Boundary Atlas
Concepts connected by assumptions, not keywords.
Each entry identifies its domain, boundary, formal claim, computational consequences, and relationship to experiments and buildable mathematical objects.
Foundation Cluster
Begin at the edge of the domain
Four foundational entries establish the language needed to discuss singular values, finite accumulation, constrained solutions, and unreliable computation.
Limits and approach behavior
Separate the value at a point from finite, one-sided, infinite, or nonexistent approach behavior.
Discontinuities
Diagnose removable, jump, infinite, and oscillatory failures through point values and one-sided limits.
Endpoint singularity
Irregular behavior at a boundary: unbounded values, undefined derivatives, non-integrability, or loss of regularity.
Improper integrals
How limits assign meaning to integrals with unbounded intervals or singular integrands.
Boundary conditions
Constraints at domain boundaries that help select a solution from a family of possibilities.
Numerical instability
When approximation error grows until a computed trajectory no longer represents the intended model.