{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__logistics_supply_chain","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"logistics_supply_chain","decision":"CANDIDATE","problem_id":"multi_echelon_replenishment_oscillation","causal_lever_id":"modal_damping_of_replenishment_feedback","proposal":{"problem":"Multi-echelon replenishment systems can exhibit recurring inventory, backlog, and order oscillations that amplify across locations even when individual SKU-location metrics appear acceptable. HYPOTHESIS: coupled ordering, forecasting, and lead-time feedback contains weakly damped or unstable combinations of state variables that coordinate-level alerts and isolated parameter changes miss.","actors_substrate":["Planners and inventory-control owners","Suppliers, warehouses, and stores or fulfillment nodes","Customers exposed to shortages or delay","SKU-echelon replenishment states and order pipelines"],"observable_state":"Per review period and SKU-echelon: on-hand and inventory position, backlog, open orders by remaining lead time, demand and forecast error, replenishment orders, receipts, capacity constraints, and service outcomes.","consequence":"Growing or persistent joint modes can produce alternating excess inventory and shortages, expedite activity, unstable supplier orders, and misleading local corrective action.","affected_objective":"Reduce endogenous replenishment oscillation and shortage/excess exposure without degrading service, throughput, or safety-stock protections.","structural_mapping":[{"archetype_element":"Coupled transformation","domain_realization":"INFERENCE: one review-cycle transition maps the network state—inventory, backlog, pipeline orders, forecasts, and replenishment decisions—to its next state.","claim_kind":"INFERENCE"},{"archetype_element":"Invariant directions and scalar response","domain_realization":"HYPOTHESIS: locally repeatable combinations of echelon states decay, persist, oscillate, or grow under the fitted transition.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Dominant or unstable modes","domain_realization":"HYPOTHESIS: a small set of replenishment-feedback modes explains decision-relevant oscillation better than isolated SKU-location excursions.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Modal intervention","domain_realization":"Policy parameters such as forecast smoothing, order-up-to feedback gains, review cadence, and lead-time treatment are mapped to their effects on risky modes.","claim_kind":"INFERENCE"},{"archetype_element":"Residual and drift governance","domain_realization":"Holdout reconstruction, mode stability, spectral separation, and residual structure determine whether the modal model remains usable.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One replenishment review-cycle transition for selected SKUs and connected echelons."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Scaled inventory, backlog, pipeline, forecast-error, order, receipt, and constraint variables."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of a fitted local state-transition operator, with conditioning checks."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalue magnitude and phase describe decay, growth, persistence, and oscillation."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes crossing preregistered stability, outcome-sensitivity, or reconstruction thresholds."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Partition relative to the discrete-time unit-circle boundary, including marginal and oscillatory modes."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Estimate how bounded replenishment-policy changes move risky modal gains and service outcomes."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Measure holdout state and outcome residuals; inspect structured errors."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Track mode rotation, gain movement, reordering, and residual growth by review window."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Limit conclusions to selected SKUs, echelons, demand range, policy regime, and local perturbation size."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record non-normality, near-degenerate modes, and cross-effects among proposed controls."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Specify admissible demand, lead-time, capacity, assortment, and policy ranges."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require adequate retained/dropped separation and mode-identification stability."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the fitted review-cycle transition; require complete-basis and conditioning diagnostics.","counterfactual_removal":"Without dynamic modes and gains, the claimed hidden unstable feedback direction is not identified."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb bounded policy parameters in simulation and rank their effects on risky modes and service.","counterfactual_removal":"The decomposition would diagnose oscillation but would not identify an actionable damping lever."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify fitted discrete-time modes within the declared local regime.","counterfactual_removal":"Mode prominence could not be distinguished from growth or weak damping."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor-based mode recovery do not match transactional replenishment data.","counterfactual_removal":"No material change; empirical operator fitting supplies the domain-appropriate observation route."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Node centrality ranks topology, not the coupled temporal inventory-feedback dynamics at issue.","counterfactual_removal":"No material change to diagnosis or intervention."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only probe could miss a decision-critical subdominant or near-degenerate unstable mode.","counterfactual_removal":"No material change because the bounded pilot permits full decomposition."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not be invariant directions of replenishment dynamics.","counterfactual_removal":"No material change; removing it avoids conflating variance with dynamic gain."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use retained modes as a shadow simulator for bounded policy perturbations, not live control.","counterfactual_removal":"The causal diagnosis remains, but the first intervention test becomes slower and less safely isolated."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Evaluate holdout reconstruction and consequential residual structure before trusting mode selection.","counterfactual_removal":"A compact but decision-unsafe decomposition could pass without detecting omitted behavior."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Use singular values and conditioning to detect non-normal transient amplification or fragile eigenvectors; do not call singular vectors invariant modes.","counterfactual_removal":"Eigenmode fragility and transient amplification would be less visible, though the core chain remains."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document scope, uncertainty, coupling, residuals, and prohibited causal interpretations.","counterfactual_removal":"Operational handoff could overstate local descriptive modes as globally causal."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Re-estimate gap, mode alignment, gains, and residuals during the pilot.","counterfactual_removal":"There would be no hard gate for detecting loss of modal identifiability or regime validity."}],"causal_chain":["Coupled replenishment rules transform the multi-echelon state each review cycle.","HYPOTHESIS: the fitted local operator contains oscillatory modes with weak damping or gain above the stability boundary.","Sensitivity analysis links bounded policy parameters to those modes rather than to isolated coordinates.","A shadow policy adjustment that lowers risky modal gain should reduce oscillation in reconstructed inventory, backlog, and orders.","Holdout residual, service, constraint, gap, and drift checks determine whether that apparent improvement is valid."],"baseline":"Ordinary baseline: planners monitor SKU-location exceptions and tune forecasts, safety stock, or order quantities locally, often after shortages or excesses appear.","nearest_rival":"A conventional bullwhip or system-dynamics simulation that tunes replenishment parameters against aggregate variance and service metrics without extracting, validating, and monitoring invariant modes.","authority_safety":{"affected_parties":["Customers","Warehouse and store operators","Suppliers and carriers","Inventory planners and finance owners"],"decision_authority":"The inventory-control owner may authorize analysis and shadow simulation; live policy changes require the accountable supply-chain operations owner and existing change controls.","authorized_first_step":"Run a preregistered, non-executing replay on two product families across three connected echelons, using a training window and later holdout; compare baseline with bounded candidate parameter changes on modal gain, order/inventory oscillation, service, backlog, and residuals.","excluded_actions":["Automatic live order release","Supplier commitment changes","Safety-stock reduction","Capacity or allocation overrides","Extrapolation beyond the declared operating window"],"halt_rollback":"Halt if holdout residual exceeds tolerance, modes are ill-conditioned, the spectral gap falls below threshold, mode identity drifts, or any candidate worsens service/backlog beyond its guardrail. Discard the candidate model and retain current policies; no live rollback is needed."}},"negative_tests":{"strongest_counterevidence":"Oscillations that align with exogenous demand shocks, promotions, disruptions, or capacity outages and disappear after conditioning on them would undercut the proposed endogenous modal explanation; unstable estimates across holdouts would further weaken it.","analogy_break":"Supply networks are discrete, delayed, constrained, nonlinear, and policy-changing; eigenmodes of a local fitted operator are not globally invariant and may be numerically fragile under non-normality.","failure_condition":"No sufficiently stationary local window, no stable state definition, ill-conditioned or rapidly rotating modes, or residuals concentrated in shortage and service events makes the archetype unfit.","problem_falsifier":"After controlling for recorded external shocks, the selected system shows no repeatable coupled oscillation or amplification beyond independent coordinate noise and ordinary forecast error.","intervention_falsifier":"A preregistered policy perturbation predicted to damp the risky modes fails on holdout replay to lower modal gain and oscillation, or does so only by violating service, backlog, inventory, or capacity guardrails.","risks":["Spurious modes from common seasonality or data preprocessing","Policy recommendations that amplify unmodeled nonlinear behavior","Aggregation hiding SKU- or customer-level harm","Mode swapping or false confidence near a small spectral gap","Treating descriptive modes as proven causal mechanisms"]},"null_rationale":null,"classification":{"candidate_kind":"DOMAIN_TRANSFER","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":0.82,"generator_notes":"Closed-book structural fit. The candidate depends on a locally estimable transition operator and is rejected if stationarity, conditioning, residual, or drift gates fail."}