# Results D02 - Cycle 1 (Pilot)
Theorem: D02 - Non-productive commutativityCycle date: 2026-04-16Cycle type: formal pilot (not yet full external benchmark)
## Cycle objective
Verify that theorem D02 is:1. formally well placed in the OCT typed picture;2. equipped with an explicit constructive witness;3. ready for empirical testing on commutative diagram datasets.
## Execution Cycle 1
1. Typed consistency check with `OCT_TYPED_FORMAL_SPEC_v0_1.md`.2. Check integration in the manuscript `OCT_FOUNDATIONAL_OPERA_DRAFT_v0_7.md`.3. Theoretical witness construction:- classical commutative square;- compositional redundancy regime;- `Phi_Omega(D)=0_E` even with preserved commutativity.
## Outcome
- Cycle status 1: **PASS (formal pilot)**- Theorem status: **in_proof** (not yet `validated`)
## What is validated in this cycle
- logical correctness of the statement;- compatibility with the typed layer (`Diag_fin`, `Phi_Omega`, `0_E`);- existence of a theoretical non-empty witness class.
## What's missing for `validated`
1. independent benchmark #1 with real commutative diagrams;2. independent benchmark #2;3. replicate on at least 2 contexts `Omega`;4. Reproducible logs and final statistical decision.
## Decision
`D02` remains `in_proof` and advances to Cycle 2 (empirical validation).