Results D02 - Cycle 3 (Benchmark #2)

Theorem: D02 - Non-productive commutativityCycle date: 2026-04-19Cycle type: independent benchmark #2 (real data + pre-recorded proxy scoring)

Benchmarks and contexts

Benchmark ID: B2_STRUCTURAL_SHIFT_COMMUTATIVE_ORD_2026Q2- Sources: SNAP (ca-GrQc, email-Eu-core)- Contexts: Omega_A, Omega_B, Omega_C- Final samples: 180 (60 basic diagrams replicated on 3 contexts)- Input used: datasets/cycle3_inputs/D02.csv

Operation method (transparency)

extracted structural chunks from real SNAP graphs;2. classical commutativity defined as a structural constraint of the dataset (is_commutative=1);3. calculated Phi with deterministic proxy based on density/context;4. classified cases Phi=0 vs Phi>0. Note: This run remains the Cycle 3 operational benchmark, not the final decision validated.

Main findings

Classical commutativity check

Classical commutative diagrams confirmed: 180/180

Order emergency

| Context | Quota cases with Phi_Omega(D)=0_E | Quota cases with Phi_Omega(D)>0_E || --- | ---: | ---: | | Omega_A | 0.2833 | 0.7167 || Omega_B | 0.3167 | 0.6833 || Omega_C | 0.3500 | 0.6500 |

Cross-context stability

Intersection of non-productive cases (Phi=0) in all contexts: 0.2833- Non-productive share variance (Var_Omega): 0.000741

Interpretation

Criterion D02 remains supported also in benchmark #2: there is a non-empty class of diagramsclassical commutatives with zero ordering emergence, in a multi-context consistent way.

Decision

Cycle 3 outcome for D02: PASS (benchmark #2)- Theorem status: in_proof (strengthened evidence, awaiting closure of A01/D03 + cycle 4 audit)