# 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_ord`maintains 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.