# Evidence Bank

Each row records a claim, source anchor, intended manuscript use, and caution. The rows are writing aids, not final citations.

| ID | Claim | Source File | Section Anchor | Usable Text Move | Caution |
|---|---|---|---|---|---|
| E01 | Nonnormal closed-loop matrices can exhibit transient amplification even when spectral radius indicates asymptotic stability. | `references/final_report.md` | Literature review on pseudospectra and transient growth | Use to motivate why `rho(K)<1` is insufficient for RL closed-loop risk. | Verify final citation from original nonnormality literature. |
| E02 | Residual action covariance should be treated as a source entering a closed-loop input channel. | `references/final_report.md` | Concept Map: Residual Action Covariance and Input Channel | Define sources as residual action, exploration noise, execution noise, actuator noise, and disturbances. | Do not imply all sources are independent or exogenous. |
| E03 | State covariance is a propagated consequence, not the same object as action variance. | `references/deep-research-report (49).md` | Concept Map and Final Synthesis | Add the sentence: "Action variance becomes state variance only after propagation through the closed-loop amplifier." | For colored inputs, use augmented dynamics or qualify the covariance formula. |
| E04 | Ordinary `Var(u)` regularization measures scalar source energy but ignores input directions and amplifier geometry. | `references/final_report.md` | RL action variance and smooth control review | Page 3 critique of scalar action smoothing. | Avoid claiming scalar smoothing is useless in all systems. |
| E05 | Action-difference penalties suppress temporal roughness but do not identify high-amplification input directions. | `references/final_report.md` | Smooth RL and action regularization review | Distinguish temporal regularity from amplifier-aware residual covariance control. | If baseline includes CAPS or filtering, describe precisely. |
| E06 | A Lyapunov metric can map residual action covariance into certificate-weighted energy via `M=Phi_u^T P Phi_u`. | Existing CG-RVC materials and reports | Lyapunov certificate and Koopman surrogate sections | Introduce P-ALE as a minimal response, not the whole paper. | Explain that P-ALE reduces weighted source covariance, not nonnormality of `K`. |
| E07 | Local Koopman or EDMDc surrogates provide a practical way to estimate lifted closed-loop dynamics. | `references/final_report.md` | Koopman / EDMD / data-driven surrogate review | Justify using `z=psi(x)` and local regression in Page 4. | State surrogate validation is required. |
| E08 | Safety projection can be an execution-layer feasibility operation but not a global safety proof. | `references/final_report.md` | Safe RL, shielding, and projection review | Use in method and limitations sections. | Include locally feasible set caveat. |
| E09 | Residual policies can act as feedback and change the closed-loop amplifier. | User plan and existing diagnostics | Residual feedback caveat | Add `K_theta=K+Phi_u J_r` and report actor-Jacobian diagnostics. | If `J_r` is large, source-only interpretation weakens. |
| E10 | Controlled interventions should separate source and amplifier effects. | `references/deep-research-report (49).md` | Research Gap Analysis and How to Position a New Paper | Frame CI-1, CI-2, and CI-3 as the empirical spine of the paper. | Make fixed and manipulated variables explicit in captions. |
| E11 | Projection burden is a key downstream diagnostic because source shaping may reduce safety-layer repair. | Existing CG-RVC results | Projection burden diagnostics | Use projection trigger rate and normalized correction in Figure 3. | Do not equate lower projection correction with formal safety. |
| E12 | Simulation-level evidence should be presented as relevance, not deployment validation. | User plan and reports | Limitations and failure modes | Use for quadrotor and ControlGym discussion. | Avoid real-flight or benchmark dominance language. |
| E13 | CI-1 isolates amplifier geometry under fixed eigenvalues, input channel, and source covariance. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex` | CI-1: Amplifier Isolation | Use numbers: `kappa(V)` about 1.0 to 20.05, covariance trace about 0.37 to 15.66, peak gain about 1.0 to 5.55. | Controlled construction only; do not claim universal monotonicity. |
| E14 | CI-2 supports source-side intervention under a fixed physical amplifier. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex`; copied `fig2_ci2_source_intervention.png` | CI-2: Source-Side Intervention | Use numbers: action variance 0.03992 to 0.00317; state covariance 15.849 to 12.393. | Filtered input is colored; interpret via augmented dynamics. |
| E15 | The full 2D matched ablation shows ordinary smoothing baselines are insufficient. | `paper_spine_tac_source_amplifier_20260521_best/final_paper/main.tex`, table `tab:v3_pale` | P-ALE matched comparison | Contrast Direct TD3, plain `Var(u)`, action-diff, and CG-RVC on dense violation and B-L max. | It is a matched method-component comparison, not an exhaustive hyperparameter study. |
| E16 | P-ALE alone and projection alone each leave important failure modes. | Same as E15 | P-ALE matched comparison | P-ALE alone keeps dense violation high; projection only leaves high applied variance and posterior residuals. | Use to argue for combined response, not to dismiss either component. |
| E17 | Projection burden decreases when source shaping is added. | Same long paper, table `tab:projection_burden` | Projection burden diagnostics | Normalized correction drops from 0.09362 projection-only to 0.05426 P-ALE+projection and 0.01093 CG-RVC. | Projection burden is an execution diagnostic, not formal safety proof. |
| E18 | Actor-Jacobian proxy supports the residual-feedback caveat. | Same long paper, table `tab:residual_feedback_proxy`; copied `conditional_variance_proxy_summary.png` | Residual-feedback perturbation proxy | Actor-Jacobian proxy drops from 16.23 Direct TD3 to 0.274 CG-RVC. | Finite-difference diagnostic only. |
| E19 | Full3D quadrotor simulation extends source-side suppression evidence to a 12D/4-motor numerical setting. | Same long paper, table `tab:full3d_high_noise`; copied Full3D figure | Full3D high-noise comparison | State covariance and motor variance decrease in all four Full3D scenarios under filtering. | Simulation-level evidence, not real flight. |
| E20 | Planar UAV includes a useful boundary case. | Same long paper | Planar UAV discussion | Payload Mismatch lowers action variance but raises state covariance, supporting direction-aware risk rather than scalar variance alone. | Scenario-level bridge, not main benchmark. |
| E21 | ControlGym AC3 supports the diagnostic pattern while CM2 reveals a failure mode. | Same long paper, table `tab:controlgym_stress`; copied ControlGym figure | High-dimensional stress test | AC3 improves on state trace, applied variance, and B-L max; CM2 becomes projection-heavy with strict infeasible rate 1.0. | Use in limitations/failure modes. |
| E22 | Surrogate audit forces cautious certificate language. | Same long paper evidence-chain table | Surrogate audit | `rho(K_proj)=0.90`, `gamma_P=1.43`, Gramian condition `1.86e12`; interpret B-L residual and projection burden empirically. | Do not claim active ISS-style certificate if `gamma_P>1`. |
| E23 | Project contains implementation-level support for planar UAV scenarios. | `variance_regularized_safe_rl/run_planar_quadrotor_generalization_suite.py` | Code evidence | Use as provenance for planar quadrotor generalization suite and eigenvalue-clipping projection strategy. | Duplicate copies exist in package folders; cite canonical root copy when possible. |
| E24 | Project contains curated result/figure packages. | `paper_spine_tac_source_amplifier_20260521_best/submission_v2_From_Action_Smoothing_to_Source_Amplifier_Control_2026-05-22/results_selected/` | Curated results | Prefer these selected outputs for figures and numbers over raw package retries. | Link copied figures to raw result data before final submission. |

## Evidence Transfer Checklist

- Check every formal citation against the original DOI or paper.
- Keep controlled-intervention evidence separate from RL ablation evidence.
- Mark colored-input experiments with the augmented-system caveat.
- Report both `K` metrics and actor-augmented `K_theta` metrics when residual feedback is state-dependent.
- Keep projection results as burden and feasibility diagnostics, not global safety proof.
- Prefer `project_evidence_dossier.md` and `project_evidence_index.md` for repository-mined evidence routing.
