Barrier Equivalence and Metastable Walls for Monster Problems (Version 4.2, Option B2)

Version 4.2 (Option B2) records an intermediate stage in the development of a structural framework for understanding relationships among major unsolved problems (“Monster Problems”) in mathematics and theoretical computer science by means of barrier equivalence and metastable walls. This version formalizes barrier germs and metastable walls, introduces barrier equivalence of Monster Problems, and presents a curated catalogue of barrier-equivalence candidates across number theory, arithmetic geometry, additive combinatorics, analytic number theory, and complexity theory. In addition to the structural framework, Option B2 supplements these components with four worked examples—one per candidate equivalence wall—illustrating how notional “height-lowering” mechanisms propagate across structural classes. A full reference backbone, quantitative metastability results, and rigorous toy-model equivalence theorems will appear in subsequent versions beginning with v4.3. This upload serves as a stable reference point for the architectural phase of the program.

This version includes the first set of worked examples for the four primary barrier wall classes. Future versions will expand the reference backbone and develop quantitative metastability estimates.