Performance

Performance Model & Constraints

This page explains the performance budget model and the key formulas that keep CORTEX sublinear.

Williams Sublinear Bound

CORTEX uses the Williams 2025 result:

S = O(√(t · log t))

This bound is applied to multiple budgets (hotpath index size, hierarchy fanout, neighbor degrees, maintenance batch sizes) to ensure the system stays efficient as the graph grows.

Hotpath Capacity

The resident hotpath index is capped to a sublinear growth function, often expressed as:

H(t) = ⌈c · √(t · log₂(1 + t))⌉

Budgeting & Fanout Limits

The same sublinear law is used for:

• Hierarchy fanout limits
• Semantic neighbor degree caps
• Daydreamer maintenance batch sizing

See the code in core/HotpathPolicy.ts and hippocampus/HierarchyBuilder.ts for the concrete implementations.