Semantic Lifting and Inference Geometry in SAT

This work develops a semantic lifting framework for Boolean satisfiability in which inference is treated as transport over a space of inference configurations rather than purely syntactic rewriting. Within this framework, inference transport may be path-dependent even when propositional truth is preserved. We identify inference monodromy as a structural obstruction to global semantic collapse and explain why polynomial-time fragments correspond to regimes of trivial monodromy. Charged syllogisms are interpreted as local gauge choices that stabilize inference locally but cannot eliminate global obstructions. The work is structural and explanatory in nature and does not claim a resolution of the P vs. NP problem. This work provides a structural framework underlying punctures and metastable barriers in SAT. A focused treatment of puncture obstructions appears in the companion note Puncture Theorem.