Solve · 2026-10-17 · 5 agents + root · 3 h 18 min wall clock

What each agent did

• Agent 1 · Trace formalism
  Explained why the trace of Frobenius cannot give the converse, proved criteria that force a counterexample, and found the norm torus independently.
• Agent 2 · Non-split forms
  Twisted the group case into hermitian forms: sheaves generate over F̄_q, spherical generation fails over F_q((t)) for every split H ≠ 1.
• Agent 3 · Split varieties
  Made Sakellaridis's split example concrete: spherical generation fails over every local field; sheaves generate, given the standard sheaf inputs for it.
• Agent 4 · Audit: counterexample and mechanism
  Recomputed the non-split counterexample and the trace mechanism step by step: no step fails; nine one-line repairs.
• Agent 5 · Audit: split candidate
  Recomputed the split example: spherical generation fails, proved; the sheaf geometry holds; sheaf generation needs Chen–Yi's framework for it.
• Root · root: registry, redirects, synthesis