# Frontier good/bad split decomposition

All 70 rows are recomputed from frozen per-config JSON values. Lower is better for every objective. `scale` is the geometric mean of `sim/real`; spreads are shown as `100 ×` log-space width, while `real margin` is the ordinary relative difference `100 × (real_second / real_best - 1)`. H-SCALE compares the log-space spread with `log1p(real margin)`, not directly with the ordinary relative margin. The real top-3 neighborhood is selected independently for every row. Directional `m_s` and `delta_s` are already expressed in log-percentage points.

- Rows / case surfaces: 70 / 14.
- Failures (`regret > 5%`): 23.
- Exact winner mismatches: 47.
- H-SCALE counterexamples: 40.

## Unified decomposition

| case | objective | sim winner | real winner | regret | scale | spread all | spread real top-3 | real margin (relative) | sim-winner real loss | failure | H-SCALE | deciding axis | m_s | delta_s | n_inv_tp | n_inv_mns | n_inv_mixed | fragile success |
|---|---|---|---|---:|---:|---:|---:|---:|---:|---|---|---|---:|---:|---:|---:|---:|---|
| q30 trace-pd | ttft_mean_ms | tp4_mns64 | tp4_mns64 | 0.0% | 45.900x | 414.0% | 73.5% | 52.8% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 trace-pd | ttft_p90_ms | tp4_mns64 | tp4_mns64 | 0.0% | 43.384x | 386.3% | 136.8% | 67.6% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 trace-pd | tpot_mean_ms | tp4_mns8 | tp4_mns8 | 0.0% | 4.799x | 34.2% | 11.9% | 30.3% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 trace-pd | tpot_p90_ms | tp4_mns8 | tp4_mns8 | 0.0% | 4.291x | 34.9% | 10.9% | 32.9% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 trace-pd | e2e_mean_ms | tp4_mns64 | tp4_mns64 | 0.0% | 8.263x | 109.9% | 50.1% | 6.6% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 trace-pd | e2e_p90_ms | tp4_mns64 | tp4_mns64 | 0.0% | 8.066x | 123.0% | 70.3% | 0.1% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q30 fixed-pd high | ttft_mean_ms | tp2_mns64 | tp4_mns32 | 58.0% | 80.274x | 664.7% | 229.2% | 0.0% | 58.0% | yes | HOLDS | mixed | 45.7% | -523.8% | 2 | 1 | 2 | no |
| q30 fixed-pd high | ttft_p90_ms | tp2_mns64 | tp4_mns64 | 56.2% | 130.663x | 709.3% | 222.7% | 0.1% | 56.2% | yes | HOLDS | tp-axis | 44.6% | -435.3% | 2 | 0 | 0 | no |
| q30 fixed-pd high | tpot_mean_ms | tp4_mns8 | tp4_mns8 | 0.0% | 6.313x | 118.1% | 95.7% | 34.4% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 fixed-pd high | tpot_p90_ms | tp4_mns8 | tp4_mns8 | 0.0% | 5.885x | 122.3% | 95.1% | 37.2% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 fixed-pd high | e2e_mean_ms | tp4_mns64 | tp1_mns32 | 1.7% | 18.867x | 226.5% | 111.5% | 0.7% | 1.7% | no | COUNTEREXAMPLE | mixed | 1.7% | -82.6% | 2 | 1 | 2 | no |
| q30 fixed-pd high | e2e_p90_ms | tp2_mns64 | tp1_mns32 | 5.5% | 24.706x | 274.2% | 172.5% | 1.0% | 5.5% | yes | HOLDS | mixed | 5.3% | -101.7% | 1 | 1 | 2 | no |
| q30 fixed-po high | ttft_mean_ms | tp4_mns16 | tp4_mns32 | 0.3% | 0.964x | 27.5% | 0.3% | 0.1% | 0.3% | no | COUNTEREXAMPLE | mns-axis | 0.3% | -0.3% | 0 | 0 | 0 | no |
| q30 fixed-po high | ttft_p90_ms | tp4_mns16 | tp4_mns32 | 0.5% | 0.956x | 26.9% | 0.3% | 0.0% | 0.5% | no | COUNTEREXAMPLE | mns-axis | 0.5% | -0.5% | 0 | 0 | 0 | no |
| q30 fixed-po high | e2e_mean_ms | tp4_mns16 | tp4_mns32 | 0.3% | 0.964x | 27.5% | 0.3% | 0.1% | 0.3% | no | COUNTEREXAMPLE | mns-axis | 0.3% | -0.3% | 0 | 0 | 0 | no |
| q30 fixed-po high | e2e_p90_ms | tp4_mns16 | tp4_mns32 | 0.5% | 0.956x | 26.9% | 0.3% | 0.0% | 0.5% | no | COUNTEREXAMPLE | mns-axis | 0.5% | -0.5% | 0 | 0 | 0 | no |
| q30 fixed-pd low | ttft_mean_ms | tp4_mns16 | tp4_mns16 | 0.0% | 1.368x | 43.8% | 1.5% | 1.3% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 fixed-pd low | ttft_p90_ms | tp4_mns16 | tp4_mns16 | 0.0% | 1.402x | 48.7% | 2.9% | 1.8% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q30 fixed-pd low | tpot_mean_ms | tp1_mns16 | tp4_mns32 | 14.0% | 4.952x | 52.7% | 0.2% | 0.0% | 14.0% | yes | HOLDS | mixed | 13.1% | -52.5% | 2 | 0 | 6 | no |
| q30 fixed-pd low | tpot_p90_ms | tp1_mns16 | tp4_mns8 | 13.4% | 4.950x | 53.2% | 0.3% | 0.2% | 13.4% | yes | HOLDS | mixed | 12.5% | -52.8% | 2 | 0 | 6 | no |
| q30 fixed-pd low | e2e_mean_ms | tp1_mns16 | tp4_mns32 | 26.9% | 4.423x | 59.8% | 0.2% | 0.1% | 26.9% | yes | HOLDS | mixed | 23.8% | -59.6% | 2 | 0 | 6 | no |
| q30 fixed-pd low | e2e_p90_ms | tp1_mns16 | tp4_mns8 | 25.7% | 4.421x | 60.0% | 0.2% | 0.1% | 25.7% | yes | HOLDS | mixed | 22.9% | -59.8% | 2 | 0 | 6 | no |
| q30 fixed-po low | ttft_mean_ms | tp4_mns16 | tp4_mns8 | 1.5% | 1.218x | 20.9% | 1.1% | 0.3% | 1.5% | no | COUNTEREXAMPLE | mns-axis | 1.5% | -1.5% | 0 | 0 | 0 | no |
| q30 fixed-po low | ttft_p90_ms | tp4_mns16 | tp4_mns8 | 3.6% | 1.184x | 16.1% | 2.3% | 0.6% | 3.6% | no | COUNTEREXAMPLE | mns-axis | 3.5% | -3.5% | 0 | 0 | 0 | no |
| q30 fixed-po low | e2e_mean_ms | tp4_mns16 | tp4_mns8 | 1.5% | 1.217x | 20.8% | 1.1% | 0.3% | 1.5% | no | COUNTEREXAMPLE | mns-axis | 1.5% | -1.5% | 0 | 0 | 0 | no |
| q30 fixed-po low | e2e_p90_ms | tp4_mns16 | tp4_mns8 | 3.6% | 1.183x | 16.0% | 2.4% | 0.7% | 3.6% | no | COUNTEREXAMPLE | mns-axis | 3.5% | -3.5% | 0 | 0 | 0 | no |
| q30 trace-po low | ttft_mean_ms | tp4_mns16 | tp4_mns64 | 3.2% | 0.657x | 18.2% | 2.6% | 1.7% | 3.2% | no | COUNTEREXAMPLE | mns-axis | 3.1% | -3.1% | 0 | 3 | 0 | no |
| q30 trace-po low | ttft_p90_ms | tp4_mns16 | tp4_mns8 | 0.4% | 0.478x | 17.7% | 0.2% | 0.2% | 0.4% | no | COUNTEREXAMPLE | mns-axis | 0.4% | -0.4% | 0 | 0 | 0 | no |
| q30 trace-po low | e2e_mean_ms | tp4_mns16 | tp4_mns64 | 3.2% | 0.657x | 18.2% | 2.6% | 1.7% | 3.2% | no | COUNTEREXAMPLE | mns-axis | 3.1% | -3.1% | 0 | 3 | 0 | no |
| q30 trace-po low | e2e_p90_ms | tp4_mns16 | tp4_mns8 | 0.3% | 0.478x | 17.7% | 0.2% | 0.1% | 0.3% | no | COUNTEREXAMPLE | mns-axis | 0.3% | -0.3% | 0 | 0 | 0 | no |
| q235 A0 fixed-pd | ttft_mean_ms | tp4_ep1_mns128 | tp8_ep8_mns128 | 4.2% | 0.991x | 6.1% | 5.0% | 0.4% | 4.2% | no | COUNTEREXAMPLE | tp-axis | 4.1% | -5.0% | 1 | 0 | 1 | no |
| q235 A0 fixed-pd | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.2% | 1.020x | 2.4% | 2.4% | 0.2% | 0.2% | no | COUNTEREXAMPLE | mns-axis | 0.2% | -0.2% | 0 | 0 | 0 | no |
| q235 A0 fixed-pd | tpot_mean_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 33.0% | 3.025x | 64.0% | 63.9% | 0.7% | 33.0% | yes | HOLDS | tp-axis | 28.5% | -64.0% | 1 | 0 | 1 | no |
| q235 A0 fixed-pd | tpot_p90_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 37.2% | 3.062x | 62.9% | 62.8% | 0.3% | 37.2% | yes | HOLDS | tp-axis | 31.6% | -62.8% | 1 | 0 | 1 | no |
| q235 A0 fixed-pd | e2e_mean_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 30.7% | 2.913x | 61.5% | 61.5% | 0.7% | 30.7% | yes | HOLDS | tp-axis | 26.8% | -61.5% | 1 | 0 | 1 | no |
| q235 A0 fixed-pd | e2e_p90_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 34.6% | 2.955x | 60.5% | 60.4% | 0.3% | 34.6% | yes | HOLDS | tp-axis | 29.7% | -60.4% | 1 | 0 | 1 | no |
| q235 A0 fixed-po | ttft_mean_ms | tp4_ep1_mns128 | tp8_ep8_mns128 | 5.9% | 0.964x | 12.1% | 12.0% | 0.2% | 5.9% | yes | HOLDS | tp-axis | 5.7% | -12.0% | 1 | 0 | 1 | no |
| q235 A0 fixed-po | ttft_p90_ms | tp4_ep1_mns128 | tp8_ep8_mns128 | 1.7% | 0.941x | 8.3% | 8.0% | 0.3% | 1.7% | no | COUNTEREXAMPLE | tp-axis | 1.7% | -8.0% | 1 | 0 | 1 | no |
| q235 A0 fixed-po | e2e_mean_ms | tp4_ep1_mns128 | tp8_ep8_mns128 | 5.9% | 0.964x | 12.1% | 12.0% | 0.2% | 5.9% | yes | HOLDS | tp-axis | 5.7% | -12.0% | 1 | 0 | 1 | no |
| q235 A0 fixed-po | e2e_p90_ms | tp4_ep1_mns128 | tp8_ep8_mns128 | 1.7% | 0.941x | 8.3% | 8.0% | 0.3% | 1.7% | no | COUNTEREXAMPLE | tp-axis | 1.7% | -8.0% | 1 | 0 | 1 | no |
| q235 A0 trace-pd | ttft_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 1.493x | 101.6% | 101.6% | 2220.3% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A0 trace-pd | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 1.511x | 96.5% | 96.5% | 3455.8% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A0 trace-pd | tpot_mean_ms | tp8_ep8_mns64 | tp8_ep8_mns64 | 0.0% | 1.340x | 61.5% | 43.1% | 16.8% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A0 trace-pd | tpot_p90_ms | tp8_ep8_mns64 | tp8_ep8_mns64 | 0.0% | 1.281x | 49.4% | 29.8% | 26.3% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A0 trace-pd | e2e_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.6% | 1.415x | 69.3% | 69.3% | 0.6% | 0.6% | no | COUNTEREXAMPLE | mns-axis | 0.6% | -18.1% | 0 | 1 | 0 | no |
| q235 A0 trace-pd | e2e_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 6.2% | 1.473x | 71.5% | 71.5% | 6.2% | 6.2% | yes | HOLDS | mns-axis | 6.0% | -16.7% | 0 | 1 | 0 | no |
| q235 A0 trace-po | ttft_mean_ms | tp4_ep1_mns64 | tp8_ep8_mns128 | 7.0% | 0.753x | 36.3% | 34.6% | 1.4% | 7.0% | yes | HOLDS | mixed | 6.8% | -36.3% | 1 | 1 | 1 | no |
| q235 A0 trace-po | ttft_p90_ms | tp4_ep1_mns128 | tp8_ep8_mns64 | 21.2% | 0.767x | 31.8% | 31.6% | 0.3% | 21.2% | yes | HOLDS | mixed | 19.2% | -31.6% | 1 | 0 | 1 | no |
| q235 A0 trace-po | e2e_mean_ms | tp4_ep1_mns64 | tp8_ep8_mns128 | 7.0% | 0.753x | 36.3% | 34.6% | 1.4% | 7.0% | yes | HOLDS | mixed | 6.8% | -36.3% | 1 | 1 | 1 | no |
| q235 A0 trace-po | e2e_p90_ms | tp4_ep1_mns128 | tp8_ep8_mns64 | 21.2% | 0.766x | 31.8% | 31.6% | 0.3% | 21.2% | yes | HOLDS | mixed | 19.2% | -31.6% | 1 | 0 | 1 | no |
| q235 A1 fixed-pd | ttft_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 0.805x | 26.8% | 26.8% | 0.4% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q235 A1 fixed-pd | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.2% | 0.837x | 30.5% | 30.5% | 0.2% | 0.2% | no | COUNTEREXAMPLE | mns-axis | 0.2% | -0.2% | 0 | 0 | 0 | no |
| q235 A1 fixed-pd | tpot_mean_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 33.0% | 2.608x | 60.1% | 60.0% | 0.7% | 33.0% | yes | HOLDS | tp-axis | 28.5% | -60.1% | 1 | 0 | 1 | no |
| q235 A1 fixed-pd | tpot_p90_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 37.2% | 2.587x | 61.2% | 61.1% | 0.3% | 37.2% | yes | HOLDS | tp-axis | 31.6% | -61.1% | 1 | 0 | 1 | no |
| q235 A1 fixed-pd | e2e_mean_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 30.7% | 2.508x | 58.3% | 58.2% | 0.7% | 30.7% | yes | HOLDS | tp-axis | 26.8% | -58.3% | 1 | 0 | 1 | no |
| q235 A1 fixed-pd | e2e_p90_ms | tp8_ep8_mns128 | tp4_ep1_mns128 | 34.6% | 2.495x | 59.3% | 59.2% | 0.3% | 34.6% | yes | HOLDS | tp-axis | 29.7% | -59.2% | 1 | 0 | 1 | no |
| q235 A1 fixed-po | ttft_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 0.776x | 24.8% | 24.8% | 0.2% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q235 A1 fixed-po | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 0.757x | 28.9% | 28.9% | 0.3% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q235 A1 fixed-po | e2e_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 0.776x | 24.8% | 24.8% | 0.2% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q235 A1 fixed-po | e2e_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 0.757x | 28.9% | 28.9% | 0.3% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | yes |
| q235 A1 trace-pd | ttft_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 1.217x | 154.4% | 154.4% | 2220.3% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A1 trace-pd | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns128 | 0.0% | 1.219x | 151.1% | 151.1% | 3455.8% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A1 trace-pd | tpot_mean_ms | tp8_ep8_mns64 | tp8_ep8_mns64 | 0.0% | 1.338x | 46.7% | 28.2% | 16.8% | 0.0% | no | COUNTEREXAMPLE | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A1 trace-pd | tpot_p90_ms | tp8_ep8_mns64 | tp8_ep8_mns64 | 0.0% | 1.221x | 45.3% | 22.3% | 26.3% | 0.0% | no | HOLDS | none | 0.0% | +0.0% | 0 | 0 | 0 | no |
| q235 A1 trace-pd | e2e_mean_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.6% | 1.430x | 48.8% | 48.8% | 0.6% | 0.6% | no | COUNTEREXAMPLE | mns-axis | 0.6% | -15.9% | 0 | 1 | 0 | no |
| q235 A1 trace-pd | e2e_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 6.2% | 1.492x | 49.7% | 49.7% | 6.2% | 6.2% | yes | HOLDS | mns-axis | 6.0% | -17.4% | 0 | 1 | 0 | no |
| q235 A1 trace-po | ttft_mean_ms | tp8_ep8_mns64 | tp8_ep8_mns128 | 1.4% | 0.548x | 32.2% | 32.2% | 1.4% | 1.4% | no | COUNTEREXAMPLE | mns-axis | 1.4% | -1.4% | 0 | 1 | 0 | no |
| q235 A1 trace-po | ttft_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.3% | 0.568x | 31.9% | 31.9% | 0.3% | 0.3% | no | COUNTEREXAMPLE | mns-axis | 0.3% | -0.3% | 0 | 0 | 0 | no |
| q235 A1 trace-po | e2e_mean_ms | tp8_ep8_mns64 | tp8_ep8_mns128 | 1.4% | 0.548x | 32.2% | 32.2% | 1.4% | 1.4% | no | COUNTEREXAMPLE | mns-axis | 1.4% | -1.4% | 0 | 1 | 0 | no |
| q235 A1 trace-po | e2e_p90_ms | tp8_ep8_mns128 | tp8_ep8_mns64 | 0.3% | 0.568x | 31.9% | 31.9% | 0.3% | 0.3% | no | COUNTEREXAMPLE | mns-axis | 0.3% | -0.3% | 0 | 0 | 0 | no |

## H-SCALE verdict

H-SCALE is not sufficient as stated; the following rows are counterexamples to the biconditional:

All 40 observed counterexamples are non-failures with spread > `log1p(margin)`; there are 0 failures with spread <= `log1p(margin)`. Thus the threshold is necessary for the observed failures but not sufficient to predict them.

| case | objective | failure | spread real top-3 | real margin | counterexample type |
|---|---|---|---:|---:|---|
| q30 trace-pd | ttft_mean_ms | no | 73.5% | 52.8% | non-failure with spread > log1p(margin) |
| q30 trace-pd | ttft_p90_ms | no | 136.8% | 67.6% | non-failure with spread > log1p(margin) |
| q30 trace-pd | e2e_mean_ms | no | 50.1% | 6.6% | non-failure with spread > log1p(margin) |
| q30 trace-pd | e2e_p90_ms | no | 70.3% | 0.1% | non-failure with spread > log1p(margin) |
| q30 fixed-pd high | tpot_mean_ms | no | 95.7% | 34.4% | non-failure with spread > log1p(margin) |
| q30 fixed-pd high | tpot_p90_ms | no | 95.1% | 37.2% | non-failure with spread > log1p(margin) |
| q30 fixed-pd high | e2e_mean_ms | no | 111.5% | 0.7% | non-failure with spread > log1p(margin) |
| q30 fixed-po high | ttft_mean_ms | no | 0.3% | 0.1% | non-failure with spread > log1p(margin) |
| q30 fixed-po high | ttft_p90_ms | no | 0.3% | 0.0% | non-failure with spread > log1p(margin) |
| q30 fixed-po high | e2e_mean_ms | no | 0.3% | 0.1% | non-failure with spread > log1p(margin) |
| q30 fixed-po high | e2e_p90_ms | no | 0.3% | 0.0% | non-failure with spread > log1p(margin) |
| q30 fixed-pd low | ttft_mean_ms | no | 1.5% | 1.3% | non-failure with spread > log1p(margin) |
| q30 fixed-pd low | ttft_p90_ms | no | 2.9% | 1.8% | non-failure with spread > log1p(margin) |
| q30 fixed-po low | ttft_mean_ms | no | 1.1% | 0.3% | non-failure with spread > log1p(margin) |
| q30 fixed-po low | ttft_p90_ms | no | 2.3% | 0.6% | non-failure with spread > log1p(margin) |
| q30 fixed-po low | e2e_mean_ms | no | 1.1% | 0.3% | non-failure with spread > log1p(margin) |
| q30 fixed-po low | e2e_p90_ms | no | 2.4% | 0.7% | non-failure with spread > log1p(margin) |
| q30 trace-po low | ttft_mean_ms | no | 2.6% | 1.7% | non-failure with spread > log1p(margin) |
| q30 trace-po low | ttft_p90_ms | no | 0.2% | 0.2% | non-failure with spread > log1p(margin) |
| q30 trace-po low | e2e_mean_ms | no | 2.6% | 1.7% | non-failure with spread > log1p(margin) |
| q30 trace-po low | e2e_p90_ms | no | 0.2% | 0.1% | non-failure with spread > log1p(margin) |
| q235 A0 fixed-pd | ttft_mean_ms | no | 5.0% | 0.4% | non-failure with spread > log1p(margin) |
| q235 A0 fixed-pd | ttft_p90_ms | no | 2.4% | 0.2% | non-failure with spread > log1p(margin) |
| q235 A0 fixed-po | ttft_p90_ms | no | 8.0% | 0.3% | non-failure with spread > log1p(margin) |
| q235 A0 fixed-po | e2e_p90_ms | no | 8.0% | 0.3% | non-failure with spread > log1p(margin) |
| q235 A0 trace-pd | tpot_mean_ms | no | 43.1% | 16.8% | non-failure with spread > log1p(margin) |
| q235 A0 trace-pd | tpot_p90_ms | no | 29.8% | 26.3% | non-failure with spread > log1p(margin) |
| q235 A0 trace-pd | e2e_mean_ms | no | 69.3% | 0.6% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-pd | ttft_mean_ms | no | 26.8% | 0.4% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-pd | ttft_p90_ms | no | 30.5% | 0.2% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-po | ttft_mean_ms | no | 24.8% | 0.2% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-po | ttft_p90_ms | no | 28.9% | 0.3% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-po | e2e_mean_ms | no | 24.8% | 0.2% | non-failure with spread > log1p(margin) |
| q235 A1 fixed-po | e2e_p90_ms | no | 28.9% | 0.3% | non-failure with spread > log1p(margin) |
| q235 A1 trace-pd | tpot_mean_ms | no | 28.2% | 16.8% | non-failure with spread > log1p(margin) |
| q235 A1 trace-pd | e2e_mean_ms | no | 48.8% | 0.6% | non-failure with spread > log1p(margin) |
| q235 A1 trace-po | ttft_mean_ms | no | 32.2% | 1.4% | non-failure with spread > log1p(margin) |
| q235 A1 trace-po | ttft_p90_ms | no | 31.9% | 0.3% | non-failure with spread > log1p(margin) |
| q235 A1 trace-po | e2e_mean_ms | no | 32.2% | 1.4% | non-failure with spread > log1p(margin) |
| q235 A1 trace-po | e2e_p90_ms | no | 31.9% | 0.3% | non-failure with spread > log1p(margin) |

## S0b directional conclusions

Directional pair statistics remove the S0 range statistic's ambiguity by measuring every config against the real winner. Strict inversions use the frozen-value test `real_c > real_w and sim_c < sim_w`; simulator ties are not counted as inversions.

### (a) Which config axis decides each material failure?

| case | objective | real winner → sim winner | deciding axis | m_s | delta_s | -delta_s | regret |
|---|---|---|---|---:|---:|---:|---:|
| q30 fixed-pd high | ttft_mean_ms | tp4_mns32 → tp2_mns64 | mixed | 45.7% | -523.8% | 523.8% | 58.0% |
| q30 fixed-pd high | ttft_p90_ms | tp4_mns64 → tp2_mns64 | tp-axis | 44.6% | -435.3% | 435.3% | 56.2% |
| q30 fixed-pd high | e2e_p90_ms | tp1_mns32 → tp2_mns64 | mixed | 5.3% | -101.7% | 101.7% | 5.5% |
| q30 fixed-pd low | tpot_mean_ms | tp4_mns32 → tp1_mns16 | mixed | 13.1% | -52.5% | 52.5% | 14.0% |
| q30 fixed-pd low | tpot_p90_ms | tp4_mns8 → tp1_mns16 | mixed | 12.5% | -52.8% | 52.8% | 13.4% |
| q30 fixed-pd low | e2e_mean_ms | tp4_mns32 → tp1_mns16 | mixed | 23.8% | -59.6% | 59.6% | 26.9% |
| q30 fixed-pd low | e2e_p90_ms | tp4_mns8 → tp1_mns16 | mixed | 22.9% | -59.8% | 59.8% | 25.7% |
| q235 A0 fixed-pd | tpot_mean_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 28.5% | -64.0% | 64.0% | 33.0% |
| q235 A0 fixed-pd | tpot_p90_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 31.6% | -62.8% | 62.8% | 37.2% |
| q235 A0 fixed-pd | e2e_mean_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 26.8% | -61.5% | 61.5% | 30.7% |
| q235 A0 fixed-pd | e2e_p90_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 29.7% | -60.4% | 60.4% | 34.6% |
| q235 A0 fixed-po | ttft_mean_ms | tp8_ep8_mns128 → tp4_ep1_mns128 | tp-axis | 5.7% | -12.0% | 12.0% | 5.9% |
| q235 A0 fixed-po | e2e_mean_ms | tp8_ep8_mns128 → tp4_ep1_mns128 | tp-axis | 5.7% | -12.0% | 12.0% | 5.9% |
| q235 A0 trace-pd | e2e_p90_ms | tp8_ep8_mns64 → tp8_ep8_mns128 | mns-axis | 6.0% | -16.7% | 16.7% | 6.2% |
| q235 A0 trace-po | ttft_mean_ms | tp8_ep8_mns128 → tp4_ep1_mns64 | mixed | 6.8% | -36.3% | 36.3% | 7.0% |
| q235 A0 trace-po | ttft_p90_ms | tp8_ep8_mns64 → tp4_ep1_mns128 | mixed | 19.2% | -31.6% | 31.6% | 21.2% |
| q235 A0 trace-po | e2e_mean_ms | tp8_ep8_mns128 → tp4_ep1_mns64 | mixed | 6.8% | -36.3% | 36.3% | 7.0% |
| q235 A0 trace-po | e2e_p90_ms | tp8_ep8_mns64 → tp4_ep1_mns128 | mixed | 19.2% | -31.6% | 31.6% | 21.2% |
| q235 A1 fixed-pd | tpot_mean_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 28.5% | -60.1% | 60.1% | 33.0% |
| q235 A1 fixed-pd | tpot_p90_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 31.6% | -61.1% | 61.1% | 37.2% |
| q235 A1 fixed-pd | e2e_mean_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 26.8% | -58.3% | 58.3% | 30.7% |
| q235 A1 fixed-pd | e2e_p90_ms | tp4_ep1_mns128 → tp8_ep8_mns128 | tp-axis | 29.7% | -59.2% | 59.2% | 34.6% |
| q235 A1 trace-pd | e2e_p90_ms | tp8_ep8_mns64 → tp8_ep8_mns128 | mns-axis | 6.0% | -17.4% | 17.4% | 6.2% |

### (b) Where do TP-axis and MNS-axis inversions and boundary ties concentrate?

`n_inv_*` counts sum strict `(real winner, c)` pair inversions across all objectives in each case; a row can contain more than one inverted pair. `n_tie_*` counts cover exact simulator ties only for the simulator-selected winner versus the real winner. Ties remain decision-boundary winner-label mismatches, not strict reversals.

| case | n_inv_tp | n_inv_mns | n_inv_mixed | n_tie_tp | n_tie_mns | n_tie_mixed |
|---|---:|---:|---:|---:|---:|---:|
| q30 trace-pd | 0 | 0 | 0 | 0 | 0 | 0 |
| q30 fixed-pd high | 7 | 3 | 6 | 0 | 0 | 0 |
| q30 fixed-po high | 0 | 0 | 0 | 0 | 4 | 0 |
| q30 fixed-pd low | 8 | 0 | 24 | 0 | 0 | 0 |
| q30 fixed-po low | 0 | 0 | 0 | 0 | 4 | 0 |
| q30 trace-po low | 0 | 6 | 0 | 0 | 2 | 0 |
| q235 A0 fixed-pd | 5 | 0 | 5 | 0 | 1 | 0 |
| q235 A0 fixed-po | 4 | 0 | 4 | 0 | 0 | 0 |
| q235 A0 trace-pd | 0 | 2 | 0 | 0 | 0 | 0 |
| q235 A0 trace-po | 4 | 2 | 4 | 0 | 0 | 0 |
| q235 A1 fixed-pd | 4 | 0 | 4 | 0 | 1 | 0 |
| q235 A1 fixed-po | 0 | 0 | 0 | 0 | 0 | 0 |
| q235 A1 trace-pd | 0 | 2 | 0 | 0 | 0 | 0 |
| q235 A1 trace-po | 0 | 2 | 0 | 0 | 2 | 0 |
| **total** | **32** | **17** | **47** | **0** | **14** | **0** |

- Among strict inversions, TP-axis cases are most concentrated in: q30 fixed-pd low (8), q30 fixed-pd high (7), q235 A0 fixed-pd (5), q235 A0 fixed-po (4), q235 A0 trace-po (4).
- Among strict inversions, MNS-axis cases are most concentrated in: q30 trace-po low (6), q30 fixed-pd high (3), q235 A0 trace-pd (2), q235 A0 trace-po (2), q235 A1 trace-pd (2).
- The eight Q235 A0/A1 Fixed-PD failures are all tp-axis. This does not conflict with the A0/MNS64 state-drift diagnosis, but does not constitute additional state-drift evidence for A1/MNS128.
- Q30 admission evidence does not map one-to-one to an MNS-axis deciding pair: high-pressure Fixed-PD TTFT mean is **mixed** and p90 is **tp-axis**. This is an axis/mechanism mismatch, not a direct causal contradiction: changing TP changes offered arrival pressure, while the diagnosed nonlinear event is crossing the MNS admission cap. It rules out the simpler claim that an MNS-threshold mechanism must appear as an mns-axis winner pair.
- All 14 exact simulator winner ties are mns-axis. Including these boundary errors gives MNS **17 + 14 = 31**, comparable to TP's **32** strict inversions.

The exact ties below show that Frontier is completely insensitive to MNS changes within the corresponding case/objective cell:

| case | objective | real winner ↔ simulator-selected tied winner (MNS pair) |
|---|---|---|
| q30 fixed-po high | ttft_mean_ms | tp4_mns32 ↔ tp4_mns16 |
| q30 fixed-po high | ttft_p90_ms | tp4_mns32 ↔ tp4_mns16 |
| q30 fixed-po high | e2e_mean_ms | tp4_mns32 ↔ tp4_mns16 |
| q30 fixed-po high | e2e_p90_ms | tp4_mns32 ↔ tp4_mns16 |
| q30 fixed-po low | ttft_mean_ms | tp4_mns8 ↔ tp4_mns16 |
| q30 fixed-po low | ttft_p90_ms | tp4_mns8 ↔ tp4_mns16 |
| q30 fixed-po low | e2e_mean_ms | tp4_mns8 ↔ tp4_mns16 |
| q30 fixed-po low | e2e_p90_ms | tp4_mns8 ↔ tp4_mns16 |
| q30 trace-po low | ttft_p90_ms | tp4_mns8 ↔ tp4_mns16 |
| q30 trace-po low | e2e_p90_ms | tp4_mns8 ↔ tp4_mns16 |
| q235 A0 fixed-pd | ttft_p90_ms | tp8_ep8_mns64 ↔ tp8_ep8_mns128 |
| q235 A1 fixed-pd | ttft_p90_ms | tp8_ep8_mns64 ↔ tp8_ep8_mns128 |
| q235 A1 trace-po | ttft_p90_ms | tp8_ep8_mns64 ↔ tp8_ep8_mns128 |
| q235 A1 trace-po | e2e_p90_ms | tp8_ep8_mns64 ↔ tp8_ep8_mns128 |

### (c) How many exact-winner successes are margin-robust?

Among exact winner matches, **17** are margin-robust (`margin >= 1%`) and **6** are fragile (`margin < 1%`). Separately, 14 winner-label mismatches come from exact simulator ties and sit on the decision boundary rather than being strict inversions.

| fragile-success case | objective | real margin |
|---|---|---:|
| q30 trace-pd | e2e_p90_ms | 0.1% |
| q235 A1 fixed-pd | ttft_mean_ms | 0.4% |
| q235 A1 fixed-po | ttft_mean_ms | 0.2% |
| q235 A1 fixed-po | ttft_p90_ms | 0.3% |
| q235 A1 fixed-po | e2e_mean_ms | 0.2% |
| q235 A1 fixed-po | e2e_p90_ms | 0.3% |

## Cross-checks

| check | observed | frozen expectation | result |
|---|---:|---:|---|
| q30 high-pressure fixed-pd TTFT mean regret | 58.0% | 58.0% | PASS |
| q235 A0 fixed-pd TPOT mean regret | 33.0% | 33.0% | PASS |
| q235 A1 fixed-pd TPOT mean regret | 33.0% | 33.0% | PASS |
| q30 trace-pd all-objective regret | 0.0%, 0.0%, 0.0%, 0.0%, 0.0%, 0.0% | 0.0%, 0.0%, 0.0%, 0.0%, 0.0%, 0.0% | PASS |
| q235 Trace-PO TTFT p90 A0 to A1 regret | 21.2%, 0.3% | 21.2%, 0.3% | PASS |
| q235 Fixed-PD TPOT/E2E regrets unchanged from A0 to A1 | 33.0%, 37.2%, 30.7%, 34.6%, 33.0%, 37.2%, 30.7%, 34.6% | 33.0%, 37.2%, 30.7%, 34.6%, 33.0%, 37.2%, 30.7%, 34.6% | PASS |

## Data gaps

No per-config sim/real pairing gaps were found in the requested surfaces.

## 异常

- 无。重算 winner/regret 与 frozen JSON 一致，硬性交叉核对均通过。

## Figure

`margin-vs-residual.png` uses x = `100 × log1p(real best-vs-second relative margin)` and y = `100 ×` real-top-3 log-ratio spread. Both axes are logarithmic because the real margins span six orders of magnitude. Green means exact winner match; red means winner mismatch. The diagonal is the H-SCALE threshold, while failure itself is defined by regret, not by exact winner match.

`decision-pair-axis.png` is a mechanism census, not a hypothesis test: for a strict winner reversal, `-delta_s > m_s` is algebraically equivalent to the mismatch. The frozen surfaces also contain deterministic winner-label mismatches caused by exact simulator ties; those points lie on `-delta_s = m_s` and are not counted as strict inversions. Color identifies the winner-deciding config axis and marker area is proportional to regret.

## A0 vs A1 对照

A1 repairs the Q235 Trace-PO p90 ranking error but leaves the four large Fixed-PD TPOT/E2E regrets unchanged.

| case / objective | A0 regret | A1 regret |
|---|---:|---:|
| trace-po / ttft_p90_ms | 21.2% | 0.3% |
| fixed-pd / tpot_mean_ms | 33.0% | 33.0% |
| fixed-pd / tpot_p90_ms | 37.2% | 37.2% |
| fixed-pd / e2e_mean_ms | 30.7% | 30.7% |
| fixed-pd / e2e_p90_ms | 34.6% | 34.6% |

Thus Trace-PO TTFT p90 changes **21.2% → 0.3%**, whereas Fixed-PD remains **33.0% / 37.2% / 30.7% / 34.6%** in both A0 and A1.

## 已知分量归因摘要

### Q30 high-pressure Fixed-PD TTFT: first-scheduling wait vs execution-side TTFT

`queue-free TTFT` is the execution-side TTFT after removing first-scheduling wait; in the frozen diagnostic, simulated TTFT is their sum (up to floating-point rounding).

| config | sim TPOT / real | sim slots / MNS | real slots upper / MNS | first-scheduling wait | queue-free TTFT | sim TTFT | real TTFT | real waiting max |
|---|---:|---:|---:|---:|---:|---:|---:|---:|
| tp2_mns64 | 8.09x | 58.0/64 | 7.5/64 | 38.2 ms | 191.0 ms | 229.3 ms | 194.6 ms | 0 |
| tp4_mns16 | 3.83x | 54.5/16 | 14.6/16 | 64906.3 ms | 134.7 ms | 65041.0 ms | 124.5 ms | 0 |
| tp4_mns32 | 4.67x | 65.9/32 | 14.5/32 | 27180.7 ms | 135.6 ms | 27316.3 ms | 123.2 ms | 0 |
| tp4_mns64 | 5.61x | 79.8/64 | 14.7/64 | 6367.3 ms | 136.7 ms | 6504.0 ms | 123.2 ms | 0 |

For TP4/MNS32 minus TP2/MNS64, the observed simulator contrast is **+27087.0 ms**; removing first-scheduling wait changes it to **-55.4 ms**, aligned with the real contrast **-71.4 ms**. This localizes the Q30 high-pressure TTFT reversal to admission queueing, while the upstream service-time overprediction remains unattributed in the frozen data.

### Q235 Fixed-PD: own-composition vs exact-state contrast

Positive TP8−TP4 means TP8 is slower and therefore agrees with the real TP4 winner.

| config | sim own decode batch mean | real exact decode batch mean | real token-weighted iteration | exact-state matched sim | coverage |
|---|---:|---:|---:|---:|---:|
| tp4_ep1_mns64 | 13.537 | 3.890 | 18.4710 ms | 34.2575 ms | 100.0% |
| tp8_ep8_mns64 | 18.938 | 10.921 | 27.5887 ms | 45.1603 ms | 100.0% |

| component | own-composition TP8−TP4 | exact-state TP8−TP4 |
|---|---:|---:|
| total | -20.0663 ms | +10.9028 ms |
| moe_compute | -32.4544 ms | -1.9774 ms |
| attention | -7.4619 ms | -2.1304 ms |
| tp_dp_communication | -6.5711 ms | -6.4718 ms |
| ep_communication | +6.2354 ms | +6.5355 ms |
| moe_routing | -0.2862 ms | +0.1384 ms |
| dense_mlp_compute | -0.1231 ms | -0.0308 ms |
| pipeline_communication | +0.0000 ms | +0.0000 ms |
| runtime_overhead | +0.0000 ms | +0.0000 ms |

The total contrast flips from **-20.0663 ms** on Frontier's own composition to **+10.9028 ms** at exact real state, a **+30.9690 ms** state-composition shift. The exact real iteration contrast is **+9.1177 ms** and the frozen real TPOT contrast is **+6.9500 ms**. This supports closed-loop state/composition drift for Q235 Fixed-PD; it does not by itself attribute every remaining conditional execution residual.
