Banked Quota Resets with Reanchored Renewal Clocks

A banked quota reset is an expiring right to restore an allowance. When redemption replaces the next automatic renewal date, it changes both current inventory and future supply timing. We formulate the optimization of expected served work under this controlled-renewal mechanism, separating dated public documentation from assumptions about activation, demand, and eligibility. A matched structural comparison shows why familiar diminishing returns can fail: with unit capacity and binary demand, rights have concave value under a fixed replenishment calendar, whereas reanchoring produces complementary identical rights, including under IID demand and positive discounting. Expiry can defeat a countdown threshold; we recover near-terminal ordering and an arbitrary-finite-horizon threshold at empty quota with saturated observed demand and IID future demand. A single-right family has an exact middle-demand exercise interval. Under narrower infinite-horizon assumptions with constant work-conserving demand and nonexpiring rights, we prove strict postponement until depletion and derive an exact logarithmic threshold; fresh-state concavity does not extend to every renewal phase. In 36 synthetic configurations, a reset-when-blocked heuristic loses an average of 0.705 served work units relative to a causal optimizer; a planner that incorrectly preserves the old calendar loses 0.427. In this grid, policies have the same current observations, while the optimizer exploits the stipulated future demand laws. A passive-learning extension finds an exact but small Bayes advantage over posterior-mean replanning. These are conditional model comparisons, not measured productivity gains. The results identify renewal phase, expiry profile, applicable windows, workload information, and horizon as potentially decision-relevant inputs.Supporting materials: This record includes the 33-page manuscript, its LaTeX source and four figure assets, and a standalone Python reproducibility package. The package documents synthetic inputs, reference results, software requirements, and the scope of completed verification. These results are not measurements of real account limits or user productivity.AI-use disclosure: An OpenAI-powered multi-agent assistant was used substantially for research planning, public-source retrieval, mathematical development and critique, code implementation and testing, numerical checks, and manuscript drafting. Separate automated implementations and review passes were used where documented; these do not constitute human scholarly review. The work presents conditional mathematical models and synthetic numerical experiments.