# Dyadic modularity assumption ledger

Family 010: Unrestricted pro-modularity at the prime two. First application triage, 9 October 2026 Australia/Brisbane.

## Problem and potential new use

Arithmetic researchers can track residual-unrestricted pro-modularity and the additional de Rham/distinct-weight classical conclusion.

## Applicability and commercial boundary

Occurrence in a completed Hecke algebra is not an efficient modular form constructor or a generic representation 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

Identify finite computable invariants and a CAS workflow that repeatedly needs the distinction.

## 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).

[Unrestricted pro-modularity at the prime two](https://github.com/openai/math/blob/fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb/preprints/Unrestricted-pro-modularity-at-the-prime-two-October-6-2026/two-adic-promodularity.pdf).