# Results D02 - Cycle 2 (Benchmark #1)
Theorem: D02 - Non-productive commutativityCycle date: 2026-04-17Cycle Type: Independent Benchmark #1 (Controlled/Synthetic)
## Cycle objective
Quantitatively test the D02 criterion on a dedicated benchmark:1. verify classical commutativity;2. measure `Phi_Omega(D)`;3. identify the commutative-non-productive class (`Phi_Omega(D)=0_E`).
## Benchmarks and contexts
- Benchmark ID: `B1_SYNTH_COMMUTATIVE_ORD_2026Q2`- Benchmark nature: controlled, synthetic, reproducible (not yet external dataset)- Number of diagrams: 120- Diagrammatic families: 6- Observational contexts: `Omega_A`, `Omega_B`
## Main results
### Classical commutativity check
- Classical commutative diagrams confirmed: 120/120
### Order emergency
| Context | Quota cases with `Phi_Omega(D)=0_E` | Quote cases with `Phi_Omega(D)>0_E` || --- | ---: | ---: |
| `Omega_A` | 0.325 | 0.675 || `Omega_B` | 0.292 | 0.708 |
### Cross-context stability
- Intersection of non-productive cases (`Phi=0`) in both contexts: 0.250- Non-productive share variance (`Var_Omega`): 0.00054
## Interpretation
Criterion D02 is confirmed in benchmark #1: there is a non-empty class of diagramsclassical commutatives which remains ordinally non-productive.
## Loop limits
1. benchmark still synthetic, not external;2. independent benchmark #2 is missing;3. final sensitivity audit on operational thresholds of `Phi` is missing.
## Decision
- Cycle 2 outcome for D02: **PASS (benchmark #1)**- Theorem status: **in_proof** (strengthened evidence, not yet `validated`)- Next action: replication on benchmark #2 and stress test in Cycle 3.