{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__earth_sciences","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"earth_sciences","decision":"CANDIDATE","problem_id":"multisensor_landslide_instability_hidden_by_univariate_alerts","causal_lever_id":"growth_rate_aware_modal_landslide_alerting","proposal":{"problem":"Landslide observatories often evaluate rainfall, pore pressure, groundwater level, displacement, and tilt separately, although impending instability may appear first as a growing combination of small changes across sensors. Coordinate-wise thresholds can therefore issue late or noisy warnings when no single measurement is yet extreme. This coupled hidden-mode failure is a HYPOTHESIS to be tested at instrumented slopes.","actors_substrate":["instrumented landslide or unstable slope","rain gauges, piezometers, inclinometers, GNSS, and tilt sensors","geotechnical analysts and geological-survey hazard staff","emergency managers, residents, workers, and road users in the threatened area"],"observable_state":"A time-indexed state vector of standardized hydrologic and deformation measurements, missingness indicators, and estimated rates, evaluated within a documented seasonal and operating regime.","consequence":"A weakly damped or growing slope-instability pattern can remain below individual sensor thresholds until accelerating deformation leaves insufficient time for investigation, access closure, or evacuation; alternatively, correlated benign forcing can cause false alarms.","affected_objective":"Increase warning lead time at a fixed false-alarm burden while preserving visibility of behavior unexplained by the modal model.","structural_mapping":[{"archetype_element":"coupled transformation","domain_realization":"A locally fitted transition operator maps the slope's multivariate sensor state at one interval to the next; whether this approximation is stable enough is a HYPOTHESIS.","claim_kind":"HYPOTHESIS"},{"archetype_element":"invariant directions and scalar responses","domain_realization":"Eigenvectors represent recurring combinations of hydrologic and deformation variables, while eigenvalues estimate their decay, persistence, oscillation, or growth within the fitted window.","claim_kind":"INFERENCE"},{"archetype_element":"hidden unstable direction","domain_realization":"A mode combining modest pore-pressure rise and spatially coherent deformation may grow before any constituent crosses its ordinary threshold.","claim_kind":"HYPOTHESIS"},{"archetype_element":"action-relevant selection","domain_realization":"Modes are retained by out-of-sample reconstruction, stability, consequence-weighted sensitivity, and spectral-separation criteria rather than variance alone.","claim_kind":"INFERENCE"},{"archetype_element":"intervention in modal coordinates","domain_realization":"The intervention is informational: route review, corroborating measurement, inspection, and authorized warning escalation according to the unstable mode's score and growth rate.","claim_kind":"HYPOTHESIS"},{"archetype_element":"residual and drift governance","domain_realization":"Structured reconstruction error, rotating modes, or a closing spectral gap suspends modal interpretation and returns decisions to conventional review.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"direct","domain_realization":"One monitored slope, fixed sampling interval, and a locally estimated state-transition operator."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Standardized hydrologic, deformation, rate, and data-quality variables with documented sensor inclusion."},{"component":"Invariant Mode Basis","status":"direct","domain_realization":"Eigenvectors of the fitted transition operator, traced back to sensor weights and locations."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues with uncertainty estimates for decay, persistence, oscillation, or growth."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes meeting stability-risk, validation, and consequence thresholds, not merely largest magnitude."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify modes relative to the discrete-time stability boundary, including uncertainty and marginal cases."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map mode scores to corroboration, analyst review, inspection, and existing alert-protocol steps rather than direct slope control."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample state reconstruction error plus tests for spatially or temporally structured residuals."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Scheduled comparison of mode direction, ordering, gain, and uncertainty."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Modes are local statistical-dynamical summaries, not proof of a failure mechanism or unconditional forecasts."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, or perturbation-linked modes that cannot be acted upon independently."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Explicit bounds for season, moisture state, deformation range, sensor configuration, and forcing intensity."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Predeclared minimum separation and mode-direction stability required for operational interpretation."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the estimated local transition operator and retain eigenpair uncertainty and conditioning diagnostics.","counterfactual_removal":"Without invariant directions and gains, the proposal becomes ordinary multivariate thresholding and loses its causal lever."},{"slug":"modal_sensitivity_sweep","disposition":"selected_supporting","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Perturb modal scores and gains in replay to quantify effects on lead time, false alerts, and coupling.","counterfactual_removal":"Mode selection could rely on magnitude rather than decision consequence, weakening but not eliminating the core chain."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify growth only inside the documented local regime and propagate eigenvalue uncertainty.","counterfactual_removal":"The system could describe covariance patterns but could not distinguish growing from decaying directions."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Deliberate excitation of a hazardous slope is unsafe, while passive observations are already used to fit and validate the transition model.","counterfactual_removal":"No material change; safe observational validation remains."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Sensor importance is not assumed to arise from graph adjacency or dominant-eigenvector centrality.","counterfactual_removal":"No change because the proposed transformation is temporal state evolution, not network connectivity."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only approximation would conceal competing or near-degenerate hydrologic and deformation modes.","counterfactual_removal":"No change; the bounded pilot estimates the required portion of the spectrum directly."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"PCA is the nearest descriptive rival, but high variance does not establish temporal growth or warning relevance.","counterfactual_removal":"No change to the intervention; PCA remains a comparator in evaluation."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate adds extrapolation risk and is unnecessary for shadow alerting.","counterfactual_removal":"No change; one-step modal scoring and replay suffice."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Test held-out reconstruction magnitude and structure across quiet, forced, and known-movement intervals.","counterfactual_removal":"Unmodeled behavior could be hidden while the alert system appears numerically stable, hard-gating safe use."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"SVD is reserved as a diagnostic if non-normality makes eigenvectors ill-conditioned; its singular directions do not provide repeated-time stability verdicts.","counterfactual_removal":"No change unless conditioning tests invalidate eigendecomposition, in which case the pilot halts rather than silently substitutes interpretations."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Issue a versioned report stating sensor loadings, uncertainties, coupling, residuals, valid regime, and prohibited causal readings.","counterfactual_removal":"Analysts could overread tentative modes as physical mechanisms, making operational use unacceptable."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track retained/dropped separation, eigenvector rotation, and mode-order swaps on each refit.","counterfactual_removal":"A once-valid basis could continue driving alerts after its dominance or identity disappeared."}],"causal_chain":["Fit a local multivariate transition operator from synchronized slope-monitoring data within a declared regime.","Decompose it into sensor-traceable modes and gains, rejecting ill-conditioned or weakly identified solutions.","Identify modes whose estimated gains are marginal or growing and whose scores precede hazardous deformation in held-out replay.","Use consequence-weighted sensitivity and residual tests to select only modes that improve warning performance without concealing omitted behavior.","In prospective shadow operation, route qualifying modal growth to corroboration and analyst review under the existing alert protocol.","Suspend the modal route when residual, drift, conditioning, regime, or spectral-gap limits fail."],"baseline":"Independent sensor thresholds, rate-of-change plots, rainfall-duration rules, and expert review of dashboards.","nearest_rival":"A PCA or generic multivariate anomaly detector that flags unusual covariance patterns but does not estimate whether a direction grows or decays under repeated state evolution.","authority_safety":{"affected_parties":["people living or working on or below the slope","road and infrastructure users","field technicians and emergency responders","landowners and local authorities"],"decision_authority":"The legally designated geological-hazard and emergency-management authorities retain all inspection, closure, warning, and evacuation decisions; the model supplies advisory evidence only.","authorized_first_step":"Run a retrospective, site-bounded replay followed by prospective shadow monitoring with predeclared lead-time, false-alert, residual, conditioning, drift, and subgroup/location coverage metrics; alerts are visible only to authorized analysts.","excluded_actions":["automated public warning, road closure, or evacuation","deliberate slope excitation","automated pumping, drainage, excavation, or loading changes","claiming that a statistical mode proves a particular geologic failure mechanism","deployment beyond the validated slope and regime"],"halt_rollback":"Halt shadow use and revert to the ordinary dashboard whenever conditioning is poor, the gap or reconstruction tolerance fails, mode identity drifts, inputs leave the declared regime, sensors materially change, or analysts observe unexplained alert clustering; retain logs and refit only after review."}},"negative_tests":{"strongest_counterevidence":"Historical failures and accelerations may be predicted as well by one displacement-rate or rainfall threshold, while fitted modes may rotate across seasons or encode sensor artifacts rather than slope dynamics.","analogy_break":"A natural slope is nonlinear, history-dependent, spatially heterogeneous, and externally forced; local eigenmodes need not be global physical modes, independent, or stable through progressive failure.","failure_condition":"The approach fails operationally if valid modes cannot be estimated with adequate conditioning and spectral separation, or if held-out reconstruction and warning performance do not remain within predeclared tolerances.","problem_falsifier":"Across representative sites and seasons, hazardous accelerations are not preceded by reproducible coupled multivariate patterns, or a single observable variable captures the same usable lead time and false-alarm performance.","intervention_falsifier":"Coupled patterns exist, but growth-aware modal scoring adds no held-out or shadow-operation improvement over the baseline and nearest rival, or its residual/drift gates make it unavailable when decisions are needed.","risks":["false reassurance from a locally stable classification","false alarms caused by storms, maintenance, missingness, or sensor drift","unstable eigenvectors under non-normality or near-degeneracy","unequal sensor coverage producing weaker protection for parts of the slope","analysts mistaking statistical modes for verified physical mechanisms","alert latency introduced by corroboration and review"]},"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":0.78,"generator_notes":"Closed-book structural transfer. The candidate is limited to instrumented slopes with enough local stationarity for an estimable transition operator; empirical effectiveness and mode reproducibility remain untested hypotheses."}