# Causal Isolation Suite Report

## Purpose

This suite reframes the paper around **controlled interventions** rather than around certificates alone.
The causal chain under study is:

`source -> suppressor -> applied input statistics -> non-normal amplifier -> transient gain -> state covariance`

The suite is not presented as a structural-causal-model paper. Instead, it uses control-theoretic interventions:

- `do(source)`: hold `A_cl` fixed and change input statistics or spectrum.
- `do(amplifier)`: hold `Lambda`, `rho`, `G`, and `W_eff` fixed and change only the eigenvector geometry of `A_cl`.

Projection and certificates are treated as an **analysis branch**, not as part of the physical performance path.

## Mechanism and Controlled Interventions

We define four objects:

- `source`: the pre-suppression disturbance statistics and spectrum.
- `suppressor F`: the input-side variance suppression layer that shapes the applied input.
- `amplifier`: the non-normal geometry of `A_cl`, summarized by `kappa(V)` and peak transient gain.
- `outcome`: `peak gain`, `trace(Sigma_x)`, and `E[max_t ||x_t||]`.

The main state covariance equation is

`Sigma_x = sum_k A_cl^k G W_eff G^T (A_cl^k)^T`

with `W_eff` determined by the source and the suppressor, while the geometry of `A_cl` determines how strongly disturbances are propagated and transiently amplified.

### Amplifier-isolation proposition

When the eigenvalue set, spectral radius, input channel, and `W_eff` are held fixed, changes in `trace(Sigma_x)` and peak gain are attributable to the non-normal geometry of `A_cl`.

### Source-intervention proposition

When `A_cl` is held fixed, the suppressor acts by modifying `W_eff` or its effective spectrum; any reduction in state covariance is then attributable to altered disturbance propagation rather than altered closed-loop geometry.

## CI-1: Amplifier-only synthetic sweep

- Intervention target: `amplifier`
- Evidence role: `mechanism_isolation`
- Held constant: fixed eigenvalues, `rho = 0.93`, fixed `G`, fixed white `W`.
- Manipulated factor: `similarity shear alpha -> kappa(V)`

Key findings:

- `kappa(V)` vs `trace(Sigma_x)`: Pearson = 0.970 (95% CI 0.958, 0.985)
- `kappa(V)` vs `peak gain`: Pearson = 0.996 (95% CI 0.993, 1.000)
- Across the sweep, the covariance-trace change is 15.2854 and the peak-gain change is 4.5486.

Interpretation:

This is the main mechanism-isolation evidence for the claim that non-normality acts as an amplifier. Because `rho`, `Lambda`, `G`, and `W` are fixed, the growth in `trace(Sigma_x)` and peak gain cannot be attributed to nominal instability.

## CI-2: Source-only intervention under fixed strongly non-normal dynamics

- Intervention target: `source`
- Evidence role: `mechanism_isolation`
- Held constant: fixed strongly non-normal `A_cl`, fixed `rho = 0.930`, fixed `kappa(V) = 20.050`.
- Manipulated factor: `white vs filtered applied input statistics`

Measured effects:

- White applied-action variance: 0.03992
- Filtered applied-action variance: 0.00317
- White state covariance trace: 15.84928
- Filtered state covariance trace: 12.39272
- `delta_action_var = -0.03675`
- `delta_state_cov = -3.45656`
- `delta_peak_gain = 0.00000` (zero by construction because the amplifier is held fixed)

Interpretation:

This intervention isolates the source/suppressor path. The structural peak gain of the closed loop is unchanged; any change in state covariance comes from altered applied-input statistics rather than altered closed-loop geometry.

## CI-3: UAV bridge experiment

- Evidence role: `external_validation`
- Positioning: mechanism-consistent external validation only

Bridge summary:

- Mean action-variance reduction across scenarios: 87.97%
- Mean state-covariance reduction across scenarios: 36.88%
- Mean raw peak gain across scenarios: 9.29
- Mean raw `kappa(V)` across scenarios: 37.02

Interpretation:

The UAV suite should be described as realistic external validation that is **consistent with** the controlled-isolation evidence. It should not be described as strict causal identification. If projected peak gain does not improve, projection must remain a certificate/diagnostic branch rather than a performance contribution.

## Writing Guardrails

Use:

- `rarely made explicit`
- `under-emphasized`
- `not treated as the central mechanism`
- `mechanism-consistent external validation`

Avoid:

- `prior RL does not consider non-normality`
- `projection improves performance`
- `variance always decreases`
- `strict SCM identification`

## Output Files

- `trace_sigma_vs_kappa.png`
- `peak_gain_vs_kappa.png`
- `source_intervention_comparison.png`
- `uav_bridge_consistency.png`
- `summary.json`
- `report.md`
