{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__psychology","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"psychology","decision":"CANDIDATE","problem_id":"recurrent_depression_coupled_symptom_escalation","causal_lever_id":"damp_person_specific_amplifying_symptom_mode","proposal":{"problem":"During recovery from recurrent depression, separately scored symptoms can appear stable while a person-specific combination of rumination, withdrawal, sleep disruption, and negative affect becomes increasingly self-reinforcing. Coordinate-by-coordinate monitoring may therefore miss impending deterioration and prompt interventions aimed at the loudest symptom rather than the coupled pattern sustaining escalation. Whether sufficiently stable person-specific modes exist is a HYPOTHESIS.","actors_substrate":["Adults receiving outpatient care for recurrent depression","Treating clinicians","Repeated self-report and passive-behavior measurements","A locally fitted symptom-transition model"],"observable_state":"A multivariate time series of consented, repeatedly measured symptoms and behaviors, plus estimated mode amplitudes, gains, reconstruction residuals, and drift indicators.","consequence":"A growing coupled symptom pattern may cross a clinically meaningful deterioration threshold before any single symptom does, delaying review or directing effort toward a low-leverage symptom.","affected_objective":"Detect and safely interrupt impending depressive deterioration while minimizing false alarms, burden, and unsupported causal interpretation.","structural_mapping":[{"archetype_element":"Many visible coordinates evolve under a shared transformation.","domain_realization":"Repeated symptom and behavior measurements are modeled as a local transition from one observation window to the next.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions reveal combinations preserved while their amplitudes change.","domain_realization":"Eigenvectors of a person-specific transition estimate represent candidate symptom combinations whose next-window direction is approximately preserved.","claim_kind":"INFERENCE"},{"archetype_element":"Scalar response distinguishes damped from amplifying modes.","domain_realization":"Estimated eigenvalue magnitude classifies candidate combinations as decaying, marginal, oscillatory, or amplifying within the fitted window.","claim_kind":"INFERENCE"},{"archetype_element":"Decision relevance depends on outcome leverage, not gain alone.","domain_realization":"A mode is actionable only if perturbation analysis links it to a prespecified deterioration outcome and its estimated effect is stable under resampling.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift checks bound the approximation.","domain_realization":"Prediction residuals, basis rotation, and spectral-gap changes determine when the model must be withheld or refit.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"A person-specific, finite-window transition from the current symptom-behavior vector to the next."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Consented measures with fixed timing, coding, missingness rules, and clinically interpretable units."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Candidate eigenvectors of the regularized transition estimate, traced back to measured variables."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues with uncertainty intervals and resampling stability."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes only when gain, outcome sensitivity, resampling stability, and residual improvement exceed preregistered thresholds."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify gains relative to the discrete-time stability boundary, without treating the classification as a diagnosis."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map low-risk clinician-approved supports to measured variables contributing to a selected mode; causal effectiveness remains unproven until tested."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample next-window error and structured residuals compared with the unreduced model."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Track basis rotation, gain changes, and repeated prediction failure across rolling windows."},{"component":"Interpretation Scope Contract","status":"adapted","domain_realization":"Use only for the enrolled person, measurement protocol, and fitted operating window; modes are predictive summaries, not latent disorders."},{"component":"Mode-Coupling Register","status":"adapted","domain_realization":"Record near-degenerate, non-orthogonal, and perturbation-linked modes that cannot be acted on independently."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Specify symptom-severity range, sampling cadence, treatment regime, and time horizon supporting local use."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Minimum resampling-stable separation between retained and excluded modes required for reduced interpretation."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit fitted transition operator; report conditioning and uncertainty rather than assuming a complete reliable basis.","counterfactual_removal":"No invariant directions or gains remain, so the proposed modal lever disappears."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb candidate modal coordinates in simulation and rank change in prespecified deterioration risk; log cross-effects.","counterfactual_removal":"Gain would be mistaken for actionable leverage, preventing selection of the proposed target."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify repeated-transition behavior only inside the declared local window.","counterfactual_removal":"The design could not distinguish decaying from amplifying symptom combinations."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor placement do not translate safely to depressive symptoms; observational validation is handled by held-out prediction.","counterfactual_removal":"No material change because the study does not identify modes by externally exciting a person."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Node importance in a connectivity graph answers a different question from temporal amplification of symptom combinations.","counterfactual_removal":"No change; centrality is not used to select the causal lever."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The small fitted operator can be decomposed directly, and dominant-only estimation would hide close competing modes.","counterfactual_removal":"No change because full decomposition supplies the required spectrum."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Covariance directions describe variance, not next-window symptom dynamics or amplification.","counterfactual_removal":"No change; the temporal operator, not covariance, defines modes."},{"slug":"reduced_order_model","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Use retained modes only as a bounded forecasting surrogate for offline comparison and alert simulation.","counterfactual_removal":"The causal theory remains, but rapid prospective comparison of modal alerts becomes harder."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Evaluate held-out prediction residual magnitude and structure as modes are added.","counterfactual_removal":"There would be no hard check that discarded behavior is acceptably small, making reduced alerts unsafe."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Singular directions may diagnose non-normal amplification but are not invariant temporal directions; reserve them for a failed-conditioning analysis.","counterfactual_removal":"No change to the primary proposal unless eigendecomposition proves ill-conditioned, which itself halts the test."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document variable loadings, uncertainty, couplings, prohibited causal readings, and validity window for clinician review.","counterfactual_removal":"The mathematics remains, but hard-gating safe interpretation and traceability becomes materially weaker."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Monitor gap uncertainty, mode rotation, and ordering changes; suppress output after threshold breach.","counterfactual_removal":"A once-valid reduced basis could continue generating alerts after losing separation or identity."}],"causal_chain":["Coupled symptoms and behaviors generate repeated person-specific state transitions.","A locally adequate transition model exposes approximately invariant symptom combinations and their gains.","Stability analysis identifies a candidate amplifying combination that univariate thresholds may not reveal.","Outcome sensitivity and coupling checks identify whether changing contributors to that mode is a plausible leverage point.","A clinician-approved support aimed at those contributors may damp the mode and reduce subsequent deterioration; this is a HYPOTHESIS.","Residual, drift, conditioning, and spectral-gap gates determine whether any modal output remains usable."],"baseline":"Usual symptom-by-symptom review using total-score change and fixed univariate thresholds, with clinician judgment determining follow-up.","nearest_rival":"A regularized full multivariate forecasting model that predicts deterioration accurately but supplies no invariant-mode reduction or modal intervention target.","authority_safety":{"affected_parties":["Enrolled patients","Clinicians responsible for care","Caregivers indirectly affected by alerts"],"decision_authority":"The patient controls participation and data collection; the licensed treating clinician retains all care and escalation authority. The model may recommend review but cannot diagnose, prescribe, or autonomously contact others.","authorized_first_step":"Run a prospective silent-mode pilot on consented historical-plus-new measurements: preregister variables and thresholds, issue no patient-facing alerts, and compare held-out prediction, calibration, lead time, residuals, and false-alert burden against the baseline and nearest rival.","excluded_actions":["Withholding usual care","Autonomous treatment changes or crisis decisions","Deliberately inducing symptoms to excite a mode","Interpreting a mode as a biological entity or diagnosis","Using passive data beyond explicit consent","Sharing individual outputs outside the care team"],"halt_rollback":"Suppress modal outputs and revert to usual review if conditioning is poor, the spectral gap or basis stability fails, residuals become structured or exceed budget, missingness shifts, false alerts exceed the preregistered ceiling, or any participant withdraws. Escalation follows existing clinical protocols, never the model alone."}},"negative_tests":{"strongest_counterevidence":"A full multivariate or univariate model matches or exceeds out-of-sample accuracy and lead time, while estimated modes rotate across resamples or people and provide no reproducible intervention ranking.","analogy_break":"Psychological measurements are noisy, treatment-responsive, and partly reflexive; unlike a fixed physical operator, the transition rule may change when a person notices, reports, or receives care. Eigenmodes may therefore lack a useful stability window.","failure_condition":"The proposal fails operationally if no mode simultaneously has stable identity, acceptable conditioning, adequate spectral separation, residual improvement, and outcome sensitivity within a clinically useful window.","problem_falsifier":"Dense prospective measurements show that deterioration is adequately signaled by one directly observed symptom or total score, with no reproducible coupled transition pattern or missed multimodal escalation.","intervention_falsifier":"A stable predictive amplifying mode is found, but clinician-approved actions mapped to its contributors do not reduce its subsequent amplitude or deterioration relative to an intensity-matched symptom-targeted rival.","risks":["False reassurance from a nominally stable mode","Alarm burden and symptom hypervigilance","Confounding treatment effects with endogenous dynamics","Mode labels stigmatizing patients","Missing-data and measurement-frequency artifacts","Privacy loss from intensive longitudinal monitoring","Unstable or non-normal operators producing misleading eigenvectors"]},"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":0.78,"generator_notes":"Closed-book structural inference from the supplied packet. Empirical existence, stability, and causal actionability of person-specific symptom modes are not established."}