2026
CLM-AI-003602<= Pi_H(m) <= sum_{i=0}^d C(m,i)UPPER BOUNDThe cited theorem establishes Pi_H(m) <= sum_{i=0}^d C(m,i) under the recorded model.Source: On the density of families of sets — Sauer–Shelah growth-function bound ↗
PROVENA VC-dimension-d class cannot realize more labelings than the binomial growth bound.
The question, scope, and sources behind this Registry record.
Under the recorded learning theory model, establish Pi_H(m) <= sum_{i=0}^d C(m,i).
Current frontiers derived from accepted Claims.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.
No accepted machine-checked reproductions are recorded for this Limit.
Limits Registry. LR-003602. Sauer–Shelah growth-function bound. 2026.