# UTFANSWF v21 — BAO H Wall Probe

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

## Original BAO z=0.706 radial/transverse pair

| Quantity | Value |
|---|---:|
| H pull | 1.716363 |
| D_M pull | -1.268904 |
| H - D_M gap | 2.985267 |
| pair mean pull | 0.223729 |
| pair half-gap | 1.492633 |

## BAO H wall after first operator

| Quantity | Value |
|---|---:|
| BAO H remaining | 0.447459 |
| SN remaining | -2.450746 |
| SH0ES remaining | -4.154173 |
| desired second transfer from SN | 2.450746 |
| allowed transfer before BAO H flip | 0.447459 |
| blocked amount | 2.003288 |
| blocked fraction of desired | 0.817419 |

## After capped second operator

| Node | Residual |
|---|---:|
| r_ell_A | 2.695192 |
| r_H_BAO | 0.000000 |
| r_D_M_BAO | 0.000000 |
| r_SN | -2.003288 |
| r_SH0ES | -3.706714 |

Final capped RSS: **5.001695**

## Interpretation

- BAO H is the wall because after the first NZ/CFGL bridge it is the smallest remaining positive early/radial residual.
- The SN-desired second operator exceeds the available BAO H headroom, so a full second transfer would flip BAO H.
- The original BAO z=0.706 H and D_M pulls form a significant radial/transverse split.
- This indicates the current wall is a radial/transverse projection constraint, not a random residual.
- More than half of the desired second transfer is blocked by BAO H headroom; current v21 operators cannot fully resolve H0 without a deeper radial/transverse mapping.

## Verdict

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