{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__systems_cybernetics","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"systems_cybernetics","decision":"CANDIDATE","problem_id":"coupled_inventory_order_oscillation_blindness","causal_lever_id":"damp_service_risk_inventory_order_modes","proposal":{"problem":"Multi-echelon inventory systems can exhibit persistent shortages, surpluses, and order oscillations because local replenishment rules interact through coupled stock, backlog, forecast, and pipeline states. Site-by-site metrics can remain acceptable while a weakly damped joint mode grows, causing planners to retune individual locations without addressing the system-level direction of amplification.","actors_substrate":["retail and distribution planners","supplier and production planners","inventory, backlog, forecast, pipeline-order, and capacity states","replenishment rules and inter-echelon information delays","customers and workers affected by service or workload variability"],"observable_state":"[HYPOTHESIS] After conditioning on external demand, combinations of inventory, backlog, forecasts, and open orders show repeatable lagged oscillation or growth that individual-variable alarms detect late.","consequence":"[HYPOTHESIS] Repeated local corrections amplify shortages, excess stock, expediting, and workload volatility rather than reliably restoring service.","affected_objective":"Maintain customer service and inventory viability while reducing endogenous oscillation, excess stock, expediting, and unstable workload.","structural_mapping":[{"archetype_element":"Many-variable transformation","domain_realization":"A review-cycle transition maps the joint inventory-order state at time t to time t+1 under current replenishment policies.","claim_kind":"INFERENCE"},{"archetype_element":"Invariant or approximately invariant directions","domain_realization":"Joint patterns across stock, backlog, forecast, pipeline orders, and capacity are candidate dynamic modes rather than independent site symptoms.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Scalar modal response","domain_realization":"Each locally estimated mode receives a persistence, decay, oscillation, or growth estimate over review cycles.","claim_kind":"INFERENCE"},{"archetype_element":"Action-relevant mode selection","domain_realization":"Modes are prioritized by stability, service-risk sensitivity, and reconstruction contribution, not eigenvalue magnitude alone.","claim_kind":"INFERENCE"},{"archetype_element":"Intervention in modal coordinates","domain_realization":"Coordinated changes to smoothing, replenishment gain, or information sharing are chosen for their projected effect on a risky joint mode.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift governance","domain_realization":"Held-out reconstruction error, mode rotation, and spectral-gap loss determine when the local modal account must be revised or retired.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One fixed review interval and a locally linearized closed-loop inventory-order transition under specified demand and capacity regimes."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Scaled inventory, backlog, forecast error, pipeline orders, replenishment decisions, and relevant capacity states by echelon."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenmodes of the estimated review-cycle operator, accepted only when identifiable and numerically conditioned."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues interpreted as local persistence, damping, growth, and oscillation by review cycle."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding preregistered stability-risk or service-sensitivity thresholds while satisfying the residual budget."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify modes as decaying, marginal, growing, or oscillatory within the declared operating window."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map feasible policy controls to changes in risky modal coordinates and record cross-mode effects."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out state transitions and inspect both residual magnitude and structured service-relevant error."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Re-estimate mode direction, ordering, and gain on rolling windows."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Declare the demand, capacity, policy, horizon, scaling, and linearization conditions under which modal claims may be used."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degeneracy, non-normal cross-talk, and controls that move multiple modes."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Bound use to observed neighborhoods without major capacity, assortment, topology, or replenishment-policy changes."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require a preregistered separation between retained and omitted modes; loss of separation suspends reduced-mode decisions."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Factor the explicit or estimated local review-cycle operator; abort modal independence claims if the basis is defective or ill-conditioned.","counterfactual_removal":"Without the dynamic basis and gains, the proposal cannot identify the coupled directions it seeks to damp."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb feasible replenishment controls in simulation and rank their effects on service loss and risky modes, logging cross-effects.","counterfactual_removal":"Removing it leaves no justified bridge from descriptive modes to actionable policy levers."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify review-cycle modes relative to the discrete-time stability boundary within the fitted regime.","counterfactual_removal":"Without it, risky growing or weakly damped modes cannot be distinguished from harmless variation."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor-based mode recovery do not fit an operational supply network; historical transition validation is safer and more relevant.","counterfactual_removal":"No change; operator estimation and held-out validation supply the needed evidence route."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Node-importance ranking does not diagnose temporal closed-loop inventory oscillations.","counterfactual_removal":"No change; node centrality is not the proposed causal lever."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Dominant-only recovery is inadequate because a service-critical weak mode may not be the largest and near-ties matter.","counterfactual_removal":"No change; full-spectrum analysis is required for the bounded test."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions are descriptive and need not equal dynamic amplification directions.","counterfactual_removal":"No change; covariance variance is not used as evidence of stability."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Build a local shadow simulator only after retained modes pass residual and gap gates.","counterfactual_removal":"The full-order model could run the test more slowly; the causal claim would remain unchanged."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use held-out transitions and service-weighted residuals to set retained order and detect omitted structure.","counterfactual_removal":"Without it, compression could silently discard a low-energy but operationally harmful mode."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use singular directions as a non-normal transient-amplification diagnostic, not as substitutes for invariant dynamic modes.","counterfactual_removal":"Eigenvalue stability could falsely reassure when short-run amplification is large, weakening the safety case."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Record scaling, mode meanings, forbidden causal readings, coupling, residuals, and validity limits for decision review.","counterfactual_removal":"The analysis remains computable but becomes easier to misapply outside its supported scope."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Track retained/omitted separation and mode rotation; threshold crossing suspends modal control recommendations.","counterfactual_removal":"There is no timely gate against using a stale or non-identifiable modal basis after regime change."}],"causal_chain":["Local replenishment rules couple inventory, backlog, forecasts, and pipeline orders across echelons.","The resulting review-cycle operator may amplify or weakly damp particular joint state directions.","A locally validated decomposition makes those directions and their gains observable.","Stability and outcome-sensitivity tests identify which modes threaten service and which feasible controls affect them.","A coordinated control adjustment projected to reduce the risky mode should reduce endogenous oscillation without indiscriminate site-level retuning.","Residual, non-normality, drift, and spectral-gap gates limit use to regimes where that inference remains credible."],"baseline":"Ordinary practice is echelon-by-echelon threshold tuning, expediting, and alerting on inventory, backlog, or forecast error separately after symptoms cross limits.","nearest_rival":"A nonlinear system-dynamics delay model with causal-loop policy simulation; it may outperform the modal approach when constraints, saturation, or long delays dominate and no stable local operator exists.","authority_safety":{"affected_parties":["customers exposed to shortages","warehouse and production workers exposed to workload swings","planners and supplier partners","business units bearing inventory and service costs"],"decision_authority":"The accountable supply-chain operations owner, with model-risk review and approval from affected echelon leads.","authorized_first_step":"Run a preregistered, offline shadow test on one product-network segment using temporally held-out review cycles; compare baseline, nearest rival, and modal policies without changing live orders.","excluded_actions":["autonomous live order changes","supplier allocation changes without partner approval","workforce or capacity changes based solely on modal scores","extrapolation beyond the declared demand and capacity window","discarding modes solely because their variance is small"],"halt_rollback":"Halt if held-out residual or service-weighted error exceeds budget, the basis is ill-conditioned, transient amplification violates limits, the spectral gap falls below threshold, modes drift beyond tolerance, or any simulated policy breaches stock, service, capacity, or workload bounds. Retain existing policy and retire the candidate model pending review."}},"negative_tests":{"strongest_counterevidence":"Oscillation may be driven mainly by exogenous demand shocks, nonlinear capacity saturation, discrete ordering constraints, or changing policies; a locally stable eigenmodel could then fit history yet miss the actual cause. Severe non-normal transient growth would also undermine an eigenvalue-only account.","analogy_break":"Unlike a fixed linear transformation, a supply network contains delays, saturation, human overrides, topology changes, and strategic responses. Modes are only approximate local summaries and cannot be treated as globally invariant or independently controllable.","failure_condition":"No sufficiently stationary operating window, identifiable state, well-conditioned modal basis, usable spectral separation, or policy lever exists within safety constraints.","problem_falsifier":"After conditioning on external demand and policy changes, held-out transitions show no reproducible coupled persistent or growing mode, and separate coordinate-level or exogenous-shock models predict oscillation and service loss equally well or better.","intervention_falsifier":"A reproducible risky mode exists, but preregistered modal-targeted policy adjustments do not reduce held-out oscillation and service loss relative to both site-level tuning and the nonlinear system-dynamics rival, or they create unacceptable cross-mode harms.","risks":["False stability from local linearization","Transient amplification from non-normal dynamics","Mode swapping or rotation near a small spectral gap","Causal overclaim from observationally estimated transitions","Service or workload harm from coordinated policy changes","Suppression of locally important low-energy behavior"]},"null_rationale":null,"classification":{"candidate_kind":"PROBLEM_REFRAME","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":"Closed-book structural candidate. The target problem and empirical modal structure are hypotheses; no prior-art or domain-data search was performed."}