# Claim Register

| Claim ID | Claim | Support | Allowed Strength | Verification Needed |
|---|---|---|---|---|
| C01 | Action jitter is better framed as a source that may be amplified by closed-loop geometry. | Reports and CG-RVC materials. | Conceptual thesis. | Check final intro wording. |
| C02 | `rho(K)<1` does not rule out transient amplification in nonnormal systems. | Nonnormal literature in reports. | Standard theory claim. | Cite original nonnormal/pseudospectra references. |
| C03 | State covariance arises from propagated source covariance, not from action variance alone. | Covariance propagation model. | Local surrogate claim. | Include local/white-noise caveat. |
| C04 | Scalar `Var(u)` and action-difference penalties are not amplifier-aware. | Smooth RL review and source-amplifier equations. | Analytical comparison. | Avoid saying they are useless. |
| C05 | `M=Phi_u^T P Phi_u` weights residual covariance by the local certificate metric and input channel. | CG-RVC math. | Local certificate claim. | Use consistent notation. |
| C06 | P-ALE reduces certificate-weighted source covariance, not nonnormality of `K`. | User plan and limitation logic. | Method boundary. | Repeat in limitations. |
| C07 | Projection burden is a downstream diagnostic of safety-layer repair. | Existing CG-RVC projection results. | Diagnostic claim. | Do not equate with global safety. |
| C08 | Residual actor feedback may change the amplifier through `K_theta=K+Phi_u J_r`. | Control feedback reasoning and user plan. | Diagnostic caveat. | Report actor-Jacobian proxy when available. |
| C09 | Controlled interventions can separate amplifier effects from source effects. | CI-1/CI-2/CI-3 design. | Empirical design claim. | Make fixed/manipulated variables explicit. |
| C10 | Current evidence is simulation-level and local-surrogate-level. | Project status. | Limitation. | Keep final paper wording conservative. |
| C11 | CI-1 provides direct evidence that fixed spectral radius and fixed source can still yield very different covariance under nonnormal geometry. | `project_evidence_index.md`; long manuscript CI-1; copied `fig1_ci1_amplifier_isolation.png`. | Controlled-intervention evidence. | Phrase as "can amplify" in this matrix family, not a universal law. |
| C12 | CI-2 provides direct evidence that source-side suppression can reduce downstream covariance when the amplifier is held fixed. | Long manuscript CI-2; copied `fig2_ci2_source_intervention.png`. | Controlled-intervention evidence. | Include colored-input augmentation caveat. |
| C13 | In the matched 2D high-noise ablation, scalar variance and temporal action-diff regularization do not control dense violation or posterior residuals. | Table `tab:v3_pale`; copied `suite_high_noise_comparison.png` and `caps_style_method_comparison_v4_1.png`. | Method-component evidence. | Do not claim smoothing baselines are useless in all settings. |
| C14 | The full response requires source shaping and execution-layer feasibility operations together. | 2D ablation plus projection burden table. | Method-composition evidence. | Do not turn CG-RVC into the sole subject of the problem paper. |
| C15 | Full3D quadrotor evidence supports mechanism relevance in a higher-dimensional numerical simulator. | `tab:full3d_high_noise`; `full3d_5seed_high_noise_summary.png`; raw route `variance_regularized_safe_rl/outputs/uav/full3d_5seed_20260510_233952/`. | External simulation support. | No real-flight, hardware, or broad quadrotor benchmark claim. |
| C16 | ControlGym stress tests are useful because they include both support and failure/boundary behavior. | `tab:controlgym_stress`; copied ControlGym figure; raw route `variance_regularized_safe_rl/outputs/controlgym_full_method/20260421_190814_v3_full_5seed/`. | Limitation and stress-test evidence. | Present CM2 as projection-heavy boundary case, not success. |
| C17 | The certificate in the current evidence stack is empirical and local, not a hard nonlinear ISS certificate. | Surrogate audit: `rho(K_proj)=0.90`, measured `gamma_P=1.43`, Gramian condition `1.86e12`. | Claim-boundary evidence. | Keep theorem-level and empirical diagnostic language separate. |
