Manuscript synopsis
Classical CEGAR checks whether independently witnessed abstract edges can be assembled into one concrete path. This manuscript generalizes that obligation to graphs with boundary objects in a Grothendieck infinity-topos. A candidate path over a context has a residual family of coherent concrete lifts. Propositional support and section data have different roles. The manuscript proves base-change and tower laws, analyzes local lifts via descent, and identifies sufficient conditions for exactification and layered predicate refinement to eliminate a selected spurious path. The ordinary finite CEGAR procedure is recovered in the discrete specialization.
The 210-page, double-column PDF contains the definitions, proofs, source correspondence, and worked finite and higher examples. The companion archive contains LaTeX source, complete case data, and two formal developments. The Lean 4 package verifies unbounded safety on finite explicitly presented graphs, exact lift tabulation, elimination of descendants by refinement, finite relational logic, and validation of layered certificates. The native HoTT development verifies selected fiber, identity, and transport laws in the HoTT kernel and checks propositional and fixed-path reflection. The general infinity-topos arguments are presented as mathematical proofs in the manuscript. The work was developed with AI assistance.
Attachments
- cegar-in-higher-toposes.pdf
- cegar-reproducibility.zip