Category: Science

Summary: Finding the leakage level where cross-module reservoir coupling destroys a reservoir-protected localized growth mode in a modular autocatalytic system.

Autocatalytic and RAF-style networks can preserve organized growth when modules are partly buffered by protected reservoir states. This experiment asks how much cross-module leakage is enough to erase that protection and eliminate a positive-growth mode that remains localized inside one module.

The script constructs dense symmetric block operators that couple active states to reservoir states, then carries a threshold bracket through larger system sizes using iterative deepening and eigensolves. The key observable is not just whether growth stays positive, but whether it remains organized in a module-localized form despite leakage.

That distinction matters because buffering can fail structurally before total growth disappears. The resulting threshold map measures when compartmentalized autocatalytic organization stops functioning as a protected reservoir-driven process.

Method: Dense symmetric block-operator eigensolves with iterative deepening across active-state sizes N=64 to 2048 and bisection on leakage strength.

What is measured: Critical leakage threshold, localization of the positive-growth mode, module-dominance ratio, leading eigenvalue behavior, and bracket width.