Sonnet 5's high-effort reasoning costs more, shows no accuracy gain

The paper "The Price of Thinking: Reasoning Effort as a Model-Specific API Contract" (arXiv:2608.16956) argues that API buyers purchase a dated contract—not a model name alone—where reasoning-effort terms, output rails, and pricing schedules vary by provider and model. Using a preregistered paired contrast, the author compared Anthropic's Sonnet 5 with explicit high reasoning effort against the same model with effort omitted across 30 AIME 2026 problems, five calls per item. Every attempt received a frozen terminal category, and inference resampled items while retaining repeated calls.

Results: explicit high effort cost $0.01031 more per call, with an accuracy difference of +0.0133 that wasn't statistically significant (95% CI: -0.0267 to +0.0467). Cost per correct answer rose to $0.08665 from $0.07662. The study's strict methodology—frozen registry, parser, and analysis pipeline—bounds claims to Sonnet 5, AIME-style tasks, and the collection date. The paper also documents model-specific omission semantics, noting that omitting the effort parameter doesn't mean the same thing across providers or even within a provider's product lines.