# GRAV-BRIDGE-I.1 — Global Full-Curve Closure Audit

## Closure question

Did the compact STRUC-I summaries used by GRAV-BRIDGE-I v0.1.0 discard useful
incremental information contained in the shapes of the full chamber curves?

The audit used all 40 kappa points of rho(kappa), A_kappa(kappa), and nu(V_kappa)(kappa).
Each channel was compressed to three fold-local principal components. Scaling and PCA were
fitted on unique training galaxies only, and the exact parent five-fold galaxy registry was reused.

## Primary combined-curve result

| Quantity | Result |
|---|---:|
| M2 held-out RMSE | 0.188389 |
| M2 + all full-curve PCs | 0.187569 |
| Delta RMSE | 0.000820 |
| Relative improvement | 0.435% |
| Full-data training delta | 0.006260 |
| Positive outer folds | 1 / 5 |
| Curve-assignment null p-value | 0.0198 |
| Bootstrap 95% interval | [-0.005244, 0.006939] |
| Bootstrap positive fraction | 59.80% |

**Audit verdict: `WEAK_FOLD_DEPENDENT_FULL_CURVE_SIGNAL`**

The combined curve representation produced a very small positive aggregate improvement,
but it failed the robustness gates. The gain was below 1%, only 1
of five folds improved, and the paired-galaxy bootstrap interval crossed zero.

The correct galaxy-to-curve assignment did outperform shuffled assignments. Thus the curves
retain galaxy-specific information, but the information is not sufficiently stable to establish
incremental gravitational prediction.

## Primary fold deltas

| Fold | Delta RMSE |
|---:|---:|
| 1 | -0.003533 |
| 2 | -0.000030 |
| 3 | -0.005383 |
| 4 | 0.010679 |
| 5 | -0.000385 |

## Bounded channel decomposition

| Model | Held-out RMSE | Delta vs M2 | Relative | Positive folds | Null p | Holm p | Bootstrap 95% interval |
|---|---:|---:|---:|---:|---:|---:|---|
| M2_FC_RHO | 0.186237 | 0.002152 | 1.142% | 4 / 5 | 0.0348 | 0.0891 | [-0.002819, 0.007208] |
| M2_FC_AK | 0.187527 | 0.000862 | 0.457% | 3 / 5 | 0.0297 | 0.0891 | [-0.005249, 0.006343] |
| M2_FC_NU | 0.191246 | -0.002857 | -1.516% | 1 / 5 |  | 1.0000 | [-0.005324, -0.000608] |

The rho(kappa) channel was the strongest diagnostic: it improved four of five folds and
exceeded the 1% relative threshold. Its raw curve-assignment p-value was below 0.05, but
it did not survive the bounded three-channel Holm correction and its bootstrap interval
crossed zero. It is therefore the **leading channel-specific transfer indication** and motivates a targeted local or regime-conditioned confirmation experiment.

## Rho fold deltas

| Fold | Delta RMSE |
|---:|---:|
| 1 | 0.001791 |
| 2 | 0.001468 |
| 3 | 0.003998 |
| 4 | 0.008421 |
| 5 | -0.006434 |

## What this closes—and what it does not

1. Summary compression was not the sole cause of the v0.1.0 negative result.
2. The combined full curves do not produce a robust, fold-stable global bridge.
3. The parent verdict remains **`NON_GENERALIZING_SIGNAL`**.
4. The generalized static whole-galaxy bridge is not reopened.
5. No single-channel result met the confirmation gate; the static global-curve branch closes.

## Branch decision

**`STATIC_GLOBAL_CURVE_BRANCH_CLOSED`**

No channel-specific confirmatory test is justified.

Any future gravity work must therefore raise a different hypothesis, such as local transition alignment or observational-stability testing, rather than retuning this static global bridge.

---

## v0.3 project interpretation

This document belongs to the external transfer experiment. Numerical, technical, protocol, or provenance content above is preserved. The transfer result tests one static global architecture: it does not negate the galaxy-specific structural information carried by the curves. Complete curves retain identity, and ρ is the leading channel for local or regime-conditioned follow-up.

