{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__statistics_experimental_design","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"statistics_experimental_design","decision":"CANDIDATE","problem_id":"coordinate_designed_experiments_miss_persistent_joint_response_drift","causal_lever_id":"randomized_perturbation_along_risk_weighted_dynamic_modes","proposal":{"problem":"In repeated multivariate process experiments, designs emphasizing named control coordinates and marginal outcomes can judge each setting acceptable while missing control combinations that produce persistent joint quality drift.","actors_substrate":["experimental-design statistician","process engineer","line operators","production batches","adjustable process controls","multivariate quality sensors"],"observable_state":"Marginal treatment estimates and average quality remain acceptable, yet particular control combinations produce repeatable, persistent movement across several quality outcomes.","consequence":"HYPOTHESIS: A setting may be promoted despite amplifying a joint response pattern that later breaches quality or safety limits.","affected_objective":"Valid estimation and safe control of treatment effects on persistent multivariate process behavior.","structural_mapping":[{"archetype_element":"coupled transformation","domain_realization":"A locally stationary state-transition matrix A links one batch's standardized quality vector to the next; a control-response matrix B links randomized settings to that state.","claim_kind":"HYPOTHESIS"},{"archetype_element":"surface coordinates","domain_realization":"Named controls and separately reported quality endpoints.","claim_kind":"CORPUS"},{"archetype_element":"invariant directions","domain_realization":"Joint response patterns approximately preserved by fitted A.","claim_kind":"INFERENCE"},{"archetype_element":"scalar response","domain_realization":"Eigenvalue magnitude and phase describe local persistence, growth, decay, or oscillation.","claim_kind":"INFERENCE"},{"archetype_element":"action relevance","domain_realization":"Risk-weighted outcome sensitivity distinguishes consequential modes from merely large modes.","claim_kind":"HYPOTHESIS"},{"archetype_element":"bounded approximation","domain_realization":"Out-of-sample residuals, spectral separation, and drift determine whether modal interpretation remains usable.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"Fitted local A for batch transitions and B for randomized control effects."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Predeclared standardized quality outcomes measured at each batch."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of A, traced to endpoint loadings."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues of A with uncertainty intervals."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding persistence, safety-weighted sensitivity, or residual-reduction thresholds."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Discrete-time classes based on eigenvalue magnitude, with an uncertainty band around one."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Use B and constrained sensitivity calculations to construct feasible control contrasts."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Held-out one-step prediction error and structured residual tests."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Re-estimate A and compare mode angles and ordering by batch window."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Applies only within tested control ranges, loads, and operating regime; descriptive modes are not automatically causal."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record non-normality, near-degenerate modes, and cross-effects from perturbations."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Certified setting ranges and observed state envelope of the pilot."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Predeclared minimum uncertainty-adjusted separation between retained and omitted modes."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly fitted square transition matrix A; propagate estimation uncertainty.","counterfactual_removal":"No invariant directions or persistence spectrum would anchor the design."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb feasible modal coordinates through B and score safety-weighted outcome response.","counterfactual_removal":"Modes could be described but not converted into prioritized experimental contrasts."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify fitted modes within the declared local regime.","counterfactual_removal":"The design could not distinguish transient variation from persistent or growing drift."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Broad excitation duplicates the bounded randomized pilot and may require unsafe settings.","counterfactual_removal":"No loss; the pilot estimates A and B directly."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Endpoints are state coordinates, not nodes whose eigenvector entries denote importance.","counterfactual_removal":"No loss."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The modest fitted matrix permits full decomposition, while near ties require multiple modes.","counterfactual_removal":"No loss."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not represent transition persistence or treatment leverage.","counterfactual_removal":"No loss."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate is unnecessary for the first identification test.","counterfactual_removal":"No loss to the pilot's causal test."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Test held-out dynamic reconstruction, residual structure, and retained-mode count.","counterfactual_removal":"A misleading low-order model could pass without a fidelity gate."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Apply SVD only to rectangular B to identify feasible control combinations and weakly reachable modes.","counterfactual_removal":"A remains decomposable, but modal perturbations may be poorly targeted."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Record endpoint loadings, uncertainty, couplings, and noncausal interpretation limits.","counterfactual_removal":"Operators could overinterpret tentative modes as independent causal mechanisms."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Gate reuse on uncertainty-adjusted gap and mode-angle drift.","counterfactual_removal":"Continued use after regime change would lack an early invalidation rule."}],"causal_chain":["Coupled batch dynamics can place persistence in combinations of outcomes rather than single endpoints.","Coordinate-focused contrasts and marginal summaries may weakly excite or obscure such combinations.","A bounded randomized pilot estimates local A and control map B.","Decomposition, stability classification, and sensitivity identify feasible contrasts aimed at consequential persistent modes.","HYPOTHESIS: Those contrasts estimate high-risk joint dynamics more precisely than an equal-sized conventional design.","Held-out residual, gap, and drift checks gate interpretation and reuse."],"baseline":"An ordinary randomized factorial or response-surface experiment analyzed with separate endpoint models and marginal control contrasts.","nearest_rival":"A D-optimal response-surface or state-space design in original coordinates that estimates the full A and B matrices without allocating runs by modal risk.","authority_safety":{"affected_parties":["line operators","process owner","customers exposed to released product","batches consumed by the experiment"],"decision_authority":"The process owner and safety/quality engineer jointly approve settings; the statistician controls randomization and analysis but cannot waive operating limits.","authorized_first_step":"Run a 24-batch, low-amplitude randomized crossover comparing modal-risk allocation with the nearest rival, entirely inside certified control ranges and with held-out batches.","excluded_actions":["settings outside certified ranges","release of nonconforming experimental product","unreviewed automated control changes","claims that a statistical mode is a physical cause"],"halt_rollback":"Stop on any existing safety or quality limit, two consecutive excessive prediction residuals, loss of spectral separation, or mode instability across refits; restore the validated baseline settings and quarantine affected batches."}},"negative_tests":{"strongest_counterevidence":"A full D-optimal design in original coordinates may estimate A and B as precisely or better; modal allocation then adds complexity without information gain.","analogy_break":"If dynamics are strongly nonlinear, rapidly shifting, or non-normal with consequential transient growth, eigenmodes of one local A do not behave as independently actionable directions.","failure_condition":"The method fails if retained modes are unstable across resamples, relevant modes are unreachable through B, or held-out residuals exceed the declared budget.","problem_falsifier":"The problem is falsified if preregistered data show negligible cross-coordinate dynamics, an approximately diagonal A, and marginal models predict joint trajectories within tolerance.","intervention_falsifier":"The intervention is falsified if, at equal batch count, modal-risk allocation does not improve precision or detection of the preregistered persistent-risk contrast over the nearest rival, or cannot pass residual and gap gates.","risks":["Small samples can make eigenvectors appear more stable than they are.","Adaptive mode selection can inflate error rates unless selection and confirmation batches are separated.","Risk-weighted endpoints may encode disputed priorities.","Modal perturbations may unintentionally approach operating constraints."]},"null_rationale":null,"classification":{"candidate_kind":"TESTABLE_CONJECTURE","prior_art_status":"UNSEARCHED","evidence_maturity":"HYPOTHESIS"},"revision_change_log":{"revision_kind":"ORIGINAL","prior_problem_id":null,"prior_causal_lever_id":null,"problem_changed":false,"causal_lever_changed":false,"conceptual_changes":[],"operational_changes":[],"repairs_addressed":[]},"confidence":0.76,"generator_notes":"Candidate retained because the target problem independently presents coupled longitudinal responses, an estimable local transformation, actionable combinations, and explicit residual and regime checks. Novelty and empirical advantage are not claimed."}