{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__nanotechnology","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"nanotechnology","decision":"CANDIDATE","problem_id":"hidden_coupled_instability_in_nanoparticle_synthesis","causal_lever_id":"unstable_synthesis_mode_detection_and_damping","proposal":{"problem":"In nanoparticle synthesis, coupled changes in temperature, reagent concentrations, mixing, surface coverage, and particle-size moments can develop into aggregation or widening size distributions while averages remain within ordinary limits. Coordinate-wise monitoring and adjustment can therefore miss a weakly damped or growing combination of states until the batch is irrecoverable. Whether this pattern occurs reproducibly in a given process is a HYPOTHESIS.","actors_substrate":["nanoparticle synthesis operators and process engineers","instrumented batch or continuous reactor","time-resolved process variables and particle-distribution summaries","downstream users of the nanomaterial","workers and environments potentially exposed to off-spec material"],"observable_state":"Time-indexed reactor and particle-population state vectors, estimated local transitions, modal gains, retained-mode residuals, mode rotation, spectral separation, and final size-distribution or aggregation outcomes.","consequence":"Late detection causes off-spec batches, unnecessary whole-coordinate adjustments, or interventions that suppress a visible symptom while amplifying another coupled direction.","affected_objective":"Maintain particle-size and dispersion specifications with earlier, traceable detection and bounded correction of coupled process instability.","structural_mapping":[{"archetype_element":"coupled transformation","domain_realization":"A locally fitted transition or Jacobian maps the reactor-plus-particle state from one sampling interval to the next.","claim_kind":"HYPOTHESIS"},{"archetype_element":"invariant directions and scalar response","domain_realization":"Eigenmodes represent combinations of measured states that approximately persist while their gains indicate decay, persistence, oscillation, or growth.","claim_kind":"INFERENCE"},{"archetype_element":"dominance by consequence rather than visibility","domain_realization":"Modes are ranked by predicted and experimentally probed effects on aggregation and distribution width, not merely present amplitude.","claim_kind":"HYPOTHESIS"},{"archetype_element":"modal intervention","domain_realization":"Permitted set-point changes are mapped to the state combinations they damp or excite before any operator-approved adjustment.","claim_kind":"INFERENCE"},{"archetype_element":"residual and drift governance","domain_realization":"Reconstruction error, mode rotation, and spectral-gap loss suspend reliance on the reduced modal view.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"direct","domain_realization":"One synthesis recipe, reactor configuration, sampling interval, and operating neighborhood."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Standardized temperature, feed, mixing, concentration, surface-coverage proxies, and particle-distribution moments with recorded missingness."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Locally estimated eigenvectors of the state-transition operator."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues with uncertainty and conditioning diagnostics."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding stability-risk, outcome-sensitivity, or reconstruction-value thresholds."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify discrete-time gains as decaying, marginal, growing, or oscillatory within the fitted window."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map allowed actuator perturbations to modal movement and predicted quality response."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample state and quality reconstruction error, including residual structure."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Scheduled comparison of modal directions, gains, and ordering."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Recipe, scale, sensor, disturbance, and state ranges within which modal claims may guide decisions."},{"component":"Mode-Coupling Register","status":"adapted","domain_realization":"Log near-degenerate, non-normal, and perturbation-induced cross-mode effects."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Explicit operating-state and perturbation bounds for the local transition model."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Minimum retained-to-dropped separation required for stable selection and monitoring."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit fitted local transition operator; report conditioning rather than assuming an orthogonal basis.","counterfactual_removal":"No invariant directions or gains remain to support the proposed diagnosis."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Use small, authorized actuator perturbations to rank outcome leverage and record cross-effects.","counterfactual_removal":"Mode ranking would not identify which controllable direction affects quality."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Partition modes using discrete-time stability boundaries only inside the declared window.","counterfactual_removal":"The proposal could not distinguish growing warnings from harmless large modes."},{"slug":"mode_shape_testing","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Adapt excitation-response testing to small reactor set-point pulses that validate predicted mode shapes.","counterfactual_removal":"The analytical modes could still be used, but their physical validity would be less directly tested."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"The state variables are dynamical coordinates, not nodes whose eigenvector entries represent importance.","counterfactual_removal":"No causal or viability change."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Dominant-only estimation is insufficient because a lower-amplitude unstable mode may matter and a full local operator is assumed available.","counterfactual_removal":"No change to the full-spectrum workflow."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance modes do not establish transition persistence or stability; PCA may describe data but cannot carry the causal chain.","counterfactual_removal":"No causal change."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Run retained modes as a bounded advisory surrogate, never as autonomous control.","counterfactual_removal":"Diagnosis remains possible, but rapid intervention screening becomes impractical."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Test held-out temporal and quality reconstruction against predeclared tolerances.","counterfactual_removal":"Discarded dynamics could remain invisible, making deployment unsafe."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"SVD is reserved as a conditioning diagnostic; its paired amplification directions are not invariant temporal modes.","counterfactual_removal":"The eigenmode causal chain remains intact."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document uncertainty, coupling, traceability, and prohibited interpretations for operators.","counterfactual_removal":"Mathematics remains, but misuse risk materially increases."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track retained/dropped separation and direction drift; alarm suspends the advisory model.","counterfactual_removal":"A once-valid basis could silently remain in service after regime change."}],"causal_chain":["Coupled synthesis states evolve through an approximately stationary local transformation (HYPOTHESIS).","Decomposition exposes combinations whose gains indicate weak damping or growth.","Sensitivity tests identify which permitted actuator combinations damp quality-relevant modes without unacceptable cross-effects (HYPOTHESIS).","Operator-approved modal guidance reduces growth before endpoint aggregation or distribution widening becomes visible (HYPOTHESIS).","Residual, gap, and drift checks halt guidance when the approximation loses validity."],"baseline":"Fixed recipes, univariate alarms on named process variables, endpoint sampling, and operator adjustment of whichever coordinate crosses a limit.","nearest_rival":"Multivariate statistical process control or PCA-based monitoring that flags correlated deviation but does not classify temporal mode stability or map actuators to invariant directions.","authority_safety":{"affected_parties":["reactor operators and workers","process and quality engineers","downstream material users","people or environments exposed to released material"],"decision_authority":"The accountable process owner approves the pilot; trained operators retain every actuator decision; safety and quality personnel set hard limits and disposition material.","authorized_first_step":"Replay historical runs, then conduct one instrumented small-scale pilot using only preapproved sub-limit perturbations; compare warning lead time, false alarms, residuals, and final quality against baseline and the nearest rival.","excluded_actions":["autonomous set-point changes","production-scale extrapolation","release of pilot material","perturbations beyond existing process and exposure limits","discarding raw-coordinate alarms"],"halt_rollback":"Stop perturbations and revert to the validated recipe if any hard safety limit is approached, residual tolerance fails, the spectral gap falls below threshold, modes rotate beyond tolerance, or quality worsens; quarantine the pilot material."}},"negative_tests":{"strongest_counterevidence":"Observed deviations may be dominated by nonlinear nucleation events, sensor artifacts, or unmeasured contamination rather than a stationary local transformation; non-normal transient amplification may also make eigenvalue stability misleading.","analogy_break":"Nanoparticle synthesis can cross abrupt phase, nucleation, or aggregation boundaries where no useful linearization window exists and invariant modes estimated on one side have no meaning on the other.","failure_condition":"The candidate fails if modes are ill-conditioned or nonreproducible, no safe perturbations excite them, or acceptable residual and drift bounds leave no useful operating window.","problem_falsifier":"Across repeated runs, quality excursions are fully predicted by one directly observable variable or show no reproducible coupled temporal structure beyond measurement error.","intervention_falsifier":"Within the bounded pilot, modal guidance fails to improve preregistered warning lead time or quality versus both baseline and the nearest rival, or improvement disappears out of sample despite acceptable residuals.","risks":["False confidence from local linearization","Unsafe correction caused by unregistered mode coupling","Missed low-amplitude quality-critical dynamics","Sensor scaling or drift changing the inferred basis","Mode swapping near a small spectral gap","Operator overreliance on an advisory surrogate"]},"null_rationale":null,"classification":{"candidate_kind":"MECHANISM_COMPOSITION","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":0.8,"generator_notes":"Closed-book structural inference. The target problem and intervention effects require empirical confirmation; no novelty or prior-art claim is made."}