3712 — The Strict Metaplectic Coherence Tower Terminates at the Cocycle Cell
Termination theorem
The metaplectic cover is an ordinary central group extension. Its section cocycle satisfies
This identity makes every longer lifted or controlled product independent of parenthesization. Equivalently, the nerve of the strict extension is 2-coskeletal: binary composition and associativity force all higher simplicial fillers.
There is therefore no independent infinite sequence of metaplectic associator towers. The hierarchy terminates as binary lifted composition, two-cocycle correction, triple cocycle gate, and forced higher coherence.
Falsifier
An arbitrary pairwise phase table on the Klein four group fails at length three. The two parenthesizations have residual phases zero and one. Thus the cocycle gate distinguishes a genuine extension from locally plausible fitted signs before any higher test is needed.
The theorem is scoped to the strict mathematical extension. Higher failures in an executable system would diagnose a non-strict, partial, noisy, or authority-sensitive implementation rather than another intrinsic metaplectic associator.
Evidence
research/strominger/the-strict-metaplectic-coherence-tower-terminates-at-the-cocycle-cell.md;research/strominger/checkers/metaplectic_nerve_coskeletality_checks.py;research/strominger/results/metaplectic_nerve_coskeletality_checks.json.
The exact checker passes 9 of 9 gates over every binary word through length
eight, including 256 words with 429 parenthesizations each. Checker SHA-256:
0d2aaa9767d1685dad82cc29f55f09797f5b4826dc45228cd673e301e8ec78cf.
Allocator claim: seqclaim-dfece9f6cbba5ad987ace119.