{"schema_version":1,"experiment_id":"eoa_inverse_innovation_exp03_full320_20260801","cell_id":"invariant_mode_decomposition_design__sport_science","trajectory_id":"R","attempt_index":0,"archetype_slug":"invariant_mode_decomposition_design","domain_slug":"sport_science","decision":"CANDIDATE","problem_id":"return_to_sport_hidden_coordination_instability","causal_lever_id":"damp_reinjury_linked_movement_mode","proposal":{"problem":"Athletes can satisfy return-to-sport thresholds for strength, symmetry, and task completion while retaining a repeatable, weakly damped coordination pattern across joints, muscles, and successive movement phases. Coordinate-by-coordinate assessment can miss this coupled instability, potentially exposing the athlete to recurrent tissue loading or loss of control during cutting and landing.","actors_substrate":["athletes nearing return after lower-limb injury","sports-medicine clinicians","rehabilitation coaches","instrumented cutting and landing trials","joint kinematics, kinetics, and muscle-activation time series"],"observable_state":"Repeated trials show apparently acceptable individual metrics but a reproducible multivariable movement direction whose estimated amplitude persists or grows across phases or perturbations.","consequence":"A concealed coordination instability may survive clearance and repeatedly concentrate load or degrade control, increasing reinjury exposure and misdirecting rehabilitation effort.","affected_objective":"Improve safe return-to-sport decisions and target rehabilitation without unnecessarily delaying athletes whose movement is dynamically stable.","structural_mapping":[{"archetype_element":"coupled transformation","domain_realization":"A locally fitted transition operator maps the athlete's movement state between consecutive phases or trials.","claim_kind":"HYPOTHESIS"},{"archetype_element":"invariant directions","domain_realization":"Approximate modes represent combinations of joint, force, and activation variables that evolve together under that operator.","claim_kind":"INFERENCE"},{"archetype_element":"scalar modal response","domain_realization":"Estimated gains distinguish rapidly damped coordination deviations from persistent or growing ones.","claim_kind":"INFERENCE"},{"archetype_element":"action-relevant mode","domain_realization":"A mode is actionable only when its perturbation changes a safety-relevant loading or control outcome and it is reproducible.","claim_kind":"HYPOTHESIS"},{"archetype_element":"modal intervention","domain_realization":"Clinician-selected exercise, cueing, or task constraints are mapped to their predicted effect on the concerning coordination mode.","claim_kind":"HYPOTHESIS"},{"archetype_element":"residual and drift governance","domain_realization":"Out-of-sample reconstruction error, basis drift, and spectral separation determine whether the modal assessment remains usable.","claim_kind":"INFERENCE"}],"component_map":[{"component":"Transformation Scope","status":"adapted","domain_realization":"Local phase-to-phase or trial-to-trial movement-state transition during a predefined cutting or landing task."},{"component":"State-Vector Definition","status":"direct","domain_realization":"Standardized joint angles and moments, ground-reaction forces, segment velocities, and selected muscle activations."},{"component":"Invariant Mode Basis","status":"adapted","domain_realization":"Eigenvectors of the fitted local transition operator, retained only when numerically identifiable and reproducible."},{"component":"Modal Gain Spectrum","status":"direct","domain_realization":"Eigenvalues quantify estimated decay, persistence, growth, or oscillation of each coordination mode."},{"component":"Dominant Mode Selection Rule","status":"direct","domain_realization":"Retain modes meeting preregistered stability-risk, outcome-sensitivity, reproducibility, and residual-improvement thresholds."},{"component":"Stable/Unstable Mode Partition","status":"adapted","domain_realization":"Classify modes within the observed task window as damped, marginal, growing, or oscillatory with uncertainty intervals."},{"component":"Modal Intervention Map","status":"adapted","domain_realization":"Map permissible exercises, feedback cues, and task constraints to predicted changes in modal coordinates and loading outcomes."},{"component":"Reconstruction Residual Check","status":"direct","domain_realization":"Out-of-sample reconstruction error and structured residuals test whether retained modes omit safety-relevant behavior."},{"component":"Mode Drift Monitor","status":"direct","domain_realization":"Repeat-session comparisons track mode rotation, gain changes, and ordering changes."},{"component":"Interpretation Scope Contract","status":"direct","domain_realization":"Results apply only to the sampled athlete, task, speed, fatigue state, equipment, and rehabilitation stage; association is not injury causation."},{"component":"Mode-Coupling Register","status":"direct","domain_realization":"Record cross-mode responses, near-degenerate modes, and intervention spillovers."},{"component":"Local Linearization Window","status":"direct","domain_realization":"Bound inference to observed ranges of task speed, fatigue, pain, and movement-state deviation."},{"component":"Spectral Gap Threshold","status":"direct","domain_realization":"Require preregistered separation and bootstrap stability between retained and excluded modes; otherwise withhold modal ranking."}],"mechanism_dispositions":[{"slug":"eigendecomposition_workflow","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Decompose the explicitly fitted local movement transition operator after conditioning and diagonalizability checks.","counterfactual_removal":"Without invariant directions and gains, the proposal collapses to coordinate-level assessment."},{"slug":"modal_sensitivity_sweep","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Perturb modal coordinates in the fitted model and bounded practice trials to rank effects on loading and control outcomes and log cross-effects.","counterfactual_removal":"Mode size could not be distinguished from intervention leverage."},{"slug":"modal_stability_analysis","disposition":"selected_load_bearing","contribution_type":"CORE_CAUSAL","adaptation_or_rejection":"Classify gains with uncertainty only inside the predefined movement regime.","counterfactual_removal":"The hidden-instability claim would lack its persistence or growth criterion."},{"slug":"mode_shape_testing","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"External excitation and vibration-style mode recovery do not match voluntary, adaptive movement in the first test.","counterfactual_removal":"No causal or operational step changes because modes come from the fitted transition operator."},{"slug":"network_spectral_centrality_analysis","disposition":"incompatible","contribution_type":"NONE","adaptation_or_rejection":"Body segments are not being ranked as nodes in a connectivity network.","counterfactual_removal":"No change; node importance is not the target construct."},{"slug":"power_iteration_probe","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A dominant-only estimate is insufficient because a complete stability partition and near-degenerate modes matter.","counterfactual_removal":"No change; full decomposition supplies the required spectrum."},{"slug":"principal_component_analysis","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"Variance directions are descriptive and need not be invariant under movement-state transitions.","counterfactual_removal":"No change; excluding PCA prevents variance from being mistaken for dynamic instability."},{"slug":"reduced_order_model","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"A runnable surrogate is unnecessary for the bounded shadow-assessment pilot.","counterfactual_removal":"The full fitted model can support the proposed analysis at pilot scale."},{"slug":"residual_reconstruction_test","disposition":"selected_load_bearing","contribution_type":"TEST_DESIGN","adaptation_or_rejection":"Use held-out trials and sessions to set retained order and detect structured omitted behavior.","counterfactual_removal":"There would be no defensible check that compression preserves safety-relevant movement."},{"slug":"singular_value_decomposition","disposition":"considered_rejected","contribution_type":"NONE","adaptation_or_rejection":"SVD is reserved as a conditioning diagnostic; singular vectors do not supply the required temporal invariant modes.","counterfactual_removal":"The primary causal interpretation remains unchanged, though numerical screening is less convenient."},{"slug":"spectral_decomposition_report","disposition":"selected_supporting","contribution_type":"SAFETY_GUARDRAIL","adaptation_or_rejection":"Provide clinicians with mode meanings, uncertainty, couplings, residuals, and explicit non-causal scope limits.","counterfactual_removal":"Clinical viability is hard-gated because tentative modes could be misread as clearance facts."},{"slug":"spectral_gap_monitor","disposition":"selected_supporting","contribution_type":"OPERATIONAL","adaptation_or_rejection":"Track retained-versus-excluded separation and basis drift across sessions; suspend use on threshold crossing.","counterfactual_removal":"A once-valid basis could continue guiding decisions after losing identifiability."}],"causal_chain":["A local transition operator captures how coupled movement deviations propagate across predefined phases or repetitions.","Decomposition exposes a reproducible mode that is weakly damped or growing despite acceptable marginal metrics.","Sensitivity testing identifies whether that mode changes a prespecified loading or control outcome.","Clinician-approved training or feedback targets the contributing variable combination rather than isolated normal-looking coordinates.","If the mode is causal and modifiable, its gain or amplitude decreases and safety-relevant outcomes improve within the valid task regime.","Residual, spectral-gap, and drift checks determine whether that interpretation remains admissible."],"baseline":"Ordinary practice uses strength, hop, symmetry, pain, task-completion, and selected biomechanical thresholds assessed largely one variable or summary score at a time.","nearest_rival":"A conventional multivariable return-to-sport risk model using the same measurements but predicting outcomes directly without a phase-transition operator, invariant modes, or stability interpretation.","authority_safety":{"affected_parties":["participating athletes","clinicians responsible for clearance","rehabilitation staff","teams relying on availability decisions"],"decision_authority":"The treating clinician retains clearance and training authority; athletes retain informed consent and may decline testing or mode-guided exercises.","authorized_first_step":"Run a preregistered shadow-mode study on approximately 30 consenting athletes across two standardized sessions; compare repeatability, held-out reconstruction, and prognostic signals with the baseline and nearest rival without changing clearance.","excluded_actions":["automatic clearance or exclusion from play","withholding indicated treatment","training beyond clinician-set pain and load limits","interpreting a mode as a diagnosed injury mechanism","sharing identifiable athlete rankings outside the care and research team"],"halt_rollback":"Stop athlete testing for pain, instability, adverse symptoms, or clinician request; suspend the model if residual, conditioning, spectral-gap, or drift thresholds fail, and revert decisions to ordinary clinical assessment."}},"negative_tests":{"strongest_counterevidence":"The concerning modes may be session-specific artifacts of measurement, preprocessing, task speed, or fatigue; ordinary thresholds or direct multivariable prediction may equal or outperform them in held-out athletes.","analogy_break":"Human movement is nonlinear, adaptive, and task-dependent. A locally estimated eigenmode is not necessarily a fixed physical mode, an independent control module, or a causal pathway to injury.","failure_condition":"The fitted operator is ill-conditioned or non-diagonalizable, modes are not repeatable across sessions, the relevant spectral gap is absent, or safety-relevant behavior remains structured in residuals.","problem_falsifier":"Across representative repeated sessions, athletes who pass ordinary criteria show no reproducible coupled dynamic pattern associated with later loss-of-control, abnormal-loading, or reinjury outcomes beyond baseline covariates.","intervention_falsifier":"In a later clinician-approved controlled pilot with adequate adherence, mode-targeted training neither changes the prespecified modal gain or amplitude nor improves loading, control, or recurrence outcomes relative to matched standard rehabilitation.","risks":["False-positive instability could delay return or increase anxiety.","False reassurance could expose an athlete to harm.","Sensor or preprocessing artifacts could masquerade as modes.","Local estimates could be extrapolated to untested tasks or fatigue states.","Sensitive performance and health data could be misused by teams.","Targeting one mode could worsen a coupled mode or shift load elsewhere."]},"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":"Candidate fit is conditional on reproducible local movement transitions and strict no-go rules for weak identifiability, nonlinearity, residual structure, and drift. No prior-art search or external empirical validation was performed."}