Why GPT’s Mathematical Foundations Cannot Guarantee Reliable Outputs

This article traces ten unproven mathematical approximations in the GPT architecture — from softmax and positional encoding to attention scaling and in-context learning — and shows that no formal analysis of their composed error propagation exists. The constraint density ρ grows quadratically with context length while mitigations remain surface-level. The condition number κ(A), applied to transformer output via Levinson-Durbin decomposition, provides the first deterministic, reproducible diagnos...