# 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](source.json).

[Global Arthur Enhancements of Cuspidal Excursion Parameters](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Global-Arthur-Enhancements-of-Cuspidal-Excursion-Parameters-October-5-2026/manuscript.pdf).