Solve · 2026-10-18 · 9 agents + root · 2 h 13 min wall clock
What each agent did
- Agent 1 · Literature and Table 1 audit
Checked what the Iwahori-generation pages prove, row by row and setting by setting, and verified the hypotheses of the criterion and the bridge for the group, \(\mathbb A^n\) and \(\mathbb G_m\). - Agent 2 · Summand criterion over levels
Proved the Iwahori summand criterion over \(\overline{\mathbb F}_q\) and \(\mathbb C\) under level hypotheses, and applied it to \(\mathbb A^n\), \(\mathbb G_m\) and the group. - Agent 3 · Functions ⇒ sheaves by traces
Proved that Iwahori generation for functions over \(\mathbb F_q(\!(t)\!)\) forces it for sheaves, by Frobenius traces, and showed why the converse needs more. - Agent 4 · The group: sign and weights
Showed for the group that no \(\Delta_\omega\) is a summand of a Hecke translate of \(\mathrm{IC}_0\), by the sign character and weights, without the Whittaker functor. - Agent 5 · 𝔸ⁿ: lattices
For \(\mathbb A^n\), identified every simple object as a translate of \(\mathrm{IC}_0\) by a length-zero element, so both levels hold. - Agent 6 · GL₂/T: the Iwahori module
Decided \(\mathrm{GL}_2/T\): functions miss a two-dimensional space and sheaves miss the two closed orbits, so both levels fail. - Agent 7 · Audit: criterion and bridge
Audited the criterion and the bridge: both survive, after making the decomposition equivariant and fixing the level axioms. - Agent 8 · Audit: group, 𝔸ⁿ, 𝔾ₘ
Audited the second proof of the group, \(\mathbb A^n\) and \(\mathbb G_m\) rows: all survive; the group over \(\mathbb C\) needs a cited comparison. - Agent 9 · Audit: GL₂/T
Audited \(\mathrm{GL}_2/T\) by independent recomputation: the row survives, with the sheaf half conditional on the level presentation I1I1 · Finite levels: LX has a level presentation in which every object of C_I is pulled back from a finite level Y_{N,M} and each level has finitely many pieces (Iwahori-generation pages, Proposition III).. - Root · root: registry, redirects, synthesis