{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__cognitive_science","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"cognitive_science","decision":"CANDIDATE","problem_id":"coupled_precursors_of_sustained_attention_lapses","causal_lever_id":"target_growing_cognitive_state_modes","proposal":{"problem":"In sustained-attention and human-supervision tasks, consequential lapses may be preceded by coupled changes in response variability, omissions, gaze, and workload proxies that separate metric thresholds fail to detect. If a repeatable joint state direction grows across trials, surface monitoring can warn too late and generic breaks can be mistimed.","actors_substrate":["People performing sustained-attention or supervisory tasks","Researchers or task-safety operators","Repeated-trial behavioral and optional noninvasive physiological measurements","Task-pacing, rest, and alert-presentation controls"],"observable_state":"Within a stable task block, standardized trial-window measurements of accuracy, omissions, response-time distribution, gaze disengagement, and optional workload proxies, followed by independently scored attention lapses.","consequence":"Undetected growth of a coupled failure precursor can produce delayed responses, missed signals, or unnecessary interruption when separate thresholds or average workload scores remain nominal.","affected_objective":"Detect and safely attenuate impending attention lapses with fewer missed events and unnecessary interventions.","structural_mapping":[{"archetype_element":"A repeated transformation acts on coupled variables","domain_realization":"A locally fitted transition operator maps one multivariate cognitive-performance window to the next under a fixed task regime.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Invariant directions expose amplification hidden in coordinates","domain_realization":"Approximate eigenmodes represent joint behavioral or sensor patterns whose amplitudes decay, persist, or grow across windows.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Scalar responses rank dynamic behavior","domain_realization":"Discrete-time eigenvalue magnitudes classify precursor modes as damped, marginal, or growing within the fitted window.","claim_kind":"INFERENCE"},{"archetype_element":"Outcome sensitivity separates loud modes from useful modes","domain_realization":"Mode-specific perturbation estimates rank which candidate controls are predicted to reduce independently scored lapse risk.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residuals and drift bound reliance","domain_realization":"Held-out prediction residuals, mode rotation, and spectral-gap loss determine when the model must not guide intervention.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"One-window-to-next transition within a prespecified stable task, session phase, and workload band."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Standardized accuracy, omission, response-time, gaze, and optional workload-proxy measurements with missingness rules."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Well-conditioned approximate eigenvectors of the fitted transition operator, traced to their observable-variable loadings."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Estimated eigenvalues with uncertainty intervals."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes only when gain or lapse-outcome sensitivity clears a preregistered threshold and held-out residual stays within budget."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify discrete-time modes by eigenvalue magnitude, with an uncertainty band around the stability boundary."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map bounded controls such as a brief rest, slower pacing, or alert reprioritization to predicted modal changes."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Reconstruct held-out state trajectories and inspect both residual magnitude and structured lapse-related error."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Track mode rotation, gain changes, and residual growth across successive task blocks."},{"component":"Interpretation Scope Contract","status":"adapted","domain_realization":"Treat modes as local predictive constructs, not established mental modules or diagnoses."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degeneracy, non-normality, and intervention cross-effects that defeat independent-mode interpretation."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Limit use to the task, workload range, session duration, and participant population represented in fitting."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require bootstrap-supported separation between retained and discarded modes; suspend use when separation is not distinguishable from estimation noise."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicit fitted transition matrix when it is diagonalizable and sufficiently well-conditioned.","counterfactual_removal":"Without dynamic invariant directions and gains, the proposal collapses to coordinate-level prediction."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Estimate local effects of each feasible control on mode amplitude and lapse outcome, logging cross-effects.","counterfactual_removal":"Modes could predict lapses but would not identify a defensible intervention lever."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify modes within the discrete-time, locally linear task regime.","counterfactual_removal":"The model could not distinguish growing precursors from harmless variation."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor-defined mode-shape recovery do not match observational cognitive-state transitions.","counterfactual_removal":"No change; modes are estimated from a transition operator."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"The target is a temporal state transition, not node importance in a connectivity graph.","counterfactual_removal":"No change to the causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate cannot support the required stability partition, coupling checks, or retained-versus-discarded gap.","counterfactual_removal":"No change because full decomposition is required."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions need not be transition-invariant or predictive of lapses.","counterfactual_removal":"No change; covariance variance is not the proposed lever."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate adds complexity before predictive and interventional validity is established.","counterfactual_removal":"The bounded pilot remains executable with the fitted transition model."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use held-out trajectory reconstruction and structured residual checks to set retained-mode order.","counterfactual_removal":"There would be no hard check that discarded behavior is acceptably small."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Singular vectors measure input-output amplification but are not generally invariant temporal directions.","counterfactual_removal":"No change unless eigenvectors prove ill-conditioned, which instead halts this proposal."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Document observable loadings, uncertainty, couplings, residuals, and prohibited psychological interpretations.","counterfactual_removal":"The mathematics remains, but misuse as diagnosis or mental-module evidence becomes materially likelier."},{"slug":"spectral_gap_monitor","disposition":"selected_load_bearing","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Re-estimate gaps, direction drift, and residuals by task block.","counterfactual_removal":"A stale modal basis could continue controlling after its simplifying warrant disappears."}],"causal_chain":["Fit a local multivariate transition operator from repeated task windows.","Extract well-conditioned invariant directions and scalar gains.","Identify growing or weakly damped modes that predict independently labeled lapses on held-out data.","Use sensitivity sweeps to map bounded controls to those modes and register cross-effects.","Randomize a low-risk control when the target mode crosses a preregistered threshold.","Test whether the control reduces target-mode amplitude and subsequent lapses without unacceptable residual or burden.","Suspend and refit when drift, gap, conditioning, or residual limits fail."],"baseline":"Separate thresholds or rolling averages for omissions, response time, gaze, or workload, followed by a generic scheduled break or operator judgment.","nearest_rival":"A regularized nonlinear lapse-risk predictor using the same observations but no invariant-mode or stability interpretation.","authority_safety":{"affected_parties":["Task participants","People affected by missed supervised events","Researchers and safety operators"],"decision_authority":"Participants retain consent and withdrawal authority; an ethics-approved investigator or designated task-safety operator authorizes the pilot and intervention thresholds.","authorized_first_step":"Run a preregistered, within-participant laboratory pilot comparing baseline, rival, and modal predictors; randomize only brief rest or pacing adjustments after offline validation.","excluded_actions":["Clinical or employment diagnosis","Punitive personnel decisions","Covert physiological monitoring","Withholding mandatory safety breaks","Automatic control outside the validated task regime"],"halt_rollback":"Stop modal triggering and revert to ordinary safety procedures if eigenvectors are ill-conditioned, the spectral gap or held-out advantage disappears, residuals become structured, modes drift beyond tolerance, or interventions increase errors, distress, or workload."}},"negative_tests":{"strongest_counterevidence":"A single observable or the nonlinear rival predicts lapses equally well across held-out participants, while fitted modes rotate across sessions or lack selective response to controls.","analogy_break":"Cognitive behavior can be nonlinear, history-dependent, strategic, and measurement-reactive; local eigenmodes may be unstable statistical mixtures rather than psychologically real invariant processes.","failure_condition":"No well-conditioned, repeatable transition modes exist inside a practically useful task window, or safe controls cannot selectively influence them.","problem_falsifier":"After calibration, separate observable thresholds or one workload variable match multivariate models, and no repeatable coupled precursor improves prospective lapse prediction.","intervention_falsifier":"A selected mode predicts lapses, but randomized mapped controls neither reduce its amplitude nor improve subsequent lapse outcomes relative to the nearest rival or sham timing.","risks":["Reifying statistical modes as mental faculties","Physiological privacy loss","Mode drift causing false reassurance","Unnecessary interruptions from false alarms","Unequal accuracy across participant groups","Local stability being mistaken for global safety"]},"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":0.74,"generator_notes":"Closed-book structural transfer. The candidate is contingent on discovering a locally stable, well-conditioned transition operator; no empirical effectiveness or novelty is claimed."}