); regime-gated (the budget does not bind on premium 3{,}000 -P/E TLC but binds at datasheet prices on commodity QLC/eMMC ; the down-crossing lies outside support); and a negative result (even where the budget binds, the wear-aware policy ties price-based routing on task value—realized value is tier-invariant).

Figure 5 : Calibrated economic primitives. Left: the wear + rent break-even ( \mathdollar/ GB-day) at Low/Base/High NAND ( \approx\mathdollar 4.8\times 10^{-5} at base). Right: the Jorgenson user cost of one erase, decomposed into datasheet cash wear plus the +5.0\% endurance markup ( \hat{m} ). The persisted item is worth M=24.3\times its per-step value (half-life 21.7 steps).

Figure 10 : The endurance budget binds on commodity storage. Device write-lifetime at the measured fleet write demand ( 24.4 TB/robot/yr) across storage classes: premium 128 -GB TLC lasts \approx 5.2 years (dormant, at the edge of deployment), but commodity QLC/eMMC ( \sim\!1{,}000 P/E [ 47 , 40 ] ) wears out in 0.2 – 1.8 years, well inside a 3 – 5 -year deployment—so the budget binds at datasheet prices and the wear-pricing lever is live.

Figure 15 : When wear-aware placement switches on. The lever needs both a binding endurance budget ( \eta>0 , the right of the map) and a positive value–write coupling ( \chi>0 , the top): only the upper-right cell activates the non-monotone optimum. Our measured datasets sit in the endurance-abundant band as run (LIBERO-Long recurrent \chi>0 ; DROID churn-driven \chi<0 ), but the binding (right) column is live today on the commodity QLC/eMMC cheaper edge robots use ( section ˜ 5.3 ), not merely future. What remains priced in advance is the upper-right corner alone—binding endurance and a recu