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.