{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__environmental_climate","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"environmental_climate","decision":"CANDIDATE","problem_id":"coupled_ecosystem_regime_shift_warning_failure","causal_lever_id":"unstable_multivariate_transition_mode_detection","proposal":{"problem":"Environmental monitoring can miss an approaching ecosystem regime shift when temperature, moisture, vegetation condition, carbon flux, and disturbance indicators remain individually inconclusive while a coupled combination of them becomes progressively less damped. Coordinate-wise thresholds and averages may therefore warn only after substantial loss of ecological function or carbon-storage capacity.","actors_substrate":["Regional ecosystem and climate-monitoring agencies","Ecologists and Earth-system modelers","Land and fire-management authorities","Communities, landholders, and Indigenous nations dependent on the monitored ecosystem","Repeated multivariate observations and locally fitted state-transition models"],"observable_state":"A locally estimated multivariate transition operator contains a persistent or growing mode whose gain approaches or crosses the chosen stability boundary, while reconstruction residuals, mode rotation, and spectral separation remain measurable.","consequence":"If the coupled mode is real and stable enough to track, agencies gain earlier and more interpretable warning of coordinated deterioration; if it is ignored, separate indicators can understate transition risk until impacts are difficult to reverse.","affected_objective":"Provide timely, auditable warning of regional ecosystem loss or carbon-sink reversal without treating a local linear approximation as a global causal model.","structural_mapping":[{"archetype_element":"Many surface variables obscure the transformation's operative directions","domain_realization":"Temperature, moisture, vegetation, carbon-flux, and disturbance measurements can move jointly, making single-indicator alarms insensitive to their combined trajectory.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant or approximately invariant modes","domain_realization":"Eigenvectors of a locally fitted lagged state-transition operator represent multivariate perturbation patterns that approximately preserve direction over the stated observation regime.","claim_kind":"INFERENCE"},{"archetype_element":"Scalar modal response and stability partition","domain_realization":"Estimated gains classify coupled ecological patterns as damped, marginal, oscillatory, or growing within the fitted time scale and regime.","claim_kind":"INFERENCE"},{"archetype_element":"Action mapping","domain_realization":"Sensitivity tests relate feasible monitoring or management variables to the risky mode and to ecological or carbon outcomes.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual, drift, and interpretation controls","domain_realization":"Out-of-sample reconstruction error, changing mode direction, and shrinking spectral separation determine when the warning model must be revised or retired.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"direct","domain_realization":"A lagged regional ecosystem state-transition operator over a fixed season, spatial extent, sampling interval, and disturbance regime."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Standardized temperature, soil or fuel moisture, vegetation condition, carbon flux, and disturbance variables with explicit units and missing-data rules."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Approximate modes of the fitted local transition operator, traced back to original indicators."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Estimated eigenvalues with uncertainty intervals at the monitoring time step."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes exceeding preregistered persistence, outcome-sensitivity, and reconstruction-contribution thresholds."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify modes relative to the discrete-time unit-circle boundary, with a marginal uncertainty band."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map feasible observation or management changes into modal coordinates and estimated ecological outcomes."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample state reconstruction error plus tests for structured residuals in vulnerable places or seasons."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Scheduled comparison of mode angles, ordering, gains, and residuals across rolling windows."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Modes are local predictive summaries, not proof of tipping, global stability, or causal effects."},{"component":"Mode-Coupling Register","status":"adapted","domain_realization":"Log near-degenerate, non-normal, or perturbation-linked modes that cannot be interpreted independently."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Document the climatic range, season, disturbance intensity, geography, and forecast horizon represented by training data."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Preregister minimum separation and mode-angle stability required for a distinct warning mode."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Apply to the explicit locally fitted transition matrix; report conditioning and uncertainty rather than assuming a perfectly complete basis.","counterfactual_removal":"Without operator modes and gains, the proposal collapses to coordinate-wise monitoring."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb modes and feasible controls only within the fitted window; record cross-effects and outcome sensitivity.","counterfactual_removal":"A growing mode could be detected but not connected to leverage or consequences."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify gains with uncertainty bands and an explicit local regime.","counterfactual_removal":"The decomposition would not distinguish harmless variation from weakly damped or growing dynamics."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Deliberately exciting a regional ecosystem as though it were a mechanical structure is infeasible and potentially harmful; passive observations are already used to fit the operator.","counterfactual_removal":"No change; empirical validation is supplied by held-out natural observations."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Node importance is not the target; the problem concerns temporal coupled state dynamics rather than a connectivity ranking.","counterfactual_removal":"No change to the causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The bounded pilot uses a moderate explicit operator and needs multiple modes plus uncertainty, so dominant-only matrix-free estimation is insufficient.","counterfactual_removal":"No change; full decomposition supplies the required spectrum."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions may describe covariance but do not establish persistence or growth under the transition operator.","counterfactual_removal":"No change; excluding it prevents variance from being mistaken for dynamics."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use retained modes as a shadow forecasting surrogate only inside the validated window.","counterfactual_removal":"Detection remains possible, but rapid prospective comparison and intervention sweeps become harder."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Evaluate held-out periods, spatially disaggregated errors, and residual structure, not only aggregate fit.","counterfactual_removal":"Omitted dynamics could be hidden by an apparently persuasive low-order warning."},{"slug":"singular_value_decomposition","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use as a robustness diagnostic for non-normal amplification and ill-conditioned eigenvectors, not as a substitute stability spectrum.","counterfactual_removal":"The core method remains, but transient amplification and fragile eigenvectors are less likely to be detected."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Publish mode meanings, uncertainty, couplings, residuals, prohibited interpretations, and retirement criteria.","counterfactual_removal":"Technical results become easier for decision-makers to overread as causal or globally valid."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track retained/dropped separation, mode angles, gain uncertainty, and residual failure on rolling windows.","counterfactual_removal":"A once-valid warning basis could silently lose identity after climatic or ecological regime change."}],"causal_chain":["Repeated observations define a bounded ecosystem state and local transition operator.","Decomposition exposes coupled directions and their estimated gains.","Stability analysis identifies a weakly damped or growing direction hidden across individual indicators.","Sensitivity analysis connects that direction to outcomes and feasible levers while registering coupling.","Residual, conditioning, gap, and drift checks gate whether the mode is decision-usable.","Only a validated warning is added to monitoring and escalation procedures; failed gates trigger re-estimation or retirement."],"baseline":"Separate dashboards compare each environmental variable with a historical threshold or trend and escalate only when one or more visible indicators breach limits.","nearest_rival":"A multivariate nonlinear forecasting model that predicts ecological or carbon outcomes directly and uses feature attribution, without requiring invariant modes.","authority_safety":{"affected_parties":["Residents and workers exposed to fire, water, livelihood, or health consequences","Indigenous nations and local communities with rights and place-based knowledge","Landholders and ecosystem-dependent industries","Future beneficiaries of ecosystem and carbon-storage services","Wildlife and ecosystems represented through responsible public authorities"],"decision_authority":"A regional monitoring agency may authorize a shadow warning pilot; any management response remains with the legally responsible land, environmental, emergency, and Indigenous governance bodies.","authorized_first_step":"Run one preregistered retrospective-plus-prospective shadow test for one region and seasonal cycle using existing observations: fit on earlier windows, freeze thresholds, compare lead time and false alarms with the baseline and nearest rival, and make no automatic management decisions.","excluded_actions":["Deliberate ecosystem perturbation to excite modes","Automated burns, closures, water allocation, relocation, or land-use restrictions","Extrapolation beyond the documented region, season, disturbance range, or forecast horizon","Treating a mode as proof of a tipping point or causal management effect"],"halt_rollback":"Suspend alerts and revert to ordinary monitoring if held-out residuals exceed budget, the spectral gap falls below threshold, mode identity drifts beyond tolerance, uncertainty spans both stable and unstable classifications, or false alarms exceed the preregistered limit; preserve results for audit and refit only under new approval."}},"negative_tests":{"strongest_counterevidence":"The apparent unstable mode may be an artifact of seasonality, sensor changes, short records, spatial aggregation, non-normal transients, or an omitted nonlinear driver; a direct nonlinear forecast may predict outcomes more accurately and reliably.","analogy_break":"Environmental regimes are open, nonlinear, forced, and nonstationary. Their estimated eigenmodes need not be truly invariant, orthogonal, causal, or valid beyond a short local window, unlike modes of a fixed well-characterized operator.","failure_condition":"The approach fails if no locally stable state definition and transition window can be estimated, modes are ill-conditioned or rapidly rotating, residuals remain structured, or no spectral separation supports a reproducible action-relevant mode.","problem_falsifier":"Across held-out regions or periods, individual thresholds and ordinary outcome forecasts provide equivalent or earlier warning, and no reproducible coupled weakly damped or growing pattern precedes adverse ecosystem change.","intervention_falsifier":"A preregistered shadow pilot finds a reproducible problem pattern, but modal alerts do not improve lead time, calibration, or decision-relevant discrimination over both the baseline and nearest rival within the residual and false-alarm budgets.","risks":["False alarms could redirect scarce monitoring or management resources.","Mode labels could be mistaken for causal mechanisms or certain tipping-point predictions.","Aggregation could obscure harms concentrated in particular communities or habitats.","Poorly conditioned or near-degenerate modes could produce unstable narratives.","A model trained on historical regimes could fail under unprecedented forcing."]},"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":0.82,"generator_notes":"Closed-book structural inference from the supplied archetype and domain packet. Empirical effectiveness, thresholds, and regional applicability remain untested."}