Extend Goose to sampling-based verification

Extend the Goose framework for speculative decoding with anisotropic spine trees from greedy decoding to sampling-based verification schemes for autoregressive large language models by specifying how to construct and verify the spine tree under sampling and determining which correctness and expected-yield guarantees can be preserved in this setting.

Background

Goose introduces an anisotropic speculation tree that combines a context-matched spine with transition-based branches and analyzes performance under a greedy verification protocol. All theoretical results and guarantees in the paper assume greedy decoding during verification.

The authors explicitly state that adapting their analysis to sampling-based verification is left for future work, indicating that a formal treatment of the spine-tree construction, verification, and guarantees under sampling remains unresolved.