{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__law_governance","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"law_governance","decision":"CANDIDATE","problem_id":"coupled_adjudication_docket_delay","causal_lever_id":"modal_docket_flow_control","proposal":{"problem":"HYPOTHESIS: In a high-volume administrative adjudication docket, delay and deadline-breach risk can grow through coupled movements among filing, evidence, hearing, deliberation, and disposition stages even while total caseload and average processing time appear stable. Stage-by-stage management may therefore miss combinations of docket conditions that repeatedly amplify delay and impair timely access to adjudication.","actors_substrate":["claimants and respondents","counsel and representatives","administrative judges or hearing officers","clerks and docket managers","tribunal leadership","oversight and data-governance officials"],"observable_state":"Monthly, aggregate or deidentified counts and age distributions by procedural stage and case class; transitions between stages; arrivals, dispositions, remands, continuances, staffing inputs, statutory-deadline breaches, and subgroup timeliness outcomes.","consequence":"Growing latent delay patterns can cause prolonged resolution, deadline breaches, unequal procedural burden, emergency staffing reactions, and reduced access to timely adjudication.","affected_objective":"Timely, procedurally fair, legally compliant, and equitable resolution of disputes without altering merits decisions.","structural_mapping":[{"archetype_element":"Coupled transformation","domain_realization":"INFERENCE: A locally estimated month-to-month docket-flow operator maps deviations in stage-specific case stocks and ages into the next month's state.","claim_kind":"INFERENCE"},{"archetype_element":"Surface coordinates obscure invariant directions","domain_realization":"HYPOTHESIS: Named queues may rise and fall together or offset one another, while a cross-stage combination persists or grows unnoticed by aggregate dashboards.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Modal gain and stability","domain_realization":"Eigenvalues of the estimated local operator represent the persistence, damping, growth, or oscillation of corresponding cross-stage docket patterns, subject to estimation uncertainty.","claim_kind":"INFERENCE"},{"archetype_element":"Action in modal coordinates","domain_realization":"HYPOTHESIS: Scheduling, clerk allocation, hearing capacity, and permitted workflow changes can be chosen for their predicted effect on a risky cross-stage mode rather than on the largest visible queue.","claim_kind":"HYPOTHESIS"},{"archetype_element":"Residual and drift governance","domain_realization":"Unreconstructed delay, changing mode shapes, and narrowing spectral separation revoke permission to rely on the modal model.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"A locally linear map of monthly deviations in one tribunal's docket-flow state; arrivals and authorized operational inputs are modeled separately."},{"component":"State-Vector Definition","status":"adapted","domain_realization":"Standardized aggregate counts and age bands by procedural stage and case class, with protected attributes reserved for fairness auditing rather than control targeting."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Estimated cross-stage directions approximately preserved by the local docket-flow operator."},{"component":"Modal Gain Spectrum","status":"adapted","domain_realization":"Estimated eigenvalues with uncertainty intervals describing each mode's month-to-month response."},{"component":"Dominant Mode Selection Rule","status":"adapted","domain_realization":"Retain modes only when holdout contribution to deadline-breach prediction exceeds a locked threshold and estimates are stable under resampling."},{"component":"Stable/Unstable Mode Partition","status":"direct","domain_realization":"Classify deviation modes as damped, marginal, growing, or oscillatory within the declared operating window."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map only legally authorized staffing, scheduling, and workflow controls to predicted changes in selected modal coordinates."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Compare reconstructed stage stocks, ages, and breach rates with held-out observations; inspect residual structure and subgroup error."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Re-estimate mode direction, ordering, and gain after policy, staffing, caseload, or procedural changes."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"State that modes describe docket dynamics, not legal merit, party deservingness, causation, or authority to change rights."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record near-degenerate, non-orthogonal, or intervention-linked modes that cannot safely be treated independently."},{"component":"Local Linearization Window","status":"adapted","domain_realization":"Limit use to the tribunal, case mix, rules, capacity range, and time regime represented in training data."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Trust retained-mode separation only when its lower uncertainty bound remains above the precommitted minimum; otherwise expand or retire the model."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Apply to the estimated square local docket-transition operator, with conditioning and uncertainty checks; completeness is treated as model-conditional, not institutional truth.","counterfactual_removal":"Without invariant directions and gains, the proposal becomes ordinary stage-level queue management and loses its causal lever."},{"slug":"modal_sensitivity_sweep","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Perturb only authorized operational inputs in the fitted model and record outcome response and cross-mode effects.","counterfactual_removal":"Modes could be diagnosed but not translated into a defensible intervention ranking."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify estimated docket modes relative to repeated monthly dynamics and attach the local regime explicitly.","counterfactual_removal":"The analysis could not distinguish transient congestion from compounding delay."},{"slug":"mode_shape_testing","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Physical excitation and sensor placement do not map safely to adjudication; deliberately perturbing real cases would be unethical.","counterfactual_removal":"No change; historical observation and model validation supply the admissible evidence."},{"slug":"network_spectral_centrality_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"The target is stage-flow dynamics, not ranking actors or cases by graph centrality.","counterfactual_removal":"No change to the docket-mode causal chain."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate is inadequate because a near-leading delay mode and spectral uncertainty must remain visible.","counterfactual_removal":"No change; the bounded operator is small enough for a fuller decomposition."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"High variance does not establish persistence or growth under the docket transition.","counterfactual_removal":"No change; covariance modes are not the proposed causal lever."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable control surrogate adds complexity before the descriptive modal hypothesis is validated.","counterfactual_removal":"No change to the initial shadow test."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Reconstruct held-out docket trajectories and inspect total, structured, and subgroup residuals against locked tolerances.","counterfactual_removal":"Poor compression or omitted legally consequential behavior could be hidden, invalidating the test."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Singular directions are useful for amplification and reconstruction but do not by themselves give invariant repeated-time docket modes.","counterfactual_removal":"No change to the selected repeated-dynamics interpretation."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Issue a reviewable report covering meanings, prohibited interpretations, uncertainty, couplings, residuals, and expiry conditions.","counterfactual_removal":"The mathematics could travel without its legal and interpretive limits, hard-gating safe institutional use."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track retained/dropped separation and mode rotation after each scheduled re-estimation or regime change.","counterfactual_removal":"A once-valid simplification could remain in use after its modal basis ceased to be identifiable."}],"causal_chain":["Procedural rules, arrivals, capacity, and case movement jointly generate a repeated cross-stage docket transformation.","Some deviations align with weakly damped or growing cross-stage modes rather than a single visible queue.","Offsets among stages can mask those modes in total-backlog and average-time metrics.","Mode-specific sensitivity estimates identify authorized controls predicted to damp the risky direction.","If the control reduces that mode, held-out deadline-breach and delay growth should fall without worsening residual or subgroup outcomes.","Residual, drift, spectral-gap, and authority gates prevent extrapolation or merits use."],"baseline":"Ordinary practice: monitor total backlog, median disposition time, deadline breaches, and stage-specific queues, then add capacity or expedite the visibly largest bottleneck.","nearest_rival":"A stage-level queueing or survival model that forecasts delay from arrivals, service rates, case class, and age but does not decompose the repeated transition into invariant cross-stage modes.","authority_safety":{"affected_parties":["claimants and respondents awaiting decisions","counsel and representatives","adjudicators and staff","groups exposed to unequal delay","the public and oversight bodies"],"decision_authority":"The tribunal's legally authorized administrator and chief adjudicator may approve a shadow analysis with data-governance review; only officials holding the relevant statutory or rulemaking authority may later alter workflow or resource policy.","authorized_first_step":"Run a retrospective, deidentified shadow test in one tribunal: fit on 24 monthly periods, lock modes and thresholds, and compare six held-out months against the baseline and nearest rival. Make no live scheduling or merits changes.","excluded_actions":["automated merits decisions or legal-reasoning substitution","individual case prioritization from modal scores","use of protected traits as control targets","changes to substantive or procedural rights without lawful process","deadline waiver, covert experimentation, or punitive staff ranking","deployment beyond the validated tribunal and regime"],"halt_rollback":"Halt reliance if holdout error exceeds the locked rival tolerance, residuals remain structured, subgroup timeliness error worsens, the spectral gap fails, modes drift beyond tolerance, or a policy regime changes. Preserve the audit record and revert to ordinary docket reporting; the shadow test itself changes no cases."}},"negative_tests":{"strongest_counterevidence":"HYPOTHESIS: Legal-case heterogeneity, discretionary continuances, policy shocks, and nonstationary behavior may make estimated modes unstable; a simple stage-level forecast may equal or outperform them out of sample.","analogy_break":"Cases are rights-bearing disputes, not interchangeable physical state units. Legal reasons, party conduct, and institutional discretion can change the transformation, and a descriptive mode confers neither causation nor authority to intervene.","failure_condition":"The fit fails if no locally stable coupled operator can be estimated, mode identity is not reproducible, residuals contain consequential structure, or safe operational controls cannot be mapped to modes.","problem_falsifier":"Disaggregated evidence shows delay is explained by one directly observable stage or case-class bottleneck, with no reproducible coupled cross-stage pattern and no predictive gain from modal state.","intervention_falsifier":"In the locked holdout or a later authorized pilot, mode-targeted controls fail to damp the selected mode or improve deadline-breach and delay outcomes beyond the nearest rival, or they worsen residual, fairness, or procedural-rights measures.","risks":["Modal labels may be mistaken for legal causes or party attributes.","Aggregation can conceal subgroup or rare-case harm.","Policy changes can invalidate the local operator abruptly.","Near-degenerate or non-normal modes can produce unstable rankings.","Optimization for timeliness can pressure due process or decision quality.","A confident report can launder model uncertainty into institutional authority."]},"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":0.77,"generator_notes":"Closed-book structural transfer. The candidate is limited to docket-flow timeliness and excludes adjudicative merits; empirical validity and practical leverage remain untested."}