# Experiment-Claim Matrix

This matrix turns the project-wide evidence search into a writing scaffold for the 6-page paper. Each row states what is manipulated, what is held fixed, what consequence is measured, and what claim boundary must remain visible.

## Main Evidence Rows

| Evidence Block | Question Answered | Manipulated Variable | Fixed Variable | Measured Consequence | Best Source Route | Claim Boundary |
|---|---|---|---|---|---|---|
| CI-1 amplifier scan | Can nonnormal geometry alone amplify downstream covariance? | Eigenvector geometry / nonnormality parameter, summarized by `kappa(V)` and peak transient gain. | Eigenvalues `diag(0.93, 0.68)`, spectral radius, input channel, source covariance. | State covariance trace, `G_peak`, empirical covariance ratio. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex`; `evidence_materials/selected_figures/fig1_ci1_amplifier_isolation.png`; `variance_regularized_safe_rl/outputs/causal_isolation/causal_isolation_suite_latest/`. | Shows an independent amplifier effect in a controlled matrix family, not universal monotonicity for every nonnormal system. |
| CI-2 source intervention | Under a fixed amplifier, can source-side suppression reduce downstream covariance? | Source statistics: white input versus causal filtered input. | Strongly nonnormal matrix from CI-1, input channel, rollout protocol. | Applied action variance and state covariance trace; structural peak gain remains fixed. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex`; `evidence_materials/selected_figures/fig2_ci2_source_intervention.png`; `variance_regularized_safe_rl/outputs/causal_isolation/causal_isolation_suite_latest/`. | Filtered input is colored; interpret via augmented colored-input dynamics, not a direct white-noise theorem. |
| CI-3 source direction scan | Does scalar source trace miss direction-dependent risk? | Principal direction of `Sigma_r` at fixed `tr(Sigma_r)`. | Amplifier `K`, input channel `Phi_u`, total source trace. | Alignment `tr(M Sigma_r)/tr(Sigma_r)`, state covariance, B-L residual. | Planned in `paper_plan.md` and project dossier; no verified completed result found in the scan. | Treat as a recommended enhancement unless an executed result table is later located or generated. |
| 2D constrained RL matched ablation | Are ordinary `Var(u)` and action-diff smoothing enough? | Method component: Direct TD3, plain variance penalty, action-diff penalty, P-ALE, smoothing, projection, full combination. | Environment, high-noise setting, seed matching, TD3 base architecture. | RMSE, applied variance, diff MSE, dense violation, B-L max. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex` table `tab:v3_pale`; `variance_regularized_safe_rl/outputs/cgrvc_revision_tables_20260519_225416/`; copied `suite_high_noise_comparison.png` and `caps_style_method_comparison_v4_1.png`. | Supports method-component necessity; do not describe it as a broad safe-RL benchmark win. |
| Projection burden | Does source shaping reduce safety-layer repair effort? | Projection-enabled method: projection only, P-ALE + projection, full method. | Same 2D high-noise task and projection layer. | Trigger rate, normalized correction magnitude. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex` table `tab:projection_burden`; `variance_regularized_safe_rl/outputs/cgrvc_revision_tables_20260519_225416/`. | Projection burden is an execution diagnostic, not a global safety certificate. |
| Residual-feedback proxy | Does the residual actor risk changing the amplifier? | Learned method: Direct TD3, projection only, full method. | Local perturbation protocol around replay states. | Local action variance, cross-state mean action variance, total proxy variance, finite-difference `||J_r||_F`. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex` table `tab:residual_feedback_proxy`; `variance_regularized_safe_rl/scripts/analyze_cgrvc_conditional_variance.py`; copied `conditional_variance_proxy_summary.png`. | Finite-difference diagnostic only; if `J_r` is large, fold feedback into `K_theta=K+Phi_u J_r`. |
| Planar UAV bridge | Is the mechanism visible in a nonlinear aerial-control numerical setting? | Source-side white versus filtered input under scenario changes. | Planar quadrotor rollout suite and scenario definitions. | State covariance, action/motor variance, smoothness metrics. | `variance_regularized_safe_rl/run_planar_quadrotor_generalization_suite.py`; `variance_regularized_safe_rl/outputs/uav/tmp_generalization_check_20260418_163406/`; copied `suite_high_noise_comparison.png`. | Use mainly as a bridge and boundary case; Payload Mismatch shows lower action variance need not always lower state covariance. |
| Full3D quadrotor simulation | Does source-side suppression persist in a 12D / 4-motor numerical simulation? | White versus filtered motor/source input across scenarios. | Full3D simulator, 5 seeds, 48 rollouts per scenario/seed, horizon 80, high noise key 0.20. | State covariance trace and motor variance. | `variance_regularized_safe_rl/outputs/uav/full3d_5seed_20260510_233952/`; `paper_spine_tac_source_amplifier_20260521_best/submission_v2_From_Action_Smoothing_to_Source_Amplifier_Control_2026-05-22/results_selected/full3d_5seed/`; copied `full3d_5seed_high_noise_summary.png`. | Simulation-level relevance only; no hardware or learned Full3D policy-dominance claim. |
| ControlGym stress test | Where does the framework help, and where does execution dominate source shaping? | Full method versus unregularized controller on AC3 and CM2. | ControlGym stress-test protocol, high-noise summary. | State trace, applied variance, B-L max, strict infeasible rate. | `variance_regularized_safe_rl/outputs/controlgym_full_method/20260421_190814_v3_full_5seed/`; copied `controlgym_suite_high_noise_comparison.png`. | AC3 is supportive; CM2 is a failure/boundary case with projection-heavy behavior. |
| Surrogate/certificate audit | Is the certificate a hard nonlinear guarantee? | Projected surrogate audit and certificate conditioning. | Fitted local surrogate and `rho(K_proj)=0.90` target. | Measured `gamma_P`, Lyapunov residual, Gramian conditioning. | Evidence-chain table in `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex`; project review notes. | Keeps claim at empirical local-surrogate diagnostic level; no global nonlinear safety theorem. |

## Writing Order Recommendation

1. Start experiments with CI-1 because it isolates the amplifier.
2. Pair CI-1 with CI-2 because it isolates the source under a fixed amplifier.
3. Use the 2D matched ablation to show why scalar/temporal smoothing and projection-only repair are incomplete.
4. Use projection burden and residual-feedback proxy as diagnostics, not as primary performance claims.
5. Move Planar UAV, Full3D, and ControlGym to external relevance and limitations unless page budget allows a compact supplementary panel.

## Claim-Level Guardrails

- Say "local surrogate", "diagnostic", "numerical simulation", and "evidence for the mechanism" when describing the current evidence.
- Do not say "global nonlinear safety guarantee", "hardware validation", or "general safe-RL dominance".
- Do not say P-ALE reduces nonnormality. It reduces certificate-weighted residual source covariance entering a nonnormal amplifier.
- Do not say ordinary action smoothing is useless. Say it is not amplifier-aware and can be insufficient under strong nonnormal amplification.
