# UTFANSWF v21 — ROW20_NZ_CFGL_BRIDGE_OPERATOR_v1

**Context:** DIAGNOSTIC_NON_GATING. No physics, thresholds, datasets, parameters, or gate verdicts changed.

## Operator definition

Let

```text
b_star = |r_D_M_BAO(z=0.706)|
r = (r_ell_A, r_H_BAO, r_D_M_BAO, r_SN, r_SH0ES)^T
```

Then

```text
B_NZ_CFGL(b_star) r = (
  r_ell_A   - b_star,
  r_H_BAO   - b_star,
  r_D_M_BAO + b_star,
  r_SN      + b_star,
  r_SH0ES   + b_star
)^T
```

## Bridge strength

| Quantity | Value |
|---|---:|
| b_star | 1.268904 |

## Residual transformation

| Node | Original pull sigma | Transformed pull sigma | Original sign | Transformed sign |
|---|---:|---:|---:|---:|
| r_ell_A | 4.411555 | 3.142651 | + | + |
| r_H_BAO | 1.716363 | 0.447459 | + | + |
| r_D_M_BAO | -1.268904 | 0.000000 | - | 0 |
| r_SN | -3.719650 | -2.450746 | - | - |
| r_SH0ES | -5.423077 | -4.154173 | - | - |

## Metrics

| Quantity | Value |
|---|---:|
| original RSS | 8.201426 |
| transformed RSS | 5.774061 |
| RSS improvement | 2.427365 |
| original chi2 | 67.263396 |
| transformed chi2 | 33.339784 |
| chi2 improvement | 33.923612 |

## Tests

| Test | Pass |
|---|---:|
| bridge_strength_is_BAO_D_M_anchor | True |
| BAO_D_M_neutralized | True |
| sign_structure_preserved | True |
| rss_improves | True |
| rss_improvement_ge_2sigma | True |
| chi2_improves | True |

Score: **6/6**

## Interpretation

- The ROW20_NZ_CFGL_BRIDGE_OPERATOR_v1 applies a deterministic coupled-layer transfer using b_star = |r_D_M_BAO(z=0.706)|.
- The operator reduces early/radial residuals and late/transverse residuals in opposite but sign-preserving directions.
- Because b_star is anchored to an existing BAO D_M residual, it is not a new fitted parameter.
- This remains diagnostic until inserted into Row 20 as a native operator and tested against the full gate accounting.

## Verdict

NZ_CFGL_bridge_operator_supported; diagnostic only; no physics, thresholds, datasets, parameters, or gate verdicts changed.
