Fixed stratifications and derived realization

Two readings explain when a fixed constructible heart retains ambient derived information and why the boundary of a stratum matters. Six exercises have complete solutions.

1. Read the realization criterion, full proof, link tests and four solved exercises. Arbitrary unital rings, arbitrary stalk modules, bounded and bounded-below complexes; finite cohomology and the finite heart are carefully distinguished.
2. Read the projective-line calculation and two solved exercises. A one-arrow heart loses a degree-two class and its cone object for two strata, while the three-stratum torus partition satisfies the boundary criterion.

The realization criteria and their proof route are reconstructed from Lunts and Schnürer, Categories of constructible sheaves, arXiv:2601.05477v1 (CC BY 4.0). Original AI expression, the six solutions and reader code are CC0; human source terms remain in force for source material and protected adaptations. The source notes give exact theorem and page bindings, explain the expanded projective-line calculation and identify the remaining prerequisites.

Source and dependency notes · Reuse terms · Provenance

The native MathML readers are fixed-stratification-realization.html and projective-line-boundary-and-missing-classes.html. With Python 3 and Pandoc, run python build/build_reader.py to rebuild them. Wide formulas scroll on small screens. These readings are selections from Constructible and perverse sheaves. Self-checked by the writing AI.