{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp05_complete_proposal_portfolio20_20260803","cell_id":"invariant_mode_decomposition_design__biology_ecology","arm":"COMPLETE_PROPOSAL_PORTFOLIO","candidate_id":"cand_bioeco_lake_recovery_mode_gate_001","proposal_index":1,"version":0,"title":"Lake Recovery Mode Gate for Coupled Bloom and Hypoxia Management","problem":"A shallow-lake manager observes phosphorus, nitrogen, cyanobacterial biomass, grazer abundance, light attenuation, sediment nutrient release, and dissolved oxygen separately. Yet these variables can evolve as coupled combinations: a lake may show a temporary decline in surface chlorophyll while a joint low-oxygen–sediment-release–cyanobacteria mode continues to grow. Coordinate-by-coordinate responses can therefore suppress a visible symptom without identifying whether the local ecological dynamics are returning toward or moving away from an acceptable regime.","actors":["Lake management authority","Field ecologists and limnologists","Watershed nutrient-control operators","Aeration or mixing operators","Downstream water users","Fish, zooplankton, phytoplankton, and benthic organisms represented in the monitored ecosystem state"],"observable_state":"At fixed sampling intervals, the authority records a state vector containing dissolved phosphorus and nitrogen, cyanobacterial and non-cyanobacterial chlorophyll, zooplankton grazing proxy, surface and bottom dissolved oxygen, water-column temperature stratification, light attenuation, and sediment phosphorus-release proxy. A locally valid transition matrix maps deviations from a defined warm-season reference state at one interval to deviations at the next. Observable decision signals are each mode's composition, estimated gain, stability class, sensitivity to permitted controls, reconstruction residual, spectral separation, and drift between estimation windows.","consequence":"Without a coupled-dynamics representation, the authority can select a control because it moves one monitored variable while leaving a less visible growing combination intact or exciting another harmful combination. The operational consequence is an unsupported escalation, continuation, or termination decision for nutrient controls or mechanical mixing; the ecological consequence could be persistent bloom conditions, bottom-water oxygen stress, or unnecessary disturbance despite an apparently favorable surface metric.","affected_objective":"Choose and continue only those bounded lake-management actions that move the monitored ecological state away from locally growing bloom–hypoxia dynamics while keeping oxygen, organism-stress, residual-error, and model-validity safeguards within preset limits.","intervention":"Establish a mode-gated management protocol. Define the warm-season state vector and reference regime; estimate an explicit local transition matrix from regularly sampled, instrumented lake mesocosms; compute its complete eigenbasis and gain spectrum; classify modes as decaying, marginal, oscillatory, or growing; and map permitted controls—reduced external nutrient input and bounded mechanical mixing—into modal coordinates. A modal sensitivity sweep ranks control settings by their predicted reduction of the action-relevant growing mode and records cross-effects on other modes. The authority may test only the lowest-intensity setting that opposes the selected mode without increasing any protected mode beyond its guardrail. The protocol withholds whole-lake use whenever retained modes fail out-of-sample reconstruction, the spectral gap is inadequate, mode identity drifts, residuals become structured, or observations leave the stated local regime.","structural_mapping":[{"archetype_element":"Transformation Scope","domain_realization":"The transformation is the one-sampling-interval transition of deviations in the defined shallow-lake ecological state during a bounded warm-season operating regime."},{"archetype_element":"State-Vector Definition","domain_realization":"Coordinates are nutrient availability, phytoplankton composition, grazing, oxygen, stratification, light, and sediment-release measurements collected with fixed units and sampling rules."},{"archetype_element":"Invariant Mode Basis and Modal Gain Spectrum","domain_realization":"Eigenvectors describe coupled ecological change patterns preserved as directions by the fitted local transition, while eigenvalues describe their estimated interval-to-interval growth, decay, persistence, or oscillation."},{"archetype_element":"Stable/Unstable Mode Partition","domain_realization":"Modes are classified against the discrete-time stability boundary within the recorded temperature, loading, and mixing window; modes near the boundary remain marginal rather than being forced into a binary verdict."},{"archetype_element":"Modal Intervention Map","domain_realization":"Candidate nutrient-input reductions and mixing duty cycles are represented by how they change modal coordinates or gains, not merely by their direct effect on phosphorus or oxygen."},{"archetype_element":"Mode-Coupling Register","domain_realization":"The protocol records when a control aimed at the bloom–hypoxia mode also changes grazer, oxygen, or sediment-release modes, including effects caused by near-degenerate or ill-conditioned modes."},{"archetype_element":"Reconstruction Residual Check","domain_realization":"Held-out state trajectories are reconstructed from the retained modes; residual magnitude and ecological structure determine whether the reduced modal account is fit for a decision."},{"archetype_element":"Mode Drift Monitor and Interpretation Scope Contract","domain_realization":"Successive estimation windows are compared for eigenvalue, eigenvector, and spectral-gap change, and every recommendation states the temperature, loading, stratification, and intervention ranges within which it may be interpreted."}],"mechanism_mapping":[{"mechanism_slug":"eigendecomposition_workflow","role":"Factor the explicit fitted transition matrix into the complete set of local ecological modes and their gains, preserving traceability to measured variables.","counterfactual_removal":"Without this mechanism, the protocol would remain a multivariable dashboard and could not identify invariant coupled directions or distinguish their scalar responses."},{"mechanism_slug":"modal_stability_analysis","role":"Classify each ecological mode as growing, decaying, marginal, or oscillatory inside the declared warm-season linearization window.","counterfactual_removal":"Without this mechanism, the spectrum would not yield the early-warning partition needed to decide which coupled direction requires attention."},{"mechanism_slug":"modal_sensitivity_sweep","role":"Perturb permitted nutrient-control and mixing settings in the local model, rank their leverage on the selected mode, and log cross-mode effects.","counterfactual_removal":"Without this mechanism, the largest or most visible mode might be targeted even when an available control has little leverage on it or adversely moves another protected mode."},{"mechanism_slug":"residual_reconstruction_test","role":"Test retained-mode trajectories against independent mesocosm observations and inspect both residual size and residual structure.","counterfactual_removal":"Without this mechanism, compression error could be mistaken for ecological stability and omitted low-amplitude but consequential behavior would be invisible."},{"mechanism_slug":"spectral_gap_monitor","role":"Track separation between retained and omitted modes and rotation or reordering of the action-relevant basis across sampling windows.","counterfactual_removal":"Without this mechanism, the authority could continue using a previously legible mode after it becomes an unstable mixture or ceases to dominate."},{"mechanism_slug":"spectral_decomposition_report","role":"Give operators a bounded account of mode composition, gains, couplings, residuals, guardrails, and prohibited interpretations.","counterfactual_removal":"Without this mechanism, tentative local modes could be communicated as independent ecological causes or as globally valid lake states."}],"causal_chain":["Nutrients, phytoplankton, grazers, oxygen, stratification, light, and sediment release change jointly under the lake's local transition dynamics.","Estimating that transition and decomposing it exposes combinations that approximately preserve their direction while growing, decaying, persisting, or oscillating.","Stability classification identifies a coupled bloom–hypoxia direction that warrants attention only if it is reproducible and locally growing or weakly damped.","Sensitivity sweeps translate permitted nutrient and mixing controls into expected movement of that direction and reveal cross-effects on protected modes.","A low-intensity, contained intervention is selected by modal leverage rather than by the largest coordinate-level symptom.","Independent trajectories test whether the selected setting reduces excitation of the targeted mode without unacceptable movement in protected modes.","Residual, spectral-gap, mode-drift, oxygen, and organism-stress checks determine whether testing may continue, must be revised, or must be rolled back."],"baseline":"The baseline is threshold-based coordinate management: review phosphorus, chlorophyll, and dissolved oxygen separately; reduce nutrient input when a nutrient or chlorophyll threshold is crossed; and activate mixing when bottom-water oxygen crosses its threshold. The baseline does not estimate a coupled transition operator, distinguish stable from growing combinations, or condition trust on modal residual and drift checks.","nearest_rivals":["A multivariate regression that predicts next-interval chlorophyll or oxygen directly from the measured variables but does not expose invariant directions or mode stability.","Principal-component monitoring that flags high-variance ecological patterns but does not model the interval-to-interval transformation or classify dynamic growth.","A mechanistic whole-lake ecosystem simulation used to compare management scenarios without a modal decision gate.","A factorial mesocosm trial that compares nutrient reduction and mixing by endpoint averages without testing which coupled trajectory each treatment excites."],"remaining_contrastive_claim":"The candidate's testable contrast is procedural: it conditions a bounded control choice on a locally estimated transformation's action-relevant mode, its gain, control sensitivity, reconstruction residual, spectral separation, and drift. This differs from rivals that choose from individual thresholds, variance directions, endpoint averages, or un-gated simulation outputs; it does not establish that the modal choice will be superior.","authority_safety":{"decision_authority":"The lake management authority owns the decision protocol. A designated study lead may operate contained mesocosms under the authority's approved field and animal-welfare procedures, but only the authority may authorize any later whole-lake action.","authorized_first_step":"Run an instrumented, contained mesocosm study using ambient lake water and biota. Prospectively collect an identification series, fit the local transition operator, preregister the action-relevant mode and guardrails, and compare an untreated arm, bounded nutrient-input reduction, bounded mixing, and the lowest-intensity mode-selected setting in an independent validation series.","excluded_actions":["No whole-lake nutrient manipulation, mixing deployment, stocking, fish removal, or sediment treatment on the basis of this first study.","No nutrient addition above the mesocosms' ambient loading envelope solely to excite a mode.","No extrapolation beyond the recorded temperature, stratification, loading, or intervention range.","No suppression of residuals, unstable eigenvector conditioning, near-degenerate modes, adverse organism observations, or null results from the report.","No automatic control actuation from model output."],"halt_rollback":"Stop the affected mesocosm treatment if dissolved oxygen, temperature, mortality, or other preregistered organism-stress guardrails are crossed; if safe, return mixing to zero and restore the assigned ambient inflow condition. Invalidate the recommendation and revert to observation-only status if held-out residuals exceed tolerance, residuals retain ecological structure, eigenvectors are ill-conditioned, the retained/dropped spectral gap falls below its preregistered threshold, mode identity drifts beyond tolerance, or observations leave the linearization window."},"negative_tests":{"strongest_counterevidence":"Across independent mesocosm trajectories, the fitted modes are not reproducible across resampling or windows, are ill-conditioned or near-degenerate, and add no out-of-sample trajectory information beyond the coordinate-threshold baseline or a direct multivariate predictor.","problem_falsifier":"The inferred local transition contains no reproducible growing or weakly damped coupled direction relevant to bloom or oxygen outcomes, or the concerning outcome is adequately determined by one directly observable variable within the study window.","intervention_falsifier":"The preregistered mode-selected setting fails to reduce the targeted modal coordinate relative to untreated mesocosms, or it performs no better on the targeted trajectory than the matched best single-control arm while worsening a protected mode, residual, or organism-safety measure.","risks":["Sparse or noisy sampling can create unstable eigenvalues and rotating eigenvectors.","A non-normal or ill-conditioned transition matrix can exhibit transient amplification that eigenvalues alone understate.","The local linear approximation can fail during abrupt weather, loading, or community-composition changes.","Mesocosm boundaries can alter mixing, sediment exchange, trophic interactions, and transferability to the lake.","Closely spaced modes can swap identity and make a single-mode intervention map misleading.","The selected control can improve the targeted mode while harming an omitted or poorly measured ecological process.","A polished modal report can be mistaken for causal proof rather than a bounded dynamic description."]},"next_evidence_step":"Conduct one bounded two-stage mesocosm experiment over a single warm-season interval. Use the identification stage to estimate the transition matrix from fixed-interval measurements without above-ambient nutrient excitation. Before opening validation outcomes, freeze the state definition, linearization window, mode-matching rule, stability and spectral-gap thresholds, residual budget, targeted mode, control setting, safety guardrails, and analysis code. In the independent validation stage, randomize contained mesocosms among untreated, nutrient-reduction-only, mixing-only, and mode-selected settings. The first evidence question is whether the targeted mode is reproducible and whether its preregistered coordinate responds in the predicted direction without a safeguard breach; no whole-lake efficacy inference follows from this step.","prior_art_status":"UNSEARCHED","diversity_from_prior_proposals":"No comparison is made because prior proposal content is outside the evidence used for this sealed candidate.","revision_record":{"parent_version":null,"progress_targets_addressed":["Produced the initial complete proposal from the supplied archetype, authored mechanisms, and biology-and-ecology domain card."],"conceptual_changes":[],"operational_changes":[],"evidence_changes":[],"claim_changes":[]}}