YangDim topological dictionary

Use this skill for topology/algebra/dictionary tasks. Keep SKILL.md as a router, not a theorem diary.

Required first packet

Read references/topological-dictionary.md, then load only the one or two child packets it names for the task.

Common child packets

• Raw Yang CM/SCM/constructible, purity, balancing, connectivity, and teaching guardrails: references/topology-raw-yang-core.md.
• Alexander-dual componentwise-linear, shellable, linear-quotient, and VC-one strata: references/topology-alexander-dual-vc1.md.
• Local-CM/Buchsbaum and profile-kernel questions: start with references/topology-local-cm.md.
• Cubical complexes, collapsibility, dimension/purity, CAT(0)/median, and VC-one graphs: references/topology-cubical-complexes.md.
• Derived complexes, teaching, Scarf refinements, h-vectors, and no-general-corner guardrails: references/topology-derived-teaching-hvector.md.

Guardrails

• CM(Delta_H) <=> ample is proved; do not treat it as conjectural.
• Do not transfer raw-Yang topological adjectives to derived, Alexander-dual, or cubical objects without checking the relevant packet.
• Put theorem-level results in main.tex or prescribed_dual_bridge_realization.tex; keep active-only status in ledgers.
• After significant TeX changes, compile with SyncTeX enabled, then commit and push the source plus generated PDF artifacts when the standing project rule applies.