Results A01 - Cycle 2 (Benchmark #1)

Theorem: A01 - Established ordering in AI pipelineCycle date: 2026-04-17Cycle Type: Independent Benchmark #1 (Controlled/Synthetic)

Cycle objective

Check on a quantitative benchmark if the ordering pipeline P_ordmaintains less semantic degeneracy than the classic P_cls pipeline.

Benchmarks and setup

• Benchmark ID: B1_SYNTH_PIPELINE_ORD_2026Q2- Benchmark nature: controlled, synthetic, reproducible (not yet external corpus)- Multi-step tasks: 240- Average pipeline length: 7.2 steps- Observational contexts: Omega_A, Omega_B- Comparison: P_ord vs P_cls

Metrics and results

Cumulative Delta (Delta_cum)

| Context | E[Delta_cum(P_ord)] | E[Delta_cum(P_cls)] | Gap (ord - cls) || --- | ---: | ---: | ---: | | Omega_A | 0.182 | 0.267 | -0.085 || Omega_B | 0.201 | 0.278 | -0.077 |

Final semantic error (Err_sem)

| Context | E[Err_sem(P_ord)] | E[Err_sem(P_cls)] | Gap (ord - cls) || --- | ---: | ---: | ---: | | Omega_A | 0.141 | 0.196 | -0.055 || Omega_B | 0.156 | 0.214 | -0.058 |

Cross-context robustness

• Advantage of P_ord over Delta_cum: confirmed in 2/2 contexts- Advantage of P_ord over Err_sem: confirmed in 2/2 contexts- Var_Omega (gap to Err_sem): 0.0000045

Interpretation

Benchmark #1 confirms the pre-registered A01 criteria:- E[Delta_cum(P_ord)] < E[Delta_cum(P_cls)]- E[Err_sem(P_ord)] < E[Err_sem(P_cls)]

Loop limits

1. still synthetic and controlled benchmark;2. independent benchmark #2 with different distribution is missing;3. final audit on sensitivity to noise and disturbances is missing.

Decision

• Cycle 2 outcome for A01: PASS (benchmark #1)- Theorem status: in_proof (strengthened evidence, not yet validated)- Next action: benchmark #2 + extended replication in Cycle 3.