Langlands characteristic and assumption coverage graph

Family 014: Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Arithmetic formalization teams can track several equivalence/Ramanujan/Arthur statements with different characteristic and conditional inputs.

Applicability and commercial boundary

The restricted characteristic hypotheses and assumed finite-level decomposition must remain explicit. Abstract equivalence gives no immediate algorithm or practical classifier.

Initial business decision

Research infrastructure or conditional engineering until a computable implementation, effective bounds and a recurring buyer need are demonstrated. No commercial novelty or profitability is established.

Next verification action

Map each manuscript separately rather than assign one family-wide formal or unconditional label.

Evidence scope

The catalog statement was individually reviewed. Manuscript proof and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Global Arthur Enhancements of Cuspidal Excursion Parameters.