Any company with a boss-and-employee setup will eventually hit a wall where it’s mathematically impossible to keep growing.
March 20, 2026
Original Paper
Optimal Scheduling and Growth Bounds in Hierarchical Production under Rival Time 
SSRN · 6357438
The Takeaway
By modeling hierarchical production systems, researchers found that terminal output is strictly bounded by polynomial growth, meaning true exponential expansion cannot happen in a standard hierarchy without a feedback loop. Furthermore, the optimal threshold for adding a new layer to a production chain consistently converges to Euler's number (2.718).
From the abstract
Hierarchical production systems transform additive time allocations into multiplicative output gains. This architecture is pervasive in economic systems: organizational hierarchies, investment chains, large engineering and infrastructure projects all rely on the sequential construction of productive capacities, where each stage builds the productive means used by the next before final output can emerge. We model a finite acyclic hierarchy in which a single agent allocates time across sequential