Math Mapgenerated 2026-10-25 · a354234
PUBLIC BUILD

EX-09

the structure is unique, so any invariant at all determines it — a second-order "the moduli space is a point" that licenses a determination without performing one

exemplar_kind
shape
state
current
created
2026-09-15
topic
geometry-topology
source
../exemplars/EX-09-mostow-rigidity.md

Coordinatesthe rigidity axis (§8.2) in its purest form: not a computation but the assertion that one suffices; the multiplicity-one criterion is its form in a setting with no geometry

Model forCASE-16, Wigner–Eckart multiplicity-one, Margulis superrigidity, the uniqueness of maximal supergravity

The shape: when a structure is rigid — a closed hyperbolic manifold of dimension ≥ 3 has a unique hyperbolic structure, its deformation space a point — any invariant determines it, because there is only one thing it could be. Rigidity licenses a determination and never performs one (the volume is computed by a separate dilogarithm machine); its no-geometry form is multiplicity-one in R ⊗ R̄ (Wigner–Eckart). Calibration question: is "X pins down Y" really "Y is rigid, so anything pins it down"?

generated 2026-10-25the lab index